Objective NHL

How often does the Best Team Win?

2011-06-25T17:24:00.000-07:00

This year’s Stanley Cup Final concluded with a somewhat surprising outcome. The Vancouver Canucks – who were widely regarded as the league’s best club – were defeated by the underdog Bruins.

To those who regard the NHL playoffs as a competition designed to determine the league’s best team, the result can mean only one thing – that the Bruins were the best team all along, and the Canucks mere pretenders.

A more reasonable explanation, however, is that shit happens over the course of a seven game series and, because of that, the better team doesn’t always win. The Canucks were better than Boston during the regular season, and were likely better in the first three rounds of the playoffs as well. They were better than Boston last year and there’s a good chance that they’ll do better next year. They were probably the better team.

The Canucks may or may not have been the best team in the league, but if they were in fact better than Boston, then that means that a team other than the best team in the league won the cup. That raises an interesting question – how often does the best team in the league end up winning the cup?

(The answer, of course, will vary as a function of the level of parity that exists in the league. Because the level of league parity has varied over time as a function of era, we’ll confine our answer to the post-lockout years).

Unfortunately, the question cannot be answered directly due to the fact that it’s not possible to identify the league’s best team in any given season with any certitude. One can only speak in terms of probability and educated guesses.

It is, however, possible to arrive at an approximate answer through assigning artificial win probabilities to each team, simulating a large number of seasons, and looking at how often the team with the best win probability ends up winning the cup.

This exercise is made possible by the fact that the distribution in team ability – which we’ll define as true talent goal ratio –can be ascertained through examining the observed spread in goal ratio and identifying the curve which best produces that spread when run through the appropriate simulator.

In order to generate an observed distribution of results, I randomly selected 40 games from every team and looked at how each of them performed with respect to goal percentage (empty netters excluded) over that sample. This exercise was performed 2000 times for each of the six post lockout seasons. The following curve resulted:

The likely ability distribution is the curve shown below – a normal distribution with a mean of 0.5 and standard deviation of 0.03.

If a large number of half-seasons are simulated through assigning artificial goal percentages based on the above ability distribution, the spread in simulated results closely matches the observed results displayed in the first graph.

As the ability distribution can be used to generate results that closely parallel those observed in reality, it can also be used in order to answer the question posed earlier in the post – that is, the probability of the best team in the league winning the cup in any given season.

Here’s how the simulations were conducted:

For each simulated season, every team was assigned an artificial goal percentage based on the ability distribution produced above
The artificial goal percentages were, in turn, used to produce GF/game and GA/game values for each team
GF/game values were calculated by multiplying a team’s goal percentage by 5.49 (5.49 being the approximate average number of non empty net goals scored per game in the post-lockout era)
GA/game values were calculated by subtracting a team’s GF/game value from 5.49
All 1230 games from the 2010-11regular season were then simulated, with a score being generated for each individual game
The probability of a team scoring ‘x’ number of goals in an individual game was determined through taking its GF/game value and adjusting it based on the GA/game value of the opponent
If each team scored an equal number of goals, each team was awarded one point and a random number generator was used to determine which of the two teams received the additional point
After all games were simulated, the division and conference standings were determined in accordance with NHL rules (that is, with the teams ranked by points, with the division winners being placed in the first three seeds in each conference)
If two teams were tied in points, greater number of wins was used as a tiebreaker
If two teams had the same number of points and wins, then a random number generator was used as a second tiebreaker
The playoff matchups were then determined based on the regular season standings
Individual playoff games were not simulated; rather, each series was simulated as a whole based on the Pythagorean expectations (which were derived from the goal percentage values) of the involved teams
Home advantage for the higher seed was valued at +0.015

20 000 Simulations were conducted in total. Here’s how the league’s best team – defined as the team with the best underlying goal percentage in each individual season – fared. We’ll start with the regular season results:

The above chart shows how the best team performed in four areas – division rank, conference rank, league rank in points, and league rank in goal differential. So, as an example, the best team ended up winning the President’s Trophy – i.e. finishing with the most points – about 32% of time.

The results are interesting. The best team does very well in general, but the range in outcomes is considerable. It wins its division a majority of the time yet still manages to finish dead last every now and then (about once every 200 seasons). It wins the conference almost half the time and finishes in the top four about 84% of the time. However, it still misses the playoffs a non-trivial percentage of the time (2.2%). The latter fact may not be too surprising – the 2010-11 Chicago Blackhawks were close to being the best team in the league but only made the playoffs by the slimmest of margins.

It wins the President’s Trophy about a third of time and does even better in terms of goal differential, posting the best mark in roughly 40% of the simulations. However, it occasionally finishes in the bottom half of the league in both categories (about 2% and 1% of the time, respectively).

The graph below shows the distribution in year end point totals for the best team. It averaged just over 107 points, with a high of 145 and a low of 73.

And the distribution in goal differential (mean = 57; max = 161; min= -34).

Finally, the chart showing the playoff outcomes for the best team, and therefore answering the question posed earlier.

It turns out that the best team wins the cup 22% of the time – about once every five seasons. This accords well with what we’ve observed since the lockout, with the 2007-08 Detroit Red Wings being the only cup winner that was also unambiguously the best team in the league. The 2009-10 Chicago Blackhawks were probably the best but it’s hard to say for sure. The 2008-09 Penguins were a good team but the Wings were probably better that year. Ditto for the 2006-07 Ducks. The 2010-11 Bruins were merely a good team, and I can’t even say that much for the 2005-06 Hurricanes, who may not have even been one of the ten best teams in the league during that season.

Caveats:

The exercise assumes that team ability is static. This is obviously untrue in reality, given injuries, roster turnover, and like variables. Consequently, the best true talent team at one point in the season may not be the best team at a different point. Moreover, the spread in team talent at any given point in the season is likely to be somewhat broader than the ability curve used in the exercise.

Scores were generated for individual games through the use of poisson probabilities, which does not take into account score effects. Thus, the model slightly underestimates the incidence of tie games. For the same reason, it also overestimates the team-to-team spread in goal differential.

Predicting Playoff Success - Part Two

2011-06-07T00:12:00.000-07:00

Rob Vollman raised an interesting question in the comments section of my last post, that being whether my findings precluded the possibility that some teams consistently perform better or worse in the playoffs.

The question can be answered by comparing each team's actual performance, as measured by winning percentage, with what would be expected based on regular season results. If the spread in [actual - expected] winning percentage is significantly greater than what would be expected by chance alone, then that suggests that some types of teams may consistently outperform or underperform in the playoffs relative to the regular season.

As with my last post, my sample consisted of all 1882 playoffs games played between 1988 and 2010. I've prepared a chart which shows, in the leftmost section, how each of the league's teams performed during that span. The middle section of the chart shows each team's expected wins and losses, based on single-game probabilities generated from regular season data. Finally, the rightmost section shows each team's winning percentage differential (defined as observed winning percentage minus expected winning percentage), as well as the probability of observing a differential at least that large by chance alone.

That last part may require some elaboration. All 1882 games were simulated 1000 times, based on the regular-season derived probability values. For each of the individual simulations, I determined each team's winning percentage and subtracted from it that team's expected winning percentage. The p value column simply indicates the proportion of simulations in which the the absolute value of that number - that is, the team's [simulated winning percentage - expected winning percentage] - exceeded the absolute value of that team's [observed winning percentage - expected winning percentage].

A specific example may be illustrative. Anaheim had an observed winning percentage of 0.576, an expected winning percentage of 0.462, and therefore an [observed winning percentage - expected winning percentage] of 0.114. In only 0.033 of the 1000 simulations did Anaheim's simulated winning percentage differ from its expected winning percentage by at least 0.114. Hence Anaheim's p value of 0.033.

As can be seen, some teams outperformed their expected winning percentage, whereas others underachieved. Based on each team's [observed winning percentage - expected winning percentage], and the probability of each differential materializing by chance alone, Edmonton, Pittsburgh and Anaheim were the three most "clutch" teams, whereas the Islanders, Columbus and Atlanta were the biggest "chokers." But is the spread between the teams any different from what would be predicted from chance alone?

There are two ways in which this question can be answered. The first is to group the observed winning percentage differentials ( expected versus actual winning percentage) into several categories, and calculate the number of values in each category as a percentage of the total sample (relative frequency). Following that, the same can be done with the simulated differentials. The two distributions can then be compared.

The second is to repeat the exact same exercise, but to use actual wins instead of winning percentage. I prefer this second method as the fact that some teams, such as Atlanta, Columbus and Quebec, played very few games has the potential to skew the results if winning percentage is used.

Here are the two graphs:

In the case of winning percentage, the actual spread is noticeably greater than the observed spread. But the difference is not too large, there being something of a general correspondence. And in the case of wins, the two lines form almost a perfect match.

If I were to issue a conclusion, it would be that although some teams over or underperform in the playoffs relative to their regular season results, this appears to be mostly the product of normal statistical variation. There isn't much support for the idea that there exists an ability to perform in the playoffs that is independent and separate from the ability to perform during the regular season.
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Predicting Playoff Success

2011-06-04T22:28:00.000-07:00

It's often said that the playoffs are a different ball game as compared to the regular season - that some teams are built for the playoffs whereas others are not.

The above statement can be evaluated by looking at how well regular season results predict playoff success. This can be done by assigning a theoretical win probability to every playoff team based on how it performed during the regular season, and determining the odds for each individual matchup on that basis. If the statement is true, the favorite - the team with the superior win probability as against its opponent - should win significantly less often than expected.

My sample consisted of all 1882 playoff games played between 1988 and 2010. Theoretical win probabilities were computed on the basis of regular season goal ratio, corrected for schedule difficulty. While goal ratio is imperfect in this respect, the data required to produce more precise estimates is simply not available for the majority of the seasons included in the sample. Thus, goal ratio is the best measure available.

Home advantage was valued at +0.056, this being the difference between the expected neutral ice winning percentage of home teams (0.505), and their observed winning percentage over the games included in the sample (0.561).

After computing the odds for each individual game, I divided the data into eight categories. The category in which a game was placed depended upon the expected winning percentage of the favorite. The cutoffs for the eight categories were as follows:

0.50-0.52
0.52-0.54
0.54-0.56
0.56-0.58
0.58-0.60
0.60-0.625
0.625-0.675
0.675-1

The cutoffs were not gerrymandered so as to produce a particular result - I simply wanted each category to contain a relatively equal number of games. As there are many more games in which the favorite has a win probability between 0.50 and 0.60 than there games in which the favorite has a win probability greater than 0.60, this necessitated making certain categories larger than others.

The results:

[The italicized 'n' column simply indicates the number of games contained within each category.]

As can be seen, using regular season data allows one to predict the results of groups of individual playoff games with surprising accuracy. On the whole, the favorite did slightly worse in reality than what the regular season results predicted - 0.573 versus 0.586. However, this is probably just a reflection of the fact that regular season goal ratio is the product of both skill and luck, and that the true talent goal ratio of the average team lies closer to the population average than does its observed goal ratio.

As for the individual categories, six of the eight show a reasonably close correspondence between expected and observed winning percentage, with the other two featuring notable discrepancies. While each gap appears significant, either could be the product of chance alone. The probability of a 0.51 team going 0.468 or worse over 263 games is 0.097. Likewise, the probability of a 0.713 team going 0.671 or worse over 204 games is 0.109.

If I were to guess, I'd say that the discrepancy in the 0.675-1 category is a real effect. As discussed earlier, goal ratio tends to overvalue the favorite and underrate the underdog, and the greater the distance from the mean, the more likely this is to be true in individual cases.
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More on Team EV Shooting Ability

2011-06-02T23:30:00.000-07:00

About a week ago, I put up a post on team even strength shooting percentage, which included a chart showing what the underlying talent distribution in that area probably looks like. I've reproduced the relevant curve below:

The curve isn't excessively narrow. The 97th percentile equates to a shooting percentage of 0.0902, meaning that, in an average season, the league's most talented EV shooting team would have an underlying shooting percentage at or around that mark. That's no trivial advantage - with neutral luck, such a team would be expected to score roughly 18 more even strength goals than a team with average EV shooting ability.

The problem is that, given that goals in the NHL are somewhat of a statistical rarity, the regular season doesn't provide us with a sample that is sufficiently large so as to be able to identify each team's true talent level with reasonable accuracy.

This estimate uncertainty is well illustrated by comparing last year's Devils, who had a league worst 0.065 EV shooting percentage, with last year's Stars, who posted the league's best mark at 0.089. That seems like a fairly large gap - almost 2 and half percent. Surely one would be able to conclude that the 2010-11 Stars possessed more EV shooting talent than the 2010-11 Devils?

In fact, there is a not-insignificant probability that the Devils were actually the better EV shooting team. This becomes immediately apparent upon viewing the ability distribution for each team and noting the overlap between the two curves.

There is an 11.6% chance that N.J was actually the more talented team last season in terms of EV shooting ability. In other words, there will be some seasons - of which 2010-11 is an example - that do not permit the conclusion that any single team has definitively more EV shooting talent than any other.
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Stanley Cup Finals 1011 Playoff Probabilities and Predictions

2011-05-30T17:27:00.001-07:00

It all comes down to this.

The best team in the West against the best team in the East.*

For the 6th straight year, the Western representative appears to be the stronger team. That's not really surprising - the West has had the better interconference record in every season since 1999-00, and often by a large margin.

I think Vancouver is clearly the better team here and that, if anything, the odds I've presented above understate their chances. That said, these two teams are close enough to one another where it should be a good series.

I'll take the Canucks to win in six games.

VAN in 6.

*As per my probability model. It's possible - perhaps even likely in Boston's case - that neither team is the best team in its respective conference. For what it's worth, I'd take a healthy Pittsburgh team over Boston all day every day. But I digress.
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Team Even Strength Shooting Talent

2011-05-29T18:20:00.000-07:00

A while back, I received a comment relating to how my playoff probability model accounts for teams that are outliers with respect to shooting percentage, with the 2009-10 Washington Capitals offered as an example of such a team.

The answer is relatively straightforward: I merely regress each team to the league average based on the extent to which the team to team variation can be attributed to luck over the sample in question. As the variation in even strength shooting percentage at the team level is approximately 66% luck over the course of a regular season, each team's even strength shooting percentage is regressed two-thirds of the way to the mean in order to generate theoretical win probabilities.

The application of above method to data from the 2010-11 regular season yields the following even strength shooting talent estimates for each the league's 30 teams.*

This method, however, is actually a shortcut that relies on assumptions that are unlikely to be true in reality. For one, it assumes that all underlying talent distributions are normally distributed, which may or may not be the case. It's also insensitive to the fact that some teams take more shots than others over the course of a season. A more certain shooting talent estimate can be made with respect to a team that takes 2000 shots as compared to a team that takes 1500 shots, although the model fails to reflect that.

The proper - albeit significantly more complicated and involved - approach would be to actually identify the nature of the underlying talent distribution and work one's way forward from there.

The first step is to look at the observed distribution in performance. I did this through randomly selecting half a season's worth of games for each team and looking at how it performed with respect to EV SH% over that sample, and repeated this 2000 times for every season from 2003-04 to 2010-11. I elected to do this as it provided me with 420 000 data points, thereby allowing me to generate a smooth curve. By comparison, using the actual end-of-season frequencies would have provided me with a mere 210 data points.

I came away with the following curve:

The distribution is slightly right-skewed and therefore not quite normal. This becomes meaningful at the tails - there were approximately 26 times more values 3 standard deviations above the mean than there were values 3 standard deviations below it. In other words, there are many more very good teams than very bad ones when it comes to even strength shooting performance.

The next step is finding a curve that best fits the observed data. This curve should have a mean of approximately 0.081, which was the observed league average shooting percentage. It should also have a standard deviation of approximately 0.0048, which is the skill standard deviation in relation to even strength shooting percentage at the team level. Finally, the curve should be slightly positively skewed.

The beta (236, 2977) curve, shown below, satisfies these criteria.

As a check on the correctness of the selection, I used a random number generator to assign each team an artificial EV shooting percentage based on the above curve. I then simulated a sufficiently large number of half seasons based on those artificial numbers and compared the results to the observed data. If the choice is correct, the simulated results should closely match those observed.

The simulated curve is only based on about 30 000 data points, so it's not as smooth as the observed distribution. That said, the fit is pretty good. The observed distribution appears to have a fatter right tail, and so it's possible that a different beta curve might provide a better match. But it's close enough.

The beta ability distribution can be used to estimate each team's true talent underlying shooting percentage, based on the 2010-11 regular season. How do these estimates compare to those produced by the simple regression approach discussed earlier?

The two approaches produce very similar results - the average difference amounting to only 0.0004. The latter approach is both more precise and principled. But the former achieves substantially similar estimates with a fraction of the effort.

* The mean used was 0.0812, this being the league average EV SH% since the lockout, even though the observed shooting percentage in 2010-11 was a bit lower - a touch under 0.08.
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3rd Round 1011 Playoff Probabilities and Predictions

2011-05-13T14:22:00.000-07:00

VAN - S.J

Another extremely even matchup. The relevant facts, as I see them:

S.J probably has the better powerplay - they generate a ridiculous number of shots
VAN very likely has the better goaltender
VAN has home ice advantage
Both teams are about equally good at controlling the play at EV
VAN is missing a key forward

If those facts give one club a clear advantage, I can't see it. These are probably the two best teams in the league and this should be a great series. I'll take the Canucks in seven games.

Van in 7.

BOS – T.B

At first glance, Boston seems like the obvious pick here. But the (Patrice) Bergeron injury complicates things. The latest reports indicate that he has yet to resume skating since the incident, so from that it seems as though he might not play at all. That would be a huge loss, as he's probably their best forward, at least by my reckoning.

The issue is whether the Bergeron injury is enough to tip the balance in Tampa Bay's favor. I don't think that it is. Based on regular season play, I have the Bruins as a 61% favorite. While the Bergeron injury necessitates a downward adjusted of that figure, I don't think the loss is profound enough to render the Bruins underdogs. This is supported by the fact that the oddsmakers - who certainly take such things into account - still have Boston as about a 56% favorite.

BOS in 7.

Team Effects and Penalty Kill Save Percentage

2011-05-10T20:50:00.000-07:00

In yesterday's post, I looked at the extent to which team effects contribute to the variation in even strength save percentage between individual goaltenders.

The results were somewhat inconclusive. On the one hand, the inter-year correlation for even strength save percentage is no stronger for goalies remaining with the same team when compared to the value for goalies that changed teams. This suggests that team effects are negligible.

On the other hand, there is a statistically significant correlation between the even strength save percentage of starters and backups. Moreover, the magnitude of the correlation is moderate when viewed in light of the fact that even strength save percentage exhibits low reliability over the course of a single season. This suggests that team effects are important.

The purpose of this post is to look at whether -- and if so, to what extent -- team effects play a role with respect to penalty kill save percentage. The same methods used in yesterday's post will be applied here. If readers are interested in the specifics of each method, I'd encourage a reading of the original post, in which the calculation steps are set out in some detail.

Firstly, a comparison of goalies that changed teams to goalies that remained with the same team. Here's a summary of what this method entails:

Goalies that played for more than one team in a single season were excluded. No minimum shots faced cutoff was employed. However, because some of the goalies in the sample faced very few shots in a given season, I used a weighted correlation in which the weight assigned to each season pair was the lower number of shots faced in the two seasons used...[a]dditionally, because the league average [PK SV%] was not uniform over the period in question, I adjusted each goalie's raw [PK SV%] by dividing it by the league average [PK SV%] in that particular season.

The results:

No evidence for team effects here. The correlation for goalies that changed teams is actually larger, although the difference is not statistically significant.

Next, determining the correlation between starters and backups. Again, a refresher as to the specifics of the method involved:

I separated starting goaltenders and backup goaltenders into two groups. A starting goaltender was defined as the goaltender that faced the most shots for his team in a particular season. All other goaltenders were defined as backups, except for goaltenders that played for more than one team in a season, who were excluded from the sample. Just like in the first method, the [PK SV%] for all goaltenders was adjusted by dividing same by the league average [PK SV%] in the particular season. I then determined the weighted correlation between the [PK SV%] of a team's starter with the collective [PK SV%] of his backups. The weight assigned to each data pair was the lower number of shots faced by either the starter or his backups. So, for example, if the starter faced 1000 shots, and his backups collectively faced 1400, the weight would be 1000.

The application of the above steps yields a correlation of 0.07 over 340 data pairs, a value which is not statistically significant - there's a roughly 19% chance that a correlation that large or larger could occur by chance alone. That said, given the low number of shots faced on the penalty kill by the average goaltender over the course of a single season, it is not possible to obtain a statistically significant correlation between starters and backups unless team effects accounted for a substantial percentage of the non-luck seasonal variation in PK SV%. For example, a correlation of 0.10 - which would barely be significant at the 5% level - would imply a very large role for team effects, given that PK SV% for individual goaltenders has a low seasonal reliability (see the next paragraph).

Proceeding on the assumption that the correlation between starters and backups is reflective of a true relationship, the next step is to compute the seasonal reliability co-efficients for each variable. I obtain approximate values of 0.28 for starters and 0.07 for backups. This implies a true correlation of 0.50.

Finally, I have goaltender data at the individual game level for the last three seasons against which the plausibility of the above results can be checked. The penalty kill data I have is inclusive of 4-on-5 situations only, but that shouldn't make a huge difference. The table below displays the split-half reliabilities for starter and backup PK SV%, as well as the split-half correlation between the two variables, both of which have been averaged over 1000 trials.

These values imply a true correlation of 0.54, which is consistent with the results of the second method.

So there you have it - comparing goalies that switched teams to goalies that remained with the same team suggests team effects are unimportant in relation to PK SV%. But there is a positive correlation between the PK performance of starters and backups, which indicates that team effects are relevant. Those who read yesterday's post will be aware that the data for even strength save percentage tells the same story.

Interestingly, the data suggests that team effects may be more important at even strength than on the penalty kill. This is unusual as penalty kill save percentage at the team level is somewhat more reliable than even strength save percentage, once you control for the disparity in sample size - that is, the fact that a team faces many more shots at even strength than it does on the penalty kill.
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Team Effects and Even Strength Save Percentage

2011-05-10T01:06:00.000-07:00

The extent to which a goaltender's team has an impact on his save percentage - and, in particular, his even strength save percentage - has received some attention in the hockey blogging world in the past - see here and here for some good articles.

One way in which team effects on even strength save percentage (EV SV%) can be gauged is to compare goalies that changed teams to goalies that remained with the same team. This can be done through creating two groups of goalies on the basis of the above criterion, and looking at how well EV SV% repeats from one year to the next for each group. If the correlation for the group of goalies that changed teams is significantly smaller than the correlation for the group of goalies that remained with the same team, then that would be evidence of team effects.

Using a spreadsheet kindly supplied by Geoff Detweiler, I performed the above exercise with respect to goaltender data from 1997-98 to 2010-11. Goalies that played for more than one team in a single season were excluded. No minimum shots faced cutoff was employed. However, because some of the goalies in the sample faced very few shots in a given season, I used a weighted correlation in which the weight assigned to each season pair was the lower number of shots faced in the two seasons used. Thus, if a goalie faced 1600 EV shots in one season, and 400 in the next, the weight assigned to the season pair would be 400.

Additionally, because the league average EV SV% was not uniform over the period in question, I adjusted each goalie's raw EV SV% by dividing it by the league average EV SV% in that particular season. Here are the results:

[ n refers to the number of season pairs in each group ]

The correlations are scarcely distinguishable, which implies that team effects aren't important at even strength. This essentially replicates what Vic Ferrari found when performing similar analysis a few years ago.

Of course, that doesn't necessarily settle the issue. For example, another approach would be to look the relationship between the EV SV% of a team's starting netminder and the collective EV SV% of its backups. If the two variables are positively correlated, then that implies the existence of team effects.

The advantage of this method is that it allows for team effects to be measured more directly by examining the relationship between the variables of importance at the within-season level. This is significant as team effects on save percentage - to the extent that they do exist - may not repeat overly well from one season to the next. For example, Tom Awad, in an excellent article written last year, found that while team differences in shot quality over the course of a single season were much larger than what would be predicted from chance alone, the metric exhibited weak season-to-season repeatability.

Using the same goaltender data referred to earlier, I separated starting goaltenders and backup goaltenders into two groups. A starting goaltender was defined as the goaltender that faced the most shots for his team in a particular season. All other goaltenders were defined as backups, except for goaltenders that played for more than one team in a season, who were excluded from the sample. Just like in the first method, the EV SV% for all goaltenders was adjusted by dividing same by the league average EV SV% in the particular season. I then determined the weighted correlation between the EV SV% of a team's starter with the collective EV SV% of his backups. The weight assigned to each data pair was the lower number of shots faced by either the starter or his backups. So, for example, if the starter faced 1000 shots, and his backups collectively faced 1400, the weight would be 1000.

After doing all of that, I obtained a correlation of 0.156. With 340 data pairs, the probability of a correlation that large materializing by chance alone is very small - slightly under 1%, in fact. Moreover, it cannot be accounted for by shot recording bias.* Therefore, it would appear that the EV SV% of individual goaltenders is affected to some degree by team effects. The question that must now be answered is this: how large is the effect?

As discussed before on this blog, the fact that two variables are weakly correlated over a given sample does not in itself mean that there is no strong underlying relationship between those variables. For example, if each of the variables exhibits low reliability over the sample in question, a weak correlation may in fact indicate a close underlying relationship. Thus, ascertaining the reliability values of the two variables is critical in interpreting the significance of the correlation between them.

Applying this to our value of 0.156, it becomes necessary to determine the seasonal reliability co-efficients of both starting goalie EV SV% and backup EV SV%. While it is not possible to perform this calculation directly,** it can be approximated by simulating seasons to match the spread of the averaged observed results and noting the average correlation between such seasons. Using this method, the approximate reliability co-efficients are 0.33 for starter EV SV% and 0.22 for backup EV SV%.

These values imply that the true correlation between the two variables is roughly 0.58. Assuming that both variables are normally distributed***, this means that the variation in one variable would be able to explain 33% of the variation in the other over the long run, suggesting that team effects are important.

As a final note, this post was intended to generate discussion more than anything. Comments demonstrating flaws in my reasoning and/or methodology are welcome, as is the presentation of contrary evidence.

* Shot recording bias causes the save percentages of goalies playing for the same team to be more similar to one another than what would be the case if shots were recorded in the same in every rink. However, because of a) the small number of shots taken over the course of the season, b) the relatively mild nature of the bias, and c) the fact that half of all games are played on the road, the effect is fairly minor. Of the observed correlation of 0.156, only 0.018 can be attributed to shot recording bias.

** Ordinarily, and as I've done in the past, I would calculate the split-half reliability values for each variable and then calculate the split-half correlation between them. This method is superior as no approximation is necessary with respect to determining the reliability co-efficients. Unfortunately, EV SV% data at the individual game level is required in order to do so. As such data is only available for 2007-08 onward, I'm only able to apply this method to the years of 2007-08, 2008-09 and 2009-10 (and even then, for 5-on-5 play rather than all EV situations). Here are the results:

The results imply that team effects have a very important role in relation to 5-on-5 SV% - indeed, that there would be a perfect correlation between the 5-0n-5 SV% of starters and backups in the long run! This being an obvious absurdity, I think it's preferable to ignore this and concern ourselves with the results from the larger 12 year sample instead.

*** This is merely a simplifying assumption. In reality, it is unlikely that either variable is normally distributed.

Loose Ends - Part III C: The Power Play

2011-05-01T00:24:00.000-07:00

[EDIT: The table relating to the penalty kill was labeled incorrectly and suggested that I was looking at shorthanded scoring ( I accidentally put 'PKSF/60' and PK 'GF/60' instead of PKSA/60' and PKGA/60, respectively). The table has now been fixed.]

This post is a tad overdue.

It's the second of two follow up posts relating to powerplay performance. While the first post dealt with the relationship between shooting percentage at even strength and shooting percentage on the powerplay, this post relates to predicting future powerplay performance.

The variation in powerplay shooting percentage at the team level, over the course of a single regular season, is approximately 90% luck, 10% skill. Not surprisingly, powerplay shot rate is a stronger predictor of future powerplay performance than raw powerplay performance (provided that the sample size with which one is dealing isn't overly large). This is precisely what Gabriel Desjardins demonstrated in a post published in early April.

What this post is concerned with, however, is whether the inclusion of missed and blocked shots in the sample has residual value with respect to predicting to predicting powerplay efficiency in the future. While such is the case at even strength, special teams may be a different ballgame. What does the data say?

One preliminary issue that must be dealt with is shot recording bias. Recording bias doesn't really present a problem with respect to even strength shot metrics due to the fact that:

A. What were ultimately interested in is shot ratio/percentage or shot differential, and
B. None of the scorers appear to favor one team over the other (i.e. recording bias is largely, if not entirely, symmetrical).

Not so with special teams. With special teams, we're generally interested with rate stats, in which case recording bias becomes relevant. This is especially true when it comes to the recording of missed and blocked shots. Below is a table showing each team's home/road ratio in recorded shots (saved shots + goals), misses and blocks over the last three regular seasons (from 2008-09 to 2010-11). All game situations were included, although empty net goals or shots that resulted in same were not.

As one might notice, the recording of shots that actually make it to the goal isn't that bad. New Jersey and Minnesota appear to undercount, and Colorado appears to overcount. But every other location is reasonably good.

The recording of misses and blocks, by contrast, is generally fucked up. The N.J, CHI, ATL and BOS scorers seem very reluctant to record misses. Conversely, the guys in L.A, CAR, DAL and TOR seem overly eager.

The data for blocks reveals a similar story. The scorers in ANA, BOS, FLA and N.J count too few, whereas the scorers in NYI, MTL, EDM, S.J, TOR and WSH count too many.

It's a god damn nightmare.

Fortunately, there is a solution. Recording bias can be more or less controlled for by dividing the observed number of home missed or blocked shots by the appropriate co-efficient (that being the applicable H/R ratio, as displayed in the above table).

Once this correction is made, one can determine whether including missed and blocked shots adds value with respect to predicting future powerplay performance.

The following experiment was performed:

- I randomly selected 40 games from the 2010-11 season
- I calculated each team's PP GF/60, PP SF/60, PP Fenwick/60, PP Corsi/60 over that selected sample
- PP Fenwick/60 = [(powerplay shots + powerplay missed shots)/PP TOI]*60
- PP Corsi/60 = [(powerplay shots + powerplay missed shots + powerplay blocked shots)/PP TOI]*60
- I then selected an independent 40 game sample, and calculated each team's PP GF/60 in respect thereof
- I then looked at how each of the four above variables ( PP GF/60 , PP SF/60, PP Fenwick/60, PP Corsi/60), as calculated over the 1st sample of games, predicted PP GF/60 over the 2nd sample of games
- I repeated this exercise 1000 times
- I then repeated the entire exercise for the 2008-09 and 2009-10 regular seasons

The results:

Just like Gabe Desjardins found, shot production is a better predictor of future powerplay success relative to raw performance (with respect to 40 game sample sizes). And while missed shots have some informational value, blocked shots do not.

Does the same apply to the penalty skill? Interestingly, no.

Unlike with the powerplay, raw performance on the penalty kill (over a 40 game sample) is a superior predictor of future PK performance than is shot prevention. Part of that can be attributed to the fact that penalty skill save percentage is considerably more reliable than powerplay shooting percentage.

Furthermore, including misses and blocks is of no assistance. It seems as though better penalty kills force their opponents to take a greater proportion of missed and blocked shots.

2nd Round 1011 Playoff Probabilities and Predictions

2011-04-28T17:37:00.000-07:00

[ For an explanation, see here ]

VAN - NSH

The Canucks get a slightly easier draw here as compared to round one. The skill difference between these teams is smaller than what the regular season results would imply, but Vancouver is clearly better and should advance.

Van in 5.

S.J – DET

Pick em'. The odds in the table above suggest that the Sharks have the edge, but I reckon that these two teams are pretty even to one another. I'll take San Jose because of home ice.

S.J in 7.

WSH-T.B

These two teams are pretty close, with the numbers suggesting that Washington is slightly better. Combine that with the fact that my instinct says that the Caps are a better team than the numbers show (based on roster composition and past performance), and I'm left with no choice but to take them.

WSH in 6.

PHI-BOS

Like S.J-DET, I suspect this is pretty close to a coinflip. I'll concede that Philly appears to have the better team on paper, but the numbers favor Boston. I'll take the Bruins in seven games.

BOS in 7
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Playoff Outcome Probabilities

2011-04-14T00:15:00.000-07:00

Self Explanatory. Based on each team's expected winning percentage, as shown here.
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1st Round 1011 Playoff Predictions

2011-04-13T15:00:00.000-07:00

VAN - CHI

I reckon the Blackhawks are the strongest 8th seed that the league has seen since the current playoff format was adopted in 1994 (runner up: 1995 New York Rangers). Very tough matchup for Vancouver, especially considering that they could have easily drawn a substantially inferior club in the Stars. All of that said, I'm going with Vancouver here. While the Canucks probably aren't as strong as their regular season numbers would suggest, they still appear to be the league's best team.

VAN in 7.

S.J –L.A

As I mentioned a few days ago, San Jose has been simply outstanding since the halfway mark. While the Kings are respectable, they're in tough here given their injuries to key players and the quality of the opponent. I expect San Jose to advance.

S.J in 5.

DET-PHX

I like both of these teams so I'm disappointed that one of them will be out when the dust settles. The evidence suggests that Phoenix will be that team. Detroit is better territorially at EV and considerably better on special teams. The Coyotes will require more than a few things to go right for them in order to win.

DET in 5.

ANA-NSH

Of the four Western series, this one captures my interest the most. I think that Anaheim is far and away the worst team to qualify this year. While their special teams seem to be above average, they were dead last in the entire league in terms of corsi ratio. The Predators, on the other hand, are competent on special teams and an average to above average club at evens. Not a difficult pick.

NSH in 6

WSH – NYR

Like in the case of VAN-CHI, these two teams are closer in ability to one another than is typical in a #1-#8 matchup. I find that the Rangers are a hard team to get a read on. Even though they're decidedly below average territorially at EV, I really like their team on paper - the forward group, in particular. Their regular season scoring chance numbers are also very good.

All things considered, I'm going to trust my model and go with the Caps.

WSH in 6.

PHI – BUF

This series doesn't really appeal to me all that much. Despite their recent struggles, and Buffalo's improved play over the course of the year, Philadelphia strikes me as the better team. I see them narrowly edging the Sabres here.

PHI in 7.

BOS – MTL

Results notwithstanding, the Canadiens might be the league's most improved team this year, given the way that they were manhandled last year in terms of shots and scoring chances. They're actually better than Boston with respect to outshooting at even strength, which I find surprising in light of last year's numbers.

The Bruins are my pick, though. I think they have the better team on paper, not to mention the fact that my model also has them as the better team.

BOS in 7.

PIT – T.B

Given Pittsburgh's injuries to two of its best players, I figure this series is pretty close to a coin flip. I prefer Pittsburgh on the basis of Crosby's potential return to the lineup and the fact that their underlying numbers remained very strong down the stretch

PIT in 7.
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1st Round 1011 Playoff Probabilities

2011-04-13T13:54:00.000-07:00

The information in the table is pretty straightforward - it simply shows each team's probability of advancing as well as the probability of winning in a particular number of games. So, for example, Vancouver has a 61.8% chance of advancing and a 9% chance of doing so in a sweep.

The manner in which the odds were computed, however, requires some explanation. The method I used was similar to the "underlying numbers" method I employed last year, but some changes have been made. They include:

Each team's expected shot differential was calculated on the basis of adjusted corsi - that is, overall corsi adjusted for how often each team played with the lead and trailed during the regular season. This is in contrast to last year's method, which used score tied corsi for this purpose. I elected to switch to adjusted corsi because it has more predictive power in relation to future results than both score tied corsi and overall corsi.
I regressed each team's EV shooting and save percentage based on the extent to which the seasonal variation for each statistic can be attributed to non-luck. This differs from last year's method, in which each team was assigned a league average EV shooting percentage, with team EV save percentage computed on the basis of the overall career EV save percentage of the starting goaltender
I regressed each team's PP and PK shot rates and percentages on the same basis as above when calculating each team's expected special teams scoring rates. Last year, I (erroneously) assumed no skill component for the percentages and elected not to regress shooting rates.
Each team's expected PP and PK time on ice was calculated on the basis of it's predicted powerplay differential as well as its expected special teams scoring rates ( the latter adjustment is necessary given that a more efficient powerplay, as well as a less efficient penalty kill, will lead to fewer powerplay and penalty kill minutes, respectively). I actually performed the exact same calculation last year, with the only difference being the manner in which I determined predicted powerplay differential. Last year, raw powerplay differential was used. This year, powerplay differential was adjusted to reflect the percentage of team variation attributable to luck.

The application of the above method rendered the following expected winning percentages for each playoff team:

I then simulated each series 10000 times based on each team's expected winning percentage, which produced the odds displayed in the table at the top of the post.

In terms of predictive power, I have adjusted goal differential data for every season since the lockout (up to 2009-10), in which the adjustment was made using a similar but slightly different method than the one described in this post. I found that the adjusted goal differentials proved to be a superior predictor of the results of individual playoff games during that timeframe when compared to raw goal differential (empty netters removed).

I also found that the adjusted goal differentials better predicted how a team performed in the following regular season relative to raw goal differential.

I wanted to get this post up before the puck drop for Wednesday's games, so I wasn't able to include everything I wanted to content-wise. I plan to post cup probabilities and some more information relating to the method used to calculated the above odds.
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Cumulative Score Tied Corsi

2011-04-12T00:15:00.000-07:00

I plan to put up a post on the probabilities for each 1st round series either tomorrow or Wednesday during the day. In the meantime, I figured I'd throw up these charts showing the cumulative score tied corsi totals for all of the playoff teams.

There are eight charts in all, one for each series.

Two of the league's strongest teams will engage in a first round battle. Should be a great series.

Both of these teams have improved in this measure as the year has progressed, although San Jose exhibits the more extreme profile - the Sharks have been ridiculously good since the halfway mark.

Detroit looks like the better EV team by a fair margin, actual goal differentials notwithstanding.

I've noticed that the Ducks are getting labeled as a "hot" team, but the evidence doesn't support that. They've been terrible territorially at EV all season, including down the stretch. NSH is the better team.

Not much to say here. The Caps seem inconsistent whereas the Rangers have been consistently in the red.

Two teams seemingly going in opposite directions, but Philly is still better on aggregate.

Shocking. The Bruins were +415 better than the Habs by this measure in 09-10.

T.B is pretty underwhelming here but they blocked a tonne of shots at EV. Injuries have hurt PIT.

EDIT: Accidentally used Philly's numbers for Pittsburgh. The chart has been corrected.
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Loose Ends - Part III B: The Power Play

2011-04-07T23:58:00.001-07:00

This is basically an extension of my previous post, which looked at whether team talent differences in terms of shooting percentage are larger on the powerplay or at even strength.

The purpose of this post is to explore a related issue, that being the relationship between even strength shooting percentage and powerplay shooting percentage. In particular, the extent to which even strength shooting talent and powerplay shooting talent are distinct skills.

In the six seasons from 2003-04 to 2009-10, the average seasonal correlation between the two variables at the team level was 0.296.* While that may seem small, it must be remembered that lucks accounts for a majority of the team to team variation for both metrics. That is to say, each team's single season performance with respect to each metric provides a relatively poor estimate of it's true talent.

As discussed in a previous post, the 'true' correlation between two variables can be approximated so long as three pieces of information are known:

1. The reliability co-efficient of the first variable in respect of a given sample size.
2. The reliability co-efficient of the second variable in respect of the same sample size.
3. The correlation between the two variables observed in respect of the same sample size.

I elected to use 40 games as my sample. In calculating the reliability co-efficients, I determined the correlation between one randomly selected 40 game sample and another 40 game sample, each independent of the other. I then calculated the correlation between those two variables with respect to one of the 40 game samples. Finally, I averaged all three correlations over 1000 simulations and repeated the entire exercise for every season from 2003-04 to 2009-10. Here are the results:

As indicated, the average split-half correlation between even strength and powerplay percentage over the six year sample was 0.167. The average split-half reliability of powerplay shooting percentage was 0.078, and the average split-half reliability of even strength shooting percentage was 0.205.

Having ascertained all three necessary pieces of information, those values can then be inputted into the below formula in order to approximate the true correlation between the two variables.

r xy adjusted = r xy observed/ SQRT( reliability x * reliability y)
r xy adjusted = 0.167 / SQRT ( 0.078 * 0.205)
r xy adjusted = 1.32**

This result implies that both powerplay shooting percentage and even strength shooting percentage are actually measuring the same underlying skill.

Is this result surprising? I would argue that it is not. We can reasonably assume that team differences in even strength shooting talent are concentrated at the top half of the roster. In other words, I don't think that the bottom six forwards and bottom pairing defencemen for any given team have materially more shooting talent relative to the lower end players on any other team. As powerplay time tends to be overwhelmingly awarded to players that also receive the most even strength ice time, we should therefore expect a close relationship between even strength and powerplay shooting percentage, once sample size limitations are accounted for. That's precisely what we find.

*even strength goals were removed from the data for all figures referenced in this post.

** Nothing should turn on the fact that the correlation is larger than 1. If the average observed correlation was only slightly smaller, and the average reliability values only slightly larger, the adjusted correlation would very nearly equal 1. For example, if 2009-10 is excluded from the data, the average correlation changes to 0.145, and the two reliability values become 0.122 and 0.21. If these latter values are substituted into the equation, a more reasonable adjusted correlation of 0.91 is obtained.

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Loose Ends - Part III A: The Power Play

2011-04-07T20:51:00.000-07:00

[EDIT: It appears that I made an error when calculating the skill standard deviations for EV and PP shooting percentage at the team level. The tables and numbers referenced in the post have been edited to reflect the correct values.]

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I've written about the powerplay a few times in the past, with one post focusing specifically on the powerplay itself, and the other relating to special teams performance in general.

The purpose of this post is not only to address some questions that were left unanswered by the two previous ones, but also to look at two as yet unaddressed (at least, unaddressed to the best of my knowledge) issues relating to the powerplay.

Because the treatment of each issue is relatively extensive, I've decided to address them in separate posts.

______________________________

The first issue relates to whether powerplay shooting percentage is more or less 'random' than even strength shooting percentage. Admittedly, the use of the term 'random' leads to some confusion here. For both metrics, skill - or more properly, non-luck - would account for 100% of the team to team variation over the long run. What we're really after is whether the team spread in powerplay shooting talent is wider or narrower than the team spread in even strength shooting talent.

In a post from earlier this year, I included a table that showed the percentage of variation attributable to luck for various shooting metrics over the course of the regular season, based on data from the post-lockout era. I've reproduced that table below.

As indicated, whereas roughly 90% of the team variation in powerplay shooting percentage can be attributed to luck by the end of the regular season, the corresponding figure for even strength shooting percentage is only 67%.

Unfortunately, this fails to resolve our issue, for the reasons specified earlier. Teams take much fewer shots on the powerplay over the course of the regular season as compared to even strength. The disparity in sample size must be controlled for.

Coincidentally, this very issue arose in the comments section of a post made at behindthenet earlier this week. While I was in the process of working on this post at the time, I figured I'd address the matter then and there. Here's what I had to say:

Using seasons since the lockout, the variation in EV SH% at the team level is 33% skill and 66% luck, whereas the variation in PP SH% at the team level is 9% skill and 91% luck.

But the average team takes far fewer shots on the powerplay (~500) than at even strength (~1800). It goes without saying that the % of variation due to luck varies as a function of sample size (i.e. number of shots).

In order to compare apples to apples, it’s necessary figure out how many extra goals a team that is one standard deviation above the league average with respect to EV shooting talent can expect to score over a team that is exactly league average in that respect, per X number of shots.

If the same calculation is repeated in relation to powerplay shooting percentage, the results can be compared.

We’ll use 1000 as the value for x, which is the number of shots.

The results:

EV SH% – 2.64
PP SH% – 1.43
[EDIT: The correct values are 4.83 for EV SH% and 4.77 PP SH%]

So a team one standard deviation above the mean with respect to EV shooting talent can expect to score 2.64 more goals than a team with average EV shooting talent, per 1000 shots.

(We’ll ignore the fact that EV shooting talent and EV outshooting appear to be negatively correlated at the team level).

And a team one standard deviation above the mean with respect to PP shooting talent can expect to score 1.43 more goals than a team with average PP shooting talent, per 1000 shots.

So the implication is that team talent differences in EV SH% are wider than team talent differences in PP SH%.

So there you have it. Team talent differences in shooting talent on the powerplay appear to be smaller than team talent differences in even strength shooting percentage.

[EDIT: The correct values suggest that team skill differences in powerplay shooting percentage are roughly equal in size to team skill differences in even strength shooting percentage.]

One drawback with my method was that I looked at overall powerplay shooting percentage, rather than 5-on-4 shooting percentage. It's possible that the inclusion of other man-advantage situations (5-on-3s, namely) has affected our result.

In order to make sure that that wasn't the case, I made sure to ran the numbers for 5-on-4 shooting percentage as well, using the data available on behindthenet. Here are those results:

% RANDOM = percentage of variation attributable to randomness
% Skill = percentage of variation not attributable to randomness
1 Sigma/1000 = the number of goals a team one standard deviation above the mean in 5-on-4 or EV shooting talent (as the case may be) would be expected to score, relative to an average team, over the course of 1000 shots]

While the differences between the two values are smaller when the 5-on-4 numbers are used, the conclusion remains - teams appear to be more varied with respect to even strength shooting talent as compared to powerplay shooting talent.

[EDIT: If anything, the correct values indicate the opposite - that teams appear to be more varied with respect to 5-on-4 shooting talent as compared to even strength shooting talent.]

How confident can we be that teams are, in fact, more deviated from one another in terms of even strength shooting talent than powerplay shooting talent? Not very. There is some uncertainty in our estimate for the luck component of powerplay shooting percentage at the team level over the course of a season. The figure of 91% is based on an observed standard deviation of 0.158 and a predicted standard deviation of 0.015. If the observed standard deviation was 0.0165 - i.e. slightly higher - then our estimate for the luck component would change to 84%. If the luck component was 84%, our 1 sigma/1000 value then becomes 2.55, which is comparable to the 2.64 1 sigma/1000 value obtained for even strength shooting percentage.

In other words, it's quite possible that teams are similarly distanced from one another with respect to both measures. Support for this proposition will be offered in the next post on this subject.

Loose Ends - Part II: Score Effects and Minor Penalties

2011-03-19T15:34:00.000-07:00

Back in November of last year, I looked at whether there were any score effects in relation to minor penalties. The conclusion? Playing from behind has a significant positive effect on powerplay differential. That is, teams tend to be much better at drawing penalties when trailing, as compared to when leading or when the game is tied.

While my initial article only looked at data from the 2007-08 and 2008-09 seasons, I've since ran the numbers for 2009-10 as well. Here are the aggregate numbers for all three years:

[PD=penalties drawn; PT; penalties taken; P % = penalties drawn/(penalties drawn + penalties taken)]

I should include a reminder that only penalties that were not accompanied by the calling of another penalty at the same point in time were included in the above totals.

In the original post, I asserted that trailing team's penalty advantage was not owing to its superior play, but was instead caused by favorable officiating. In support of this, I noted that actual team-to-team distributions in trailing and leading penalty percentage were roughly what one would expect them to be if the putative bias affected all teams equally.

Although I remain confident that my assertion was correct, I suspect that others may have found my explanation to be less than convincing. And in turning my attention to the subject for a second time, I think that there's a better way in which I can illustrate my point.

In determining whether the trailing team's penalty advantage is the product of bias or earned on merit, it becomes necessary to ask what result we would expect to observe, based on what we know about what causes some teams to be better at drawing penalties than others.

One of those causes is even strength outshooting. If we look at the relationship between EV tied Corsi and tied penalty differential over the last three seasons, each unit increment in the latter equates to 0.027 in the former.

It's well established that the average team does much better in terms of Corsi when playing from behind. Over the three years in question, trailing teams had a collective Corsi percentage of 0.552 (107706 For, 87079 Against). Given the positive relationship that exists between outshooting and penalty differential when the score is tied, the trailing team's advantage in Corsi may be able to account for it's advantage in penalty percentage.

However, upon performing the required calculations, it becomes clear that this factor can only explain part of the difference.

In other words, only about one third of the gap can be attributed to outshooting.

Not only that, but it's clear that the shot statistics flatter the trailing team, given that playing from behind encourages a team to take more risks and play more desperately. For example, during the period in question, trailing teams only scored 51.9% of all non-empty net even strength goals (4623 For, 4292 Against), despite, as mentioned above, generating 55.2% of all Corsi events. It's more than arguable that goal differential, and not Corsi differential, provides the best measure of how well the trailing team actually performs.

As with outshooting, there is a positive relationship between even strength goal differential and penalty differential when the score is tied. Based on data from the three seasons in question, each net goal is worth 0.26 in net penalties drawn. We're able to use this figure to determine what kind of penalty advantage we'd expect the trailing team to have, based on its goal differential.

As the table indicates, we would expect the trailing team to do only slightly better than the leading team in terms of penalty differential on the basis of its advantage in even strength goal differential. Thus, however which way you approach it, referee bias must account for a substantial part - and probably almost all - of the penalty gap.

Loose Ends - Part I: Predicting Future Success

2011-03-17T19:15:00.000-07:00

My plan is to put out a series of posts - hopefully all within the next while - that relate to subjects that I've posted on previously. The object of these posts is to address certain outstanding issues that weren't resolved when I tackled these subjects the first time around.

The first post in the series is an extension of a post that I published last month that looked at how various shot metrics - all of them calculated at even strength with the score tied - predicted future success at the team level.

One related issue that wasn't explored is how well those same shot metrics predict future success when compared to more conventional measures of team strength, such as winning percentage and goal ratio.* This question is actually more fundamental than the one investigated in the original post. After all, if shot metrics like Fenwick and Corsi failed to predict future success better than the conventional measures, then that would render them considerably less useful.

The method employed** was similar to the one used in the first post. Because of the relative complexity of the process, including a step-by-step description may be helpful.

Firstly, I randomly selected a certain number of games from each team's schedule, with each team having an equal number of home and road games selected.

Secondly, I calculated how each team performed over those games with respect to certain variables. The variables that were calculated were even strength Corsi with the score tied, overall goal ratio (with empty net and shootout goals excluded), and winning percentage. Winning percentage was defined as WINS/(WINS+LOSSES). Games that ended in a shootout were considered ties, and were therefore not included in the calculation.

I then randomly selected a second, independent group of games. That is, if a game was included in the first grouping, it was not eligible for selection in the second grouping. As with the first grouping, an equal number of home and road games were selected for each team.

I then determined how each team did in terms of winning percentage over this second group of games, and looked at how each of the three variables calculated in relation to the first group correlated with winning percentage in the second group.

The relationship between the size of the two groups can be expressed as y=(80-x), where x represents the number of games included in the first group, and y the number of games in the second group. So, for example, if 20 games were selected for the first group, the second group would consist of 60 games. Ultimately, I elected to use x values of 20, 30, 40, 50, 60 and 70.

The raw data used was from the 2007-08, 2008-09 and 2009-10 regular seasons. The table included below shows the results for each individual season, as well as the average results. The values represent the average correlation over 1000 calculations.

A couple points:

- Corsi Tied is the best predictor of how a team will perform over the remainder of its schedule, regardless of the point in the schedule at which the calculation occurs.

- Corsi Tied is only marginally more predictive of future success than goal ratio or winning percentage when looking at samples of 60 games or more. In other words, as the sample size becomes increasingly large, there are diminishing returns with respect to the predictive advantage of Corsi. By the end of the season, all three variables seem to predict future success equally well

- The above fact has implications in terms of determining playoff probabilities at the team level, with the results suggesting that a composite metric would work best

- The aggregate values for Goal Ratio and Winning Percentage are remarkably similar. The implication is that once shootout results are controlled for, winning percentage is as good of a measure of a team as goal ratio is

Next up: Score Effects and Minor Penalties.

*Some readers may have observed that the split-half reliability of goal ratio (0.417) was lower than the predictive validity co-efficients for both Corsi Tied (0.444) and Fenwick Tied (0.429). The implication is this is that the two latter variables are better able to predict goal ratio from one half of the schedule to the other than goal ratio is itself.

** I should note that this method was actually developed and first used by Vic Ferrari. See here.

Addendum

Scott Reynolds had a question in the comments section on how the results would differ if we looked at future EV performance rather than overall performance. Using the same method as the one described above, I looked at which of EV Corsi Tied and EV goal ratio (empty netters removed) was better able to predict future performance at even strength (which I operationalized as future EV goal ratio). Here are the results:

The results aren't too different - Corsi Tied is a much better predictor early in the schedule, but the two measures have about the same predictive power by the end of the year.
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EV Data for Games 1-939

2011-02-27T23:30:00.000-08:00

[If you're having difficulty viewing the document, click here to view the spreadsheet directly at googledocs.]

Notes

The document contains three worksheets. The first sheet shows even strength data for all situations. The second shows even strength data for when the score was close (i.e. whenever the score margin was 1 or 0 in the first two periods, or tied in the third period or overtime). The last sheet contains data for when the score was tied.

Empty net goals have been removed from the data.

Missing Games List

Game 124 - WSH@CAR
Game 429 - ATL@NYI

Abbreviations

GF: goals for
GA: goals against
SF: shots for, where shots = goals + saved shots
SA: shots against
SHOT%: shots for/(shots for + shots against)
SH%: shooting percentage
SV%: save percentage
PDO: shooting percentage + save percentage
FF: fenwick for, where fenwick = shots + missed shots
FA: fenwick against
F%: fenwick for/ (fenwick for + fenwick against)
CF: corsi for, where corsi = shots + missed shots + blocked shots
CA: corsi against
C%: corsi for/ (corsi for + corsi against)

Shots, Fenwick and Corsi

2011-02-16T14:28:00.000-08:00

From time-to-time, I'll find myself surfing aimlessly throughout the hockey blogging world in search of articles, discussions, and other interesting stuff. In doing so, I'll occassionally find that others have referenced or linked to my blog. Typically, the link or reference will relate to the even strength data that I've been publishing periodically throughout the season.

There seems to be a decided preference for EV tied and EV close data over the raw numbers. That makes sense - the raw data is subject to score effects, which makes the information less valuable with respect to distinguishing good teams from bad ones.

Interestingly, however, there doesn't appear to be a general agreement as to which of shot, fenwick and corsi percentage serves as the best metric to use once score effects have been controlled for. While fenwick seems to be the most popular, there are some who like corsi, and there are even a few prefer shot percentage over both. This raises the question: which of the three measures ought to be looked to for the purpose of team evaluation?

As Gabe Desjardins once correctly observed, there is a stronger relationship between fenwick and winning percentage than there is between corsi and winning or between shot differential and winning. In fact, according to Gabe's numbers, the correlation between corsi and winning percentage was about the same as the correlation between shot differential and winning percentage, even though including blocked shots substantially increased the sample size. The upshot is that the inclusion of blocked shots in the analysis doesn't add much information.

Gabe's discovery may account for the slight preference towards fenwick discussed above.

However, the weaker relationship between corsi and winning can be partially accounted for by score effects. In particular, the trailing team does better in terms of corsi than it does with respect to either shot percentage or fenwick.

As such, while overall corsi has a lower correlation with winning than overall fenwick, the same may not hold with respect to score tied corsi and score tied fenwick.

In an attempt to resolve this issue, I performed a series of calculations, the results of which have been posted below.

This table shows the split-half reliabilities for score tied corsi, score tied fenwick and score tied shot percentage. The split-half reliabilities for each variable were calculated by randomly selecting 40 games, randomly selecting an independent group of 40 games (that is, a game chosen in one group was necessarily excluded from the other), and using the two data sets to determine the correlations for each variable. This was repeated 1000 times, with the above table showing the average values.

Not surprisingly, corsi is more reliable than either fenwick or shot ratio at the half-season level, which is a product of the fact that there are simply more corsi events then fenwick or shot events in our sample. Thus, corsi should prima facie be considered the superior metric of the three due to its superior reliability.

Ignore the goal ratio column for now - it's only been included for the purpose of performing a subsequent calculation.

This table shows the predictive validity of the same three variables with respect to overall goal ratio. Here, predictive validity was determined by randomly selecting 40 games, calculating each team's score tied corsi, fenwick and shot percentage within that sample, and looking at how each variable correlated with overall goal ratio in an independently selected 40 game sample. As with the first table, the numbers here are the averaged values over 1000 trials.

The predictive validity of each variable is commensurate with its reliability co-efficient, with corsi having the most predictive validity. In other words, a team's score tied corsi over a 40 game sample is a better indicator of how it will perform over the remainder of its schedule than is score tied fenwick or score tied shot percentage.

Of course, the fact that corsi has the most predictive validity in practice doesn't necessarily mean that it serves as the best measure of team skill in theory. As discussed in a previous post, the observed correlation between two variables is contingent upon the reliability with which each variable can be measured. Fortunately, there exists a formula that can be used to calculate what the correlation between two variables would be if each could be measured with perfect reliability. That formula involves dividing the observed correlation by the product of each variable's reliability co-efficient.

r xy adjusted = r xy observed/ SQRT( reliability x * reliability y)

As we already have the split-half reliability co-efficients for all of the variables, we only need to determine the split-half correlations between score tied corsi, score tied fenwick and score tied shot percentage, on the one hand, and goal ratio, on the other.

After inputting all of the relevant variables into the above formula, the following values are obtained:

Therefore, while corsi has more predictive validity with respect to goal ratio at the within-season level, fenwick and shot percentage appear to correlate more strongly with goal ratio over a sufficiently large sample of games. In other words, in theory, both fenwick and shot percentage seem to serve as better measures of team quality than corsi does.

One caveat: the differences between the values here are small, and we only have three seasons of data. It may very well be that all three variables correlate equally well with goal ratio over the long run. This subject may require further study in the future when more data is available.

EV Data for Games 1-820

2011-02-11T10:08:00.000-08:00

[If you're having difficulty viewing the document, click here to view the spreadsheet directly at googledocs.]

Notes

The document contains three worksheets. The first sheet shows even strength data for all situations. The second shows even strength data for when the score was close (i.e. whenever the score margin was 1 or 0 in the first two periods, or tied in the third period or overtime). The last sheet contains data for when the score was tied.

Empty net goals have been removed from the data.

I didn't make an adjustment for schedule difficulty this go around because - and this is embarassing - when I recently performed a system restore, I forgot to transfer that particular file to my external hard drive. Having said that:

1. There seems to be more interest in the raw numbers.

2. The schedule adjustment would be negligible for most teams at this point in the season.

Missing Games List

Game 124 - WSH@CAR
Game 429 - ATL@NYI

Abbreviations

GF: goals for
GA: goals against
SF: shots for, where shots = goals + saved shots
SA: shots against
SHOT%: shots for/(shots for + shots against)
SH%: shooting percentage
SV%: save percentage
PDO: shooting percentage + save percentage
FF: fenwick for, where fenwick = shots + missed shots
FA: fenwick against
F%: fenwick for/ (fenwick for + fenwick against)
CF: corsi for, where corsi = shots + missed shots + blocked shots
CA: corsi against
C%: corsi for/ (corsi for + corsi against)

Even Strength Outshooting and Team Quality

2011-01-26T00:29:00.000-08:00

Readers familiar with the team even strength data that I've published over the course of the season might wonder why I seem to place a large amount of emphasis on even strength shot ratio with the score tied.

After all, only about 35% of league play occurs with the score tied. And of that 35%, one-fifth consists of special teams play. Taken together, that means that time played at even strength with the score tied represents less than 30% of a typical NHL game.

Indeed, if we examine the relationship between a team's even strength shot ratio with the score tied and it's overall goal ratio for every season since the lockout, we find an average correlation of 0.556, meaning that even strength shot ratio only accounts for roughly 30% of the variance in outscoring with respect to a single NHL season.

However, because goals in the modern-day NHL are relatively rare events, a substantial proportion of the team-to-team variation in seasonal goal ratio can be attributed to luck. For example, random variation accounted for 47, 35, and 41 percent of team variation in goal ratio in 2007-08, 2009-10 and 2009-10, respectively.

In a hypothetical season with a sufficiently long schedule, that random variation would eventually disappear, leaving each team with a goal ratio commensurate with its abilities. What each team's goal ratio might look like in such a scenario can be approximated by taking its seasonal statistics - namely, shot ratio, shooting percentage and save percentage - and adjusting them to account for the extent to which each one is affected by random variation.* For both shooting and save percentage, the adjustment is significant as luck accounts for a majority of the variation in respect of both over the course of a single season, as indicated in the table below.

For shot ratio, however, the adjustment is less severe as the impact of randomness is comparatively smaller. Consequently, as the sample size increases, so too does the correlation between shot ratio and goal ratio.

If this exercise is performed for each post-lockout season, one is able to determine the relationship between true goal ratio and even strength shot ratio with the score tied. The results:**

Therefore, in an imaginary league in which luck is a complete non-factor, EV shot ratio with the score tied would account for roughly 65% of the variance in outscoring. In other words, even though the two variables may not be strongly correlated over the course of a single season, a team's EV shot ratio with the score tied serves as a reasonably good indicator of how it can be expected to perform over the long run. This is especially true for the three most recent seasons, in which EV shot ratio accounts for 75% of the variation in outscoring ability. It seems that as the level of parity between teams has increased, even strength shooting has become even more important.

Finally, the remaining 35% of outscoring variance indicates that there are other sustainable components of team success. Apportioning the remaining proportion of the variance between these components gives us an idea of their relative importance.

As special teams ability and EV tied shot ratio are correlated variables, residual special teams skill refers to the proportion of special teams skill that cannot be accounted for by EV tied shot ratio. Residual specials teams skill accounts for about 49% of the remaining variance.

Similarly, residual EV shot ratio refers to the proportion of even strength outshooting that cannot be predicted by EV shot ratio. This accounts for 7% of the remaining variance.

The rest of the remaining variance is explained by even strength shooting, even strength save percentage and residual variance. Residual variance is the amount of variance left over after subtracting the sum of the other four components from 1. It results from the fact that the four components are not uncorrelated, independent variables.

* even strength and special teams statistics were, of course, treated separately for this part of the analysis

**There is an alternative calculation that can be applied as a check on the correctness of these values. As the seasonal reliability of both goal ratio and EV tied shot ratio is imperfect, it is necessary to upwardly adjust the observed correlations between the two variables in order to ascertain their 'true' relationship - that is, the correlation that would result if each variable was perfectly reliable.

The adjustment involves dividing the observed correlation by the square root of the product of each variable's reliability co-efficient. In other words

r adjusted = r observed/ SQRT( reliability EV tied shot ratio* reliability goal ratio )

The application of the above formula involves determining the reliability co-efficients for each variable, which can be calculated as follows:

reliability = 1- [(1- split half reliability)/SQRT(2)]

If these formulae are applied with respect to each post-lockout season, the following results:

The average adjusted correlation is 0.81, which is comparable to the average adjusted correlation obtained through the first method (0.804). It should be noted that this second method is likely to slightly overestimate the true correlation, given that the two variables are not truly independent.

EDIT: Accidentally used Fenwick ratio instead of Shot ratio when determining observed correlations for 2007-08, 2008-09 and 2009-10. Table and accompanying discussion has been edited accordingly.

EDIT 2: In re-thinking the method used in the alternative calculation, it occurred to me that the better way to adjust the observed correlations would be to calculate all three input values at the half-season level.

There's no sense in using the split-half reliabilities in order to estimate the full reason reliabilities for EV shot ratio and goal ratio when the split-half reliabilities can be used themselves, given that the split-half correlation between EV shot ratio and goal ratio is readily ascertained.

This approach produced the following results.*

* the half-season values were calculated through randomly selecting 40 games, randomly selecting another 40 games without replacement, and determining the correlation between the relevant variables across the data sets. This was repeated 1000 times, with the average values used.

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EV Data for Games 1 - 692

2011-01-19T15:07:00.000-08:00

The spreadsheet that should appear below contains detailed EV data at the team level for games 1 to 692. As NHL.com has inexplicably failed to publish play-by-play data for the following games, they were not included:

Game 124 - WSH@CAR
Game 429 - ATL@NYI
Game 491 - PHX@PIT*

*The play-by-play feed for this game was initially available, but is no longer accessible. Consequently, I have EV and EV close data for this game, but no EV tied data.

[If you're having difficulty viewing the document, click here to view the spreadsheet directly at googledocs.]

A couple of points:

The document contains three worksheets. The first sheet shows even strength data for all situations. The second shows even strength data for when the score was close (i.e. whenever the score margin was 1 or 0 in the first two periods, or tied in the third period or overtime). The last sheet contains data for when the score was tied.

Empty net goals have been removed from the data.

The abbreviations are defined as follows:

GF: goals for
GA: goals against
SF: shots for, where shots = goals + saved shots
SA: shots against
SHOT%: shots for/(shots for + shots against)
SH%: shooting percentage
SV%: save percentage
PDO: shooting percentage + save percentage
FF: fenwick for, where fenwick = shots + missed shots
FA: fenwick against
F%: fenwick for/ (fenwick for + fenwick against)
CF: corsi for, where corsi = shots + missed shots + blocked shots
CA: corsi against
C%: corsi for/ (corsi for + corsi against)
ADJ: refers to the fact that an adjustment for schedule difficulty has been made. See here for the details of the adjustment process.

Finally, as mentioned earlier, I've included EV tied data in this go around. The reason for that is that it appears that score effects are still very much relevant when the score margin is 1 in the first two periods. For example, consider the table below which shows how teams trailing by one goal in the first two periods have performed with respect to shot percentage and PDO over the last three seasons.

In other words, teams trailing by one goal in the first two periods tend to play more aggressively, which increases their shot differential yet hurts their PDO. Additionally, there appear to be strategic differences between teams with respect to style of play when the score margin is one in the first two periods. That's a topic that I plan to explore in more detail in the upcoming weeks.

The result of all of this is that Fenwick or Corsi percentage with the score tied should be a better measure of a team's true ability to control the play at even strength, given that EV score close shot statistics tend to favor teams that play more from behind and/or play more aggressively, relative to the average team, when leading or trailing by one in the first two periods.
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East vs West Follow Up

2011-01-04T23:12:00.000-08:00

In my last post, I included a detailed breakdown of how the two conferences have matched up against one another so far this season and, on the basis of the data, concluded that there wasn't much to choose between them, the West's superior record notwithstanding.

My conclusion was implicitly premised on the assumption that there's no significant skill difference between the two conferences with respect to shooting or save percentage. The rationale behind that assumption was that, while there are talent differences between teams in terms of the percentages, those differences should cancel out when comparing large groups of teams. Without taking a further look at the data, however, it's impossible to determine whether or not the assumption relied on is true.

In determining the above issue, I think that it might be helpful to look at data from interconference games over the last six seasons. I'd delve back further in time, but 2003-04 is the oldest season for which I have advanced statistics at the team level. It's well established that the West dominated the East over this timeframe, as evidenced by the table below. The West had the better record in each of the six seasons examined, with an aggregate winning percentage of 0.54. That's only slightly better than what one would expect on the basis of their goal ratio (its expected winning percentage was 0.536).

[The % column indicates the number of percentage of East wins/goals/shots/powerplay opportunities as a percentage of overall wins/goals/shots/powerplay opportunities. For the post-lockout seasons, games that went to a shootout are considered ties. Empty nets goals have been removed from the data.]

In order to determine the nature of the West's dominance, however, it becomes necessary to take a more granular look at the data. This can be achieved through looking at how each conference has done in terms of shots and the percentages, through breaking down the data by game situation (even strength and special teams), and through looking at data from when the score was tied in order to identify and/or control for playing to the score effects.

[I elected not to include data on shorthanded shots and goals given that shorthanded scoring is neither an important nor sustainable component of team success].

The first thing one might notice is that the West did better than the East across the board - both at even strength and on special teams, and both in terms of shots and the percentages. It was also a fair bit better on drawing penalties, which is noteworthy given that NHL referees tend to favor the trailing team -- Eastern teams presumably would have spent more time playing from behind than Western teams during the games sampled.

However, while the West has technically outperformed the East in respect of shooting percentage, the difference is marginal. Indeed, there's effectively no difference at all at even strength, and while the difference in terms of PP SH% is larger, it's not necessarily reflective of an underlying talent advantage. For example, if the two conferences had the same "true" PP SH%, one would expect one conference to have an advantage of at least 0.004 approximately 50% of the time.

Similarly, the fact that one conference tended to outperform the other in terms of EV SH% in specific seasons should not be construed as meaningful. Random variation requires an average difference of 0.00468 when comparing the shooting percentage of one conference to the other. The actual value? 0.00467.

The success of the Western teams was driven primarily by its outshooting advantage, and this was true at both even strength and on the powerplay. The fact that the data for this season shows no such advantage for Western teams suggests to me that it may no longer be the better conference. While it's true that the West has done better than the East in relation to the percentages, it's difficult to interpret that as a difference in underlying skill for the reasons outlined above.
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The East might be the better conference

2010-12-25T13:14:00.000-08:00

The Western Conference has had the better record in interconference games in each of the last ten seasons. That trend has continued into the current season, with the West putting together an impressive 67-50-20 against their Eastern counterparts thus far (games that ended in a shootout are counted as ties). However, upon closer inspection, it would appear that the two conferences are much closer to one another in relation to ability than the results of the interconference games would suggest.

[Note: The data in the table was calculated after removing empty net goals]

The table pretty much says it all. Firstly, while the West has 12 more non-shootout wins than the East, they're only +11 in terms of goal differential. Generally speaking, a win is worth 5 or 6 goals with respect to net goal differential, so the West should only have about four more wins than the East on merit.

Secondly, the underlying numbers are revealing. The West has done better in terms of the percentages, particularly at even strength, whereas the East has done better virtually everywhere else. Part of the shot differential gap is surely attributable to the fact that Eastern teams have (presumably, given their record) spent more time playing from behind, but it's worth noting the East has still done better with the score close. The East has also been better at generating shots on the powerplay - their six extra PP opportunities can only account for about 15-25% of the shot gap.

Holiday Data Dump

2010-12-25T01:24:00.000-08:00

Here's a brief rundown on the contents of the four sheets that can be displayed above.

- the first sheet shows each team's adjusted goal percentage (for all game situations, not just even strength), adjusted Fenwick percentage with the score close, and adjusted Corsi percentage with the score close, in that order. Information on the specifics of the adjustment can be found here.

- the second, third and fourth sheets are self-explanatory.

-all empty net goals have been removed from the data.

Adjusted Corsi Update and Goalposts

2010-11-30T18:53:00.000-08:00

I've been posting adjusted team Corsi data on a more or less bi-weekly basis over the course of the 10-11 season. As a continuation of that trend, here are the updated numbers. For those that may not be familiar, the following adjustments have been made:

only even strength events with the score close (when the score margin is one or zero in the first two periods or tied in the third period and overtime) are included
a strength of schedule correction is made with reference to both game location and oppositional strength

[Column abbreviations, from left to right: Corsi For, Corsi Against, Corsi percentage, Corsi percentage rank, Schedule difficulty rank, Adjusted Corsi For, Adjusted Corsi Against, Adjusted Corsi percentage, Adjusted Corsi percentage rank]

I received an email in relation to my last post on the subject regarding the manner in which schedule difficulty is corrected for. I figured that I should post a summary of the methodology involved in case any other readers were curious.

The method is essentially an iterative process. In the first iteration, oppositional strength is calculated with reference to each team's raw Corsi (both for and against) with the score close, and each team's Corsi numbers are adjusted on this basis. The second iteration is identical to the first iteration, except that oppositional strength is calculated with reference to each team's adjusted Corsi, as calculated in the first calculation. Each subsequent iteration proceeds on this basis (i.e. calculating schedule difficulty through the adjusted Corsi data obtained in the previous iteration).

It turns out that ten iterations are sufficient -- the average change in Corsi percentage from the 9th to the 10th iteration is 0.00000043.

Within each iteration, several other adjustments are made that are worth mentioning. Firstly, an adjustment is made in terms of the location of each individual game and whether either team is playing a back to back. Secondly, each individual game is weighted with respect to the total number of Corsi events with the score close. Finally, a correction is made to account for the extent to which each team has contributed to the Corsi percentage of its opponents (this is necessary so that the adjustment does not favour weak teams).

In addition to that, I thought it might be worthwhile to throw up some data on the number of posts that each team has hit thus far, as well as how many times their opponents have struck iron. Vic Ferrari made two posts on this very subject during the 2007-08 season, which I found to be quite interesting then. I'm not sure of the information I'm about to present is all that valuable -- the underlying numbers provide a good indication of which teams have been fortunate or unfortunate, so there's not really any need to rely on goalposts as a proxy for luck. With that said, here's the data.

Based on then above, I think it's fair to characterize the Lightning, the Predators and the Flames as teams that have been unlucky. I'd also include the Wild within that group, given how poorly they've fared on the shot clock so far. On the other end of the spectrum lie the Hurricanes, as well as the Red Wings and the Sharks (the former because of their favorable differential, the latter two because of their favorable differential relative to their shot statistics).

For what's worth, I also ran the numbers for last year. There's been some debate within the hockey blogging world as of late as to whether its appropriate to regard Colorado's 0910 season as lucky. I figure that goalpost data is probably relevant to this issue to some extent, especially among those who reject the validity of Corsi and other shot statistics. Assuming that I haven't made any errors in obtaining the data, the Avalanche hit 27 posts last season, with their opponents hitting 41. Take that for what it's worth.

In Defence of Outshooting

2010-11-23T17:00:00.000-08:00

David Johnson recently put up a post at his blog that examined the relationship between shot volume, shooting percentage and goals scored at even strength. Specifically, he determined each team's number of Fenwick shots (shots + missed shots) as well as their "Capitalization Ability" (goals scored/Fenwick shots) over the last three regular seasons and how each variable correlated with goals scored over that same period. He then repeated the exercise with respect to Fenwick shots against, save percentage (goals against/ Fenwick shots against) and goal prevention. After presenting his findings, the following conclusion was drawn:

"The conclusion we can draw from these four charts is when it comes to scoring goals, having the ability to capitalize on opportunities (shots) is far more important than having the ability to generate opportunities (getting shots). Controlling the play and generating shots does not mean you’ll score goals (just ask any Maple Leaf fan), having the talent to capitalize on those opportunities is what matters most. From my perspective, this means the usefulness of ‘Corsi Analysis’ to be minimal, at least for the purpose of evaluating players and teams."

At first glance, Johnson's findings and conclusion seem sound enough. For example, if we determine each team's Fenwick differential and Fenwick PDO (Fenwick SH% + Fenwick SV%) over the last three seasons, and look at the correlation of each with each team's even strength goal differential over that same timeframe, the following values are obtained.*

*empty netters were removed from the sample

The results appear to support Johnson's conclusion. The average correlation between outshooting ability (as measured by Fenwick differential) and goal differential is weaker than the average correlation between [shooting + save percentage] and goal differential. As Johnson might put it, the ability capitalize on opportunities and preventing the opposition from doing likewise is more important than having the ability to generate opportunities.

However, Johnson's analysis suffers in that he fails to consider the impact of random variation upon the correlations that he adduces as evidence to support his position. For example, suppose that outshooting was the sole determinant of even strength goal differential, with the percentages merely reflecting the favour (or disfavour) of the hockey gods. If a full NHL regular season was played out under such conditions, we would still expect to observe:

a) a less than perfect correlation between outshooting and goal differential
b) a substantial correlation between the percentages and goal differential

This can be illustrated by simulating the last three NHL seasons a sufficiently large number of times and averaging out the results, using the following parameters:

the number of shots taken by a team in any given simulation was the number of Fenwick shots taken by that team during the season simulated
conversely, the number of shots taken against that team corresponded to the number of Fenwick shots against it conceded during that year
each team's probability of scoring a goal on any particular shot was the league average Fenwick shooting percentage in that particular season (~5.5%).
similarly, the probability of conceding a goal on any particular shot was the same for all teams, again corresponding to the league average Fenwick shooting percentage during the season in question
after each simulation, the correlation between Fenwick differential and even strength goal differential at the team level was determined and recorded, with the same then being done with respect to [Fenwick shooting percentage + Fenwick save percentage] and even strength goal differential

The results:

So, in the three simulated seasons, the average correlation between Fenwick differential and even strength goal differential was 0.73, whereas the average correlation between [Fenwick shooting percentage + Fenwick save percentage] was 0.67. This is significant for two reasons.

Firstly, even in our imaginary world in which the only way for a team to control its goal differential is through generating and limiting shots, the correlation between the percentages and goal differential is effectively as large as the correlation between outshooting and goal differential. This despite the fact that teams have no ability to influence the former.

Secondly, the simulated values (0.73 and 0.67) are comparable to the actual values (0.54 and 0.61), suggesting that the underlying factors that dictate even strength goal differential in the real NHL are not too different from those that prevail in our simulated world. The relationship between the percentages and outscoring is slightly stronger, and the relationship between outshooting and outscoring slightly weaker, but that's to be expected. After all, we know that:

1. There is a skill component to both even strength shooting percentage and even strength save percentage at the team level.
2. Game score (whether a particular team is playing while tied, from behind or while leading) has an effect on both shot differential as well as the percentages. Over the course of a particular season, the amount of time played in each of these goal states at even strength while vary from team to team.
3. Not all teams adopt the same strategy in relation to playing to the score.

The influence of these last two factors cannot be overstated. For example, if we repeat the above exercise, but use only data from when the score was tied at even strength, the actual results are essentially indistinguishable from the simulated results.

Therefore, the fact that there exists a strong relationship between the percentages and even strength goal differential over the course of a single regular season does not in any way negate the utility of Fenwick, Corsi or even strength shot differential as a measure of a team's ability level. Results at the NHL level are strongly subject to the influence of random variation, even over what might seem like a long period of time (i.e. a single NHL season). Losing sight of this fact - or ignoring it to begin with - can only lead to misguided analysis and flawed conclusions.
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Adjusted Corsi w/ Score Close - Part III

2010-11-19T00:12:00.000-08:00

In two previous posts, I showed how each team had performed in terms of Corsi percentage with the score close at that particular point in the season, and then adjusted each team's percentage in order to account for variance in strength of schedule.

While my strength of schedule adjustment corrected for game location (i.e. whether, from a particular team's perspective, the game was being played at home or on the road), it did not account for back-to-games. As it turns out, this was a mistake on my part -- the effect of back-to-games on Corsi (with the score close) is much larger than the effect of game location.

Table Legend
GP = Games played; The number of games played in the 2010-11 season which meet the criterion in the left hand column
R Corsi = Road Corsi; The number of shots directed at the net at even strength by the road team
H Corsi = Home Corsi; The number of shots directed at the net at even strength by the home team
R Corsi % = Road Corsi Percentage; the Corsi percentage from the road team's vantage

The above table shows how game location and whether or not the game is a back to back for either team have interacted to effect Corsi percentage with the score close in games played during the 2010-11 season thus far (up to and including the 268th game).

Some observations:

Firstly, in games in which one team played the night before and the other team did not, the road team carries the burden roughly 75% of the time. I guess the league wants to give the home team every advantage it can without making it seem too obvious.

Secondly, the effect of back-to-back games on Corsi percentage with the score close is considerable -- approximately 0.04. In other words, an average team playing a likewise average team that played the previous night can expect to achieve Corsi results on par with those of the 2009-10 Boston Bruins (a strong, if underrated, team). If the positions are reversed, however, it can expect to perform more along the lines of the 2009-10 Tampa Bay Lightning. That's a sizable difference.

Thirdly, the effect of game location, in and of itself, is pretty small. In games in which both teams are playing on at least one day's rest, the home team only marginally outshoots its counterpart.

With these findings in mind, I decided to modify my method of correcting for scheduling difficulty by accounting for the effect of back-to-back games in addition to game location. Here are the results for all games played as November 17.

More observations:

The Capitals raw numbers are ok, but they really get killed by the schedule adjustment. I think that they've played the Thrashers three times already
Chicago's numbers might come across as underwhelming, given where they were last year, but they're improved in this regard as the season has progressed. I expect that to continue
The Oilers are a real outlier. They're 0.095 from the mean when the next furthest team is a mere 0.064. Things don't look good
The Wings may not be what they once were in terms of territorial dominance, but they've still managed to best everyone else. It's hard not to have some degree of admiration for that club

Adjusted Corsi w/ Score Close - Updated

2010-11-04T22:35:00.001-07:00

A couple of weeks back, I put together a post showing how each team had performed thus far in terms of Corsi (shots directed toward the net at even strength) with the score close (whenever the score margin is zero or one in the first two periods, or zero in the third period or overtime) after making an adjustment for schedule difficulty (the method of adjustment is described in the original post).

Here are the updated rankings as of game 177 (VAN@COL). I should note that Game 124 between the Capitals and Hurricanes wasn't included due to the lack of a play-by-play feed.

(Table abbreviations: C F = Corsi For; C A = Corsi Against; C % = Corsi Percentage; SD RANK = Schedule Difficulty Rank (lower values indicate a more difficult schedule); ADJ = Adjusted)

Some observations:

Anaheim, Atlanta and Edmonton are terrible
If Florida can maintain their pace, they might be the league's most improved team in this respect
What's going on in Washington?
Neither the Devils nor the Sabres are as bad as their records would indicate, but even this assessment of their abilities isn't all that positive

Score Effects and Minor Penalties

2010-11-03T18:58:00.000-07:00

The playing to the score effect has received a fair amount of coverage from the more statistically inclined members of the hockey blogosphere over the last two years or so (see here, here and here for some good overviews on the subject). In short, playing from behind tends to have a favourable effect on a team’s shot ratio, whereas playing with the lead tends to have the opposite result. The effect increases linearly as a function of goal margin, and is exaggerated in the third period.

The majority of analysis conducted in relation to the subject thus far has focused on the effect of game score on shot ratio. Little, if anything, appears to have been done in the way of determining the extent to which the effect operates in other aspects of the game. It’s conceivable, for example, that game score could have an analogous effect on team penalty percentage (defined as minor penalties drawn / ( minor penalties drawn + minor penalties taken).

In order to answer the above question, I looked at the NHL.com play-by-play data from the 2007-08 and 2008-09 seasons and created a script on excel to determine how many penalties each team drew and took during that period. However, because I was only interested in penalties that provided one of the teams with a manpower advantage (relative to the situation that existed prior to the penalty was called), I only counted “unique” penalties. I defined a unique penalty as a penalty not accompanied by the calling of any other penalty at that specific point in time. This obviously fails to account for situations where multiple penalties are called and one team emerges with a powerplay, but such situations are rare enough so as to not affect the data materially.

I then determined the goal state prevailing at the time that the penalty occurred – in other words, whether the team that drew/took the penalty was trailing, leading or tied at the time that the penalty was called. Here are the combined results for the two seasons, broken down at the team level.

Evidently, the trailing team does significantly better in terms of penalty ratio than does the leading team. During the period in question, every single team did better in terms of penalty percentage when trailing than when leading. In aggregate, the trailing team drew roughly 54.5% of all penalties, making the magnitude of the effect similar to that observed with respect to shot percentage (the trailing team had an aggregate Corsi percentage of 55.2 during the same timeframe).

One final question remains – does the trailing team earn its penalty advantage on merit, or is it a product of referee bias? Given that the trailing team also enjoys an advantage in terms of Corsi, and therefore spends more time in the opponent’s end than its own (an area of the rink in which a disproportionate percentage of penalties are drawn), one might be inclined to favour the former explanation. However, as demonstrated in the table below, there isn’t much of a relationship between Corsi percentage and Penalty percentage when the score margin is other than zero.

In other words, while the trailing team tends to both outshoot and “outdraw” the leading team, teams that outshoot the opposition by a large margin when playing from behind don’t do significantly better with respect to (trailing) penalty ratio than teams that outshoot the opposition to a lesser extent.

As alluded to above, the second possibility is that the penalty advantage accruing to the trailing team is the result of referee bias. If this explanation is correct, then the team-to-team variation in both leading and trailing penalty percentage would be the product of both randomness and team ability differences in drawing more penalties than the opposition. To test this hypothesis, the following experiment can be performed:

taking each team’s penalty percentage with the score tied over the two seasons in question and regressing each value 60% to the mean. The resulting values provide an estimate of each team’s underlying ability to draw more penalties than the opposition. The regression is necessary given that approximately 60% of the team-to-team variation in penalty percentage with the score tied (in the sample of question) can be attributed to luck

simulating the two seasons such that every “unique” penalty that occurred when each team was trailing constitutes an individual trial

designate the probability of drawing any given penalty as that team’s “true ability” penalty percentage (as determined above) plus 0.045 (0.045 being the magnitude of the referee bias)

calculate the average team-to-team spread (standard deviation) in penalty percentage after conducting a sufficiently large number of simulations

compare the predicted standard deviation to the actual value

repeat the above with respect to all penalties that occurred when each team was leading

The results:

The essentially confirms the above hypothesis in that the predicted standard deviations are virtually identical to the actual values. As such, an analogy can be drawn between the trailing team advantage in penalty percentage and home ice advantage. The probability of a team winning any given game is approximately 5% higher on home ice relative to neutral ice, but all teams benefit from the effect equally (that is, the team-to-team variation in home vs. road winning percentage is entirely random). Similarly, the referee bias in favour of the trailing team appears to be even across the board.

Corsi Corrected for Schedule Difficulty

2010-10-23T21:53:00.000-07:00

While another year of hockey is finally underway, the 2010-11 season is still very much in its infancy. The schedule has yet to reach the 100 game mark, with no team having played more than a handful of games. This being the case, drawing conclusions on the basis of the results thus far can be difficult. The sample size with which we have to work just isn’t large enough.

To illustrate this, consider the league standings as of Friday, October 22^nd, following the completion of the 97^th game. The range in standing points is 7, with a standard deviation of 2.08. In assigning each team the same winning percentage, setting home advantage at 5%, giving each game a 22% chance of going past regulation, and simulating the first 97 games of the schedule 1000 times under these conditions, the following is obtained.

In other words, virtually all of the team-to-team variation in standings points at this stage of the year is the product of randomness. (For interest’s sake, only about half of the variation in standings points over the course of an entire season can be accounted for by luck.)

As shots in hockey are relatively frequent events, it makes much more sense to rely on a shots-based metric in order to get a sense of how each team has performed thus far. But which metric in particular ought to be used? And which adjustments, if any, are necessary?

Corsi – which includes all attempted shots and therefore better attenuates any sample size concerns – serves as the best fit for this exercise, as opposed to either Fenwick or shot ratio proper. However, two adjustments are necessary. Firstly, playing to the score effects – which are known to bias the shot clock in favour of the trailing team – ought to be controlled for as much as possible. This is especially true this early in the season, as some teams will have played with the lead for much longer periods than others. Ideally, one would restrict the sample to shots attempted at even strength with the score tied in order to get around this problem. However, because of the sample size concern identified above, using Corsi with the “score close” – defined as whenever the score is within one goal in the first or second period, or tied in the third period or overtime – is to be preferred.

Secondly, a team’s Corsi depends not only on its own ability to outshoot the opposition at even strength, but also on the ability of its opponent in this respect. At this point in the year, few teams have played what could be reasonably described as a balanced schedule. Thus, regard should be had to the fact that some teams have faced stronger or weaker opponents with respect to Corsi through incorporating some sort of correction for strength of schedule.

The table below shows each team’s Corsi percentage with the score close and how that changes once an adjustment for strength of schedule is applied.

It’s important to note that, at this point in the year, roughly 43% the team-to-team variation in Corsi percentage with the score tied (raw, not adjusted) can be attributed to luck. Accordingly, some teams will see their ranking change significantly between now and the season’s end. If forced to predict, I’d wager that, relative to underlying talent, the Devils, Bruins, Capitals, Blackhawks and Sharks are better than these rankings suggest. Conversely, I’d wager that the Avalanche, Canadiens, Rangers, Panthers and Flyers are worse.

Stanley Cup Final Prediction and Probabilities

2010-05-28T21:42:00.001-07:00

[For an explanation of the table and how the odds were computed, see here].

Not much to say here.

If the regular season was any indication, all three of Chicago's playoff opponents were better teams than the Flyers.

If that doesn't reflect the imbalance between the two conferences, I'm not sure what does.

CHI in 5.

3rd Round Playoff Predictions and Probabilities

2010-05-15T10:39:00.000-07:00

[For an explanation of the table and how the odds were computed, see here].

S.J - CHI

Although Chicago was the better team during the regular season, the Sharks have, to my eye, looked more impressive through the first two rounds. Chicago has simply not been anywhere near as dominant as I would have anticipated.

That said, I thought Chicago was the best team in the conference before the playoffs started, and, while their recent play has produced some doubt in that regard, that belief still holds true.

Thus, I'm going with the Blackhawks to win the de-facto cup final.

CHI in 6.

PHI - MTL

While both of these teams have received some good fortune in order to be where they are right now, the Habs playoff run has been more luck driven. Given that luck doesn't persist over time, this works in the Flyers favor.

Philadelphia may be the weakest opponent that Montreal has faced thus far, but they're still the better team.

I've enjoyed Montreal's playoff run immensely. During my tenure as a serious fan, I had never, before this year, had the opportunity to watch my team advance beyond the second round. Although the circumstances of their advancement leave much to be desired - as any self-respecting fan would prefer to see his team win on merit -, I'm glad that it's finally happened.

I have a feeling that it ends here, though.

PHI in 6.

2nd Round Playoff Predictions and Probabilities

2010-04-28T23:44:00.000-07:00

[For an explanation of the table and how the odds were computed, see here].

S.J - DET

This series is interesting in the sense that there is no obvious favorite. The Sharks had the better regular season goal ratio by a fair amount, and have about a 65% chance to win if the odds are computed on that basis. On the other hand, the Wings had the better underlying numbers. While both teams were very good at generating shots on the powerplay and moderately good at shot prevention on the penalty kill, the Wings were better at outshooting at EV with the score tied.

I've included an excel document below that contains a list of series from 1993-94 onward where one of the teams had the better pythagorean expectation, and the other the better shot ratio. The team with the better pythagorean expectation is listed under the column heading 'T1', whereas the team with the better shot ratio is listed under the column heading 'T2'. 'W%' denotes pythagorean expectation, whereas 'SR' stands for shot ratio. 'Result' indicates which team won the series. 'W' indicates that the team with the better pythagorean expectation won, while 'L' indicates that the team with the better shot ratio won.

(I realize that shot ratio and the underlying numbers are distinct metrics; however, the data necessary to compute an expected winning percentage based on the underlying numbers just isn't available for the seasons in question. In lieu of that, I think that shot ratio provides an adequate proxy.)

Overall, there were 65 series that satisfied the above criteria. Of those series, the team with the better pythagorean expectation won 35 times, while the team with the better shot ratio won 30 times. This bodes well for the Sharks, I think.

The average difference in shot ratio between the two teams was about 0.12, which is almost identical to the difference between the Sharks and Wings. The average difference in pythagorean expectation was about 0.04, which is less than the 0.07 separating the two teams. Again, I think that this works in San Jose's favor.

On the other hand, the Wings almost certainly aren't a true talent 0.53 team, and it would be foolish to regard them as such.

All things considered, I think that this matchup is pretty close to a cointoss. I'm going with the Wings, if only because I think that the underlying numbers method provides a better measure of a team's true ability than does pythagorean expectation, even though there may or may not be an empirical basis for that viewpoint.

DET in 7.

CHI –VAN

The Canucks are a good team, but I can't help but get the sense that they're a tad overrated. I was browsing Hfboards the other day and I noticed that some 60% of the posters there have picked Vancouver to win the series. To be sure, some of that has to do with the fact that Canucks fans outnumber Hawks fans among HF users. Even so, I found the poll results interesting as the numbers suggest that Chicago is the better team. As posted above, the Hawks are about a 60% shot to win on the basis of adjusted winning percentage, and about a 70% shot if the underlying numbers are used.

The two teams were actually pretty close to one another in terms of regular season goal differential, but the Hawks were much, much better at outshooting. Chicago led the league with a shot ratio of 1.36 (awesome), whereas the Canucks were tenth at 1.05 (meh).

What interests me is how often a playoff team in the Hawks position has performed historically in terms of series wins and losses. That is to say, if two teams are facing one another in the playoffs, and one team has the better regular season shot ratio by a large margin (say, at least 0.2 better), but is only slightly better in terms of pythagorean expectation (say, no larger than 0.08), how often does that team end up winning?

Looking strictly at playoff results between 1993-94 and 2008-09, I found 32 series that met these criteria. I've arranged the series according to date in the excel document below. The headings may require some explanation. 'T1' denotes the team with the better shot and goal ratio, whereas 'T2' denotes their opponent. W% stands for adjusted winning percentage, and SR stands for shot ratio. The 'Results' column indicates which team won the series. 'W' indicates that the team with the better goal and shot ratio won the series, whereas 'L' indicates that the other team won. The bottom column shows the average adjusted winning percentage and shot ratio for the T1 and T2 teams, respectively. As it turns out, the T1 and T2 teams differed, on average, by about 0.03 in adjusted winning percentage and by about 0.3 in shot ratio, which, in both cases, is virtually identical to the gap separating the Hawks and Canucks.

All in all, the T1 team won 19 out of the 32 series, or 58%. That's hardly overwhelming and, to be honest, I would have expected that number to be higher. If the historical results are to given any weight at all, Chicago's chance of winning the series is probably closer to 60% rather than the 70% figure generated by the underlying numbers model.

In any event, the historical results are consistent with my general point that the Hawks ought to be the favorite here. The Canucks have a reasonable chance to win, but it's not somewhat that should be expected in the sense of being more likely than not.

CHI in 6.

PIT-MTL

This pick doesn't require too much deliberation. The Pens might be the best team in the conference, whereas the Habs are easily the weakest squad to advance. Pittsburgh is the heavy favorite regardless of whether the odds are determined through each team's pythagorean expectation or through the underlying numbers. That said, 29% ain't trivial and, as we observed last round, anything can happen over the course of a best-of-seven series.

PIT in 5.

BOS-PHI

I think that these two teams are relatively equal, but that the Bruins are slightly better. It's hard to pick against a team that's as good territorially at even strength as Boston is, even for a Habs fan such as yours truly. To add to that, Savard is expected to return for the series, and that should help them. I expect them to advance.

BOS in 6.

The Repeatability of Special Teams Performance

2010-04-27T20:10:00.000-07:00

In my post on playoff probabilities, one of the methods in which I calculated each team's expected winning percentage was on the basis of the underlying numbers.

Under this model, shot volume on the powerplay, shot prevention on the penalty kill, as well as penalty differential, were incorporated as determinants of special teams goal differential. However, neither shooting percentage on the powerplay nor save percentage on the penalty kill were used as predictors.

Initially, my intention was to include both variables within the model. However, after looking at the relationship between team powerplay shooting percentage in even numbered games and team powerplay shooting percentage in odd numbered games in the 09-10 regular season, I discovered that there was essentially no correlation. I then did the same thing for the 07-08 season, and the result was the same: no relationship.

I found this to be unusual, given that I had looked at the distribution of powerplay shooting percentage in the past and found that the team-to-team spread was somewhat broader than what one would expect if there was no skill component. Nevertheless, my exercise had revealed the absence of any split-half correlation, thus necessitating the exclusion of PP S% from the model.

(As mentioned above, I also excluded PK save percentage, even though I had not specifically examined its repeatability. This was somewhat unjustified given that, as discussed below, team PK SV% is somewhat repeatable. However, the regression is fairly strong and, even though I ought to have taken it into account, it's exclusion didn't affect things too greatly.)

In any event, my curious findings prompted the following question: To what degree is special teams performance repeatable?

Real Effects

Vic Ferrari had an excellent post about a year ago where he looked at the various components of team even strength performance -- specifically, shooting percentage, save percentage, and shot differential -- and determined the extent to which each component was repeatable. Specifically, his method involved looking at each team's shooting percentage, save percentage, and shot differential, all at EV with the score tied, in 38 randomly selected games from the 2008-09 season. He then looked the same variables over a separate 38 game sample, and determined the correlation between the two sets of games. The exercise was then repeated over 1000 simulations.

The rationale behind the exercise is a simple one -- as expressed by Vic, "if an element of nature is affected by something other than randomness, that it should sustain itself from one independent sample to another." Thus, if the observed correlation is significantly non-zero, it can be assumed that the variable is at least partly determined by factors other than luck. On the other hand, if the observed correlation is insignificantly different than zero, then fluctuations in the variable are assumed to be primarily luck driven.

I decided to apply a similar technique in order to determine the degree to which the components of special teams performance are governed by 'real effects.' Specifically, my methodology involved the following:

I obtained special teams data at the team level for each season from 2003-04 to 2009-10
Within each season, I looked at team performance on specials teams at the level of individual games
In particular, I looked at the following variables: powerplay shooting percentage, penalty kill save percentage, powerplay shot rate (shots for divided by time on ice), penalty kill shot rate (shots against divided by time on ice), and powerplay ratio (the ratio of powerplays drawn to powerplays conceded)
However, shooting rates were not examined for 2007-08, 2008-09, and 2009-10, as I was not able to obtain data on PP TOI and PK TOI for those seasons
Empty net goals were excluded when calculating shots and goals
For each team, I randomly selected 20 home games and 20 road games, combined the two sets of games, and looked at how that team performed within that sample with respect to the above stated variables
I then did the same thing for 40 other randomly selected games (again, consisting of 20 homes and 20 road games)
I then looked at the correlation between the two sets of games for each of the listed variables
I repeated the exercise 1000 times, for each of the six seasons

The results

I should note that the final highlighted column shows the averaged value for each variable.

As indicated by the table, both generating shots on the powerplay and preventing shots on the penalty kill appear to be largely ability driven measures. The same applies to drawing more powerplays than the opposition.

Not surprisingly, both PP S% and PK SV% are less ability driven than the other three variables. It's worth noting that PK SV% appears to be more reliable than PP S%. I presume that this can be attributed to the influence of the goaltender on PK SV%.

Corrected Playoff Probabilities

2010-04-14T14:12:00.001-07:00

Because I forgot to include EV goals when calculating each team's corsi with the score tied, I decided to re-run the UNDERLYING #'s simulation using the corrected probabilities.

The results aren't too different.

Expected Winning Percentage by Team

2010-04-14T02:59:00.000-07:00

In response to a question raised in the comments to my post on playoff probabilities, I figured that it would be useful if I posted each team's expected winning percentage according to the two described methods.

The teams are ranked according to pythagorean winning percentage.

EDIT:

I've altered the chart so as to include even strength goals in the calculation of Corsi with the score tied. The values don't change all that much -- in fact, hardly at all, but I figured that I'd post it if only for accuracy's sake.

Playoff Predictions

2010-04-13T21:18:00.000-07:00

S.J - COL

The deceptive nature of Colorado’s success this season has been well documented by some of the more statistically inclined members of the hockey blogosphere. As I presume that those reading are familiar with that fact, I won't go into any detail. The Sharks are the better team in virtually every facet of the game, save for perhaps goaltending. As with any series, an upset is always possible, but I think that a lot would have to go wrong for San Jose to lose.

S.J in 5.

CHI –NSH

There isn’t really a lot to be said about this series. I don’t think that the Predators are a bad team, but they have the worst goal differential among the playoff teams in the West. Chicago, on the other hand, is probably the best team in the entire league. They have the best goal ratio once schedule difficulty and empty netters are taken into account, and they were far and away the most dominant team in the league in terms of outshooting. I expect them to advance without too much difficulty.

CHI in 5.

VAN-L.A

I don’t find Vancouver to be all that impressive, but I think that they’re the right pick here. They have the better goal differential, the better shot ratio at EV with the score tied, the better goaltender, and they’ll be starting the series at home. The Kings are respectable and while I suspect that I’ll end up cheering for them here, I just can’t justify picking them in the result.

VAN in 7.

PHX-DET

I’ve taken quite a liking to Phoenix ever since I watched them smoke the Kings on the first Saturday of the season. Imagine my disappointment when I found out that the Red Wings finished 5th. Outside of Chicago, I don’t think that the Coyotes could have asked for a less favourable draw in the first round.

I’ve remarked in the past about how Phoenix has been one of the stronger teams in the league terms of outshooting at EV this year, which is impressive given where they were last season. However, Detroit’s numbers are even better in that respect. Additionally, Detroit’s underlying numbers have improved over the course of the season, whereas the reverse has been true for Phoenix. I’m not sure if that’s terribly relevant to each team’s chances, although it can’t be a good thing from the Coyotes’ perspective.

Finally, the Wings are clearly the better squad on special teams. There isn’t much of a difference between the two teams in terms of shot prevention on the penalty kill, but the Wings are much better at generating shots – not to mention goals – on the PP.

All in all, while I think that the Coyotes are largely legit, they’re clearly overmatched here.

DET in 6.

WSH – MTL

I don’t think that Washington is as strong as its goal differential would imply. However, even if that’s accounted for, they’re still the better team by a substantial margin. Neither club appears to have much of an advantage over the other on special teams, but the Habs get bombed in terms of shots at even strength whereas the Capitals are above average in that respect. The Capitals should dominate the play at even strength and, unless Halak can bail his team out, that should be the difference.

WSH in 5.

N.J – PHI

I agree with Sunny Mehta -- these two teams are reasonably close to one another in terms of ability, but the Devils have a clear advantage in goal. Whereas Brian Boucher has a career even strength save percentage of 0.910, the corresponding figure for Brodeur is 0.922. The true difference in ability is probably larger if one considers that the shot recorder in New Jersey undercounts and that Brodeur has generally been better post-lockout than pre-lockout. Ordinarily I try to refrain from basing a pick on goaltending alone, but when the teams are relatively evenly matched and the gap in goaltender ability is large, I think that it’s reasonable to do so.

N.J in 7.

BUF – BOS

Although the Sabres may have the better record and goal differential, the Bruins strike me as the better team here. The two teams exhibit similar profiles on special teams (good PK, poor PP), but Boston appear to be the better team at even strength. The Bruins were second to only Chicago in terms of outshooting at EV with the score tied, whereas the Sabres were around the league average in this regard. The Sabres actually had the better EV goal differential, but only by virtue of the percentages. I suspect that Boston’s territorial dominance will prevail as the percentages equalize from this point forward.

Some may argue that the Sabres have the better goaltender in Miller, but I’m not sure if that’s necessarily true. Miller finished the season at 0.928 at EV and 0.919 on the PK. His career values are 0.922 and 0.880, respectively. I think it’s reasonable to assume that his career values are more reflective of his ability than this season’s numbers. To the extent that Buffalo has the better goaltending, the difference probably isn’t large.

BOS in 6.

PIT – OTT

This matchup strikes me as the Eastern Conference analog of the Vancouver-LA series. I don’t think that the two teams are that far apart in terms of quality, but the Penguins have the advantage in pretty much every conceivable area that relates to winning – goal differential, outshooting (both in general and at EV), penalty differential, special teams and, as with the Canucks, the higher seed. Although I don’t necessarily think that the Senators will get blown out of the water, there’s simply no rational basis for picking them.

PIT in 6.

Playoff Probabilities

2010-04-13T20:28:00.000-07:00

In order to get a sense of each team's chances, I decided to run a couple simulations of the first round.

For the first set of simulations, I calculated each team's winning percentage on the basis of pythagorean expectation after correcting for schedule difficulty, empty netters and shootout goals. In the charts displayed down below, the probabilities determined on this basis can be found in top half of each individual chart (next to the cell titled 'PYTHAGOREAN').

In the second set of simulations, the methodology was somewhat more complicated. Without getting too specific, I computed each team's theoretical winning percentage on the basis of the following inputs:

Each team's corsi ratio with the score tied during the regular season (as a determinant of shots for and against at EV)
The career EV save percentage of each team's starting goalie (as a determinant of each team's EV save percentage and the shooting percentage of its opponent). Each goalie's career save percentage was regressed to the league average based on the number of career EV shots faced to date (for goalies facing fewer shots, the regression was stronger; for goalies facing more shots, the regression was weaker)
Each team's tendency to draw and surrender powerplays during the regular season (as a determinant of time spent on the powerplay and penalty kill)
Each team's shot rate on the powerplay and shot rate against on the penalty kill during the regular season (as a determinant of powerplay goals for and against)

The probabilities associated with these inputs can be found in the bottom half of each individual chart (next to the cell titled 'UNDERLYING #'s').

For each set of simulations, I simulated the first round 10 000 times. Home advantage was taken into account for both sets of simulations. The results are displayed below, with the Eastern Conference following the West.

The row next to each of the four numbers shows each team's probability of winning the series in that many games. The highlighted row shows each team's chance of winning the series.

By way of example, consider the San Jose Colorado series. If each team's winning percentage is computed on the basis of pythagorean expectation, the Sharks have a 11.3% chance of winning the series in a sweep and a 68.5% of winning the series.

If, on the other hand, the second method is applied, the Sharks have a 15.5% of winning in a sweep and a 77.9% chance of winning overall.

Overall, the two methods yield comparable results, except in the case of the DET-PHX and BUF-BOS matchups. The first method suggests that the Coyotes should win slightly over half the time, whereas the second indicates that the Wings are the clear favorite.

The discrepancy is even greater for the Sabres and Bruins matchup. According to the PYTHAGOREAN method, the Sabres should win some two-thirds of the time, yet the second method produces the opposite result.

The Leafs, Scoring Chances and Corsi

2010-04-09T23:23:00.000-07:00

I recently got around to updating my database for the 09-10 season and, in looking over the EV stats for each team, I noticed that the Leafs continue to have one of the best corsi ratios in the league at EV with the score tied.

I think that this is unusual for a couple reasons.

For one, the 08-09 Leafs were a poor team according to this metric. While last year's squad outshot the opposition in a general sense, their corsi ratio with the score tied was 0.94, good for 21st in the league. Thus, if one considers corsi ratio with the score tied to be a crude measure of a team's ability at even strength, the Leafs would appear to be one of the most improved teams in the NHL (looking strictly at EV play, of course).

Secondly, despite soundly outshooting the opposition, the Leafs have one of the worst EV goal differentials in the league. I haven't filtered out empty netters yet, but only the Lightning, Oilers, and Jackets are worse than Toronto in terms of goal differential at even strength. This despite directing some 500 more shots towards the other team's net at EV than their opponent over the course of the season. The effect isn't as extreme when the score is tied -- they're only -7 -- but the unusual profile remains.

The tendency to outshoot without outscoring has led some to question whether the Leafs do, in fact, outplay the opposition at even strength, or whether the shot numbers are deceiving.

One way to settle the issue is to look at the Leafs scoring chance numbers. If Toronto's scoring chance ratio broadly parallels its shot ratio at EV, then that ought to dispel notions that the Leafs don't legitimately outplay the opposition, or that they shoot from everywhere.

Slava Duris, whose blog can be found here, has been recording scoring chances for Toronto over the course of the season. To date, he's posted 53 of the games for which he's recorded chances.
Taking those 53 games in particular, I looked at how many even strength scoring chances the Leafs had with the score tied, and how many their opponents had. I then determined how many shots the Leafs directed towards the opposition's net -- again, only at EV with the score tied -- in those same 53 games, and did the same for their opponents. The raw data can be viewed below.

Overall, there were 474 even strength scoring chances with the score tied in the 53 games sampled. Of those 474 chances, Leafs generated 252, whereas the opposition generated the remaining 222. Thus, the Leafs scoring chance ratio with the score tied was 1.14.

In terms of corsi with the score tied, the Leafs directed 1008 shots towards the opposition's goal, and had 915 directed toward their own, thus giving them a corsi ratio of 1.10.

In other words, the Leafs actually did better in terms of scoring chances than in terms of corsi over the 53 games examined.

Granted, this doesn't allow one to conclude that the Leafs are a better team than their corsi ratio would suggest. For example, if we assume that Toronto's underlying scoring chance ratio is identical to its corsi ratio (1.10), then the probability of it generating at least 252 chances out of 474 randomly selected chances is 0.376 (or, if one prefers, the probability of it having a corsi ratio at least as good as 1.14 in a sample of 474 chances). In other words, the two values are not significantly different from each other.

Nevertheless, it would appear that the Leafs have managed to outplay the opposition at even strength over the course of the season, their rotten goal differential notwithstanding.

Shot Recording Bias: Part n

2010-03-09T22:29:00.000-08:00

This post is the third post that I've made on the subject. For a more detailed discussion of the methodology and reasoning applied, please refer to my first two posts ([1] [2]).

After looking over my previous post on the subject -- the one examining Florida and New Jersey specifically, I realized that I'd made an error in inputting the data for the 2007-08 and 2008-09 seasons. Here are the corrected charts. It may be necessary to enlarge them in order to properly view the information.

New Jersey

In my original post, I concluded that the shot recorder in New Jersey undercounts shots on goal. The corrected data does nothing but affirm that conclusion.

The only major difference is that the chart contained in my original post incorrectly showed that there were more shots counted in New Jersey home games than New Jersey road games in both 2007-08 and 2008-09. This led me to suspect that the bias may no longer persist, notwithstanding the fact that the shooting percentage in New Jersey home games was higher than the shooting percentage in New Jersey road games during the two seasons in question.

However, as is evident from the corrected chart, there were actually fewer shots in Devils home games for both 2007-08 and 2008-09. This is consistent with the data from previous seasons, the corresponding shooting percentage data for 2007-08 and 2008-09, as well as the undercounting hypothesis.

Florida

The corrected data for Florida, however, does serve to affect my conclusions somewhat. While the home-road shot gap for 2007-08 and 2008-09 is similar in magnitude to that observed in the previous three seasons, the shooting percentage data for those two seasons suggests that an overcounting bias may have emerged. However, I'm reluctant to assert the existence of a bias on the basis of two seasons worth of data alone, especially considering that the shot gap has not increased materially.

Other Arena Recording Biases

Given that we're on the subject, I figured I'd take this opportunity to explore the issue of shot recording bias more generally.

The above tables show each team's home-road splits for shots on goal and shooting percentage from 2003-04 to 2008-09. The first table shows the 15 teams that had the greatest number of recorded shots on goal in home games relative to road games, and ranks those teams in descending order. The second table basically shows the reverse.

The first highlighted column in each table displays the number of shots recorded in home games, minus the number of shots recorded in road games.

The second highlighted column displays road game shooting percentage minus home game shooting percentage.

Where there exists a significant positive value in both columns, an overrecording bias is implied.

Conversely, where both values are significantly negative, an underrecording bias is implied.

Looking at the two tables together, it would appear that the shot recorders in Colorado, Ottawa, Nashville and Boston overcount shots to some degree, whereas the recorders in Minnesota, Dallas, St. Louis and Vancouver are seemingly guilty of undercounting.

Of course, a more rigorous analysis is required before any conclusions can be reached.

Colorado

Ottawa

Nashville

Boston

Minnesota

Dallas

St.Louis

Vancouver

The above tables break down the home-road shot and shooting percentage splits by game state and season for the eight listed teams. I'm not sure if these tables add all that much on top of the aggregated data presented earlier, although I think that their inclusion is valuable for two reasons.

For one, the home games of some teams might have featured more special teams play over the period in question, even by sheer chance alone. As both shot rate and shooting percentage increase significantly on special teams relative to even strength, this factor can potentially distort the overall data.

Secondly, it's important to break down the data by season in order to see if any of the apparent recording biases are time-limited -- that is, present in some seasons but not others. For example, it's conceivable that some teams have employed more than one arena statistician at different points over the last seven years.

As for the tables themselves, one thing that strikes me as unusual is that the home-road shooting percentage gap for the Wild is quite large on special teams yet virtually non-existent at even strength (indeed, not even in the predicted direction). I can't think of any reason why this would be so, although it leads me suspect that there may be no bias. The home-road shot gap is large, but that could be a product of the Wild playing more conservatively at home.

Looking at the data collectively, there's overwhelming evidence of a recording bias in Dallas and Colorado, strong evidence of one in Vancouver and Ottawa, and moderate evidence of bias in the other four locations.

The above table requires some description. It essentially shows the 95% and 99% confidence intervals for each team's home shooting percentage (that is, the shooting percentage by both teams) during the period in question (2003-04 to 2008-09). The intervals were generated by assuming that each team had the same underlying shooting percentage on the road as at home, and that shots were recorded accurately irrespective of game location.

The final column shows what the shooting percentage in each team's home games actually was over that timeframe. Values colored light blue fall outside the 95% confidence interval. Highlighted values fall outside both confidence intervals. White colored values are within both confidence intervals.

A specific example will be illustrative. The Stars shot 0.081 at EV from 2003-04 to 2008-09. Using that value as their underlying home shooting percentage, their home shooting percentage would be expected to fall within 0.075 and 0.087 95% of the time, and between 0.073 and 0.089 99% of the time. The observed value was 0.089, which strongly implies that shots were undercounted in Dallas during this period.

Of course, assuming that each team's actual road shooting percentage is roughly equivalent to its underlying road shooting percentage is somewhat questionable. For example, if the underlying shooting percentage in a team's road games is 0.092, the 95% confidence interval after 12000 shots -- the average number of shots in road games for teams during the 5 year period -- is roughly between 0.087 and 0.098.

That being the case, the above table represents a slightly different approach. The left-hand column titled 'DIFF' shows the absolute difference in home and road shooting percentage for each team over the entire sample, for both EV and overall. The right-hand column titled 'PROB' displays the probability of a difference that large or larger occurring by change alone (over 100 simulations).

So, by way of example, the difference between the EV shooting percentage in Dallas road games and Dallas home games was 0.008. The probability of a difference at least that large arising from chance alone is 5%. In other words, it probably isn't the result of chance, but, rather, because shots have been undercounted in Dallas over that period.

Conclusions

So, what can we conclude from all that?

The shot recorder in New Jersey undercounts (this was addressed in a previous post)
The shot recorder in Dallas undercounts
The shot recorder in Colorado overcounts
The shot recorder in Vancouver almost certainly undercounts
The shot recorder in Ottawa probably overcounts
The shot recorders in Boston and Nashville may overcount, but the evidence is not conclusive
The shot recorders in St. Louis and Minnesota may undercount, but the evidence is not conclusive

The Relationship Between Outshooting and Outscoring over Time

2010-02-20T17:55:00.000-08:00

Derek Zona from coppernblue had a great post last month that examined the relationship between outshooting and outscoring at even strength over time. Specifically, he looked at aggregated EV goal and shot ratios for each team over the last three seasons as a whole (2007-08, 2008-09 and 2009-10, I presume). He found that the teams with the best EV goal ratios during this period were overwhelmingly teams that outshot the opposition at EV.

I think that his point is an important one. While the relationship between outshooting and outscoring may not be apparent over brief periods, the teams that succeed at even strength over the long run are those that spend more time in the opposition's end than their own.

Whereas Derek examined the strength of this relationship over the last three seasons taken together, I thought it would be interesting to look at the how this relationship varies over the course of an individual season.

The above table shows the correlation between EV goal ratio and Corsi ratio at the team level over certain game segments. The first bar shows the correlation between these variables over games 1-100 (-0.09). The second bar shows the same for games 1-200. The last bar shows the correlation over the entire season (games 1-1230).

It's apparent that the correlation between EV goal ratio and Corsi ratio increases over the course of the regular season. The increase is more or less linear over the first 1000 games, at which point it reaches asymptote.

The increase is even more pronounced if one looks at the relationship in terms of overall variance (r^2), rather than as a correlation. While Corsi ratio only accounts for roughly 9-15% of the variance in EV goal ratio over the first several hundred games, the r^2 value for the entire sample is in the range of 35-40%.

I've also included a chart that shows the same data for the 2008-09 season. While the increase isn't as sharp as that observed in 2007-08, the overall message is the same: as the season moves forward, the relationship between outshooting and outscoring at EV grows stronger.

Putting the Phoenix Turnaround into Context

2010-02-20T03:46:00.000-08:00

I've written before about how much better Phoenix's EV numbers are this year as compared to last season. The Coyotes actually had the worst Corsi ratio in the league in 2007-08 at 0.83. They're currently sitting at 1.09, which is a pretty marked improvement considering that team Corsi ratios tend to be relatively invariant across seasons.

I was interested to see how this improvement ranks among team season-pairings in the post-lockout era. Looking at data from 2003-04 to 2008-09, I compared each team's EV shot data in a given season to the same data from the previous season. For seasons 2007-08 and 2008-09, I looked at each team's Corsi ratio. For 2003-04, 2005-06 and 2006-07, I looked at each team's EV Shot ratio. (While there exists data on blocked and missed shots from this period, it was much easier to simply scrape the shot numbers). Thus, it is important to keep in mind that for the 2006-07/2007-08 season-pairings, two different metrics are being compared (EV shot ratio for 2006-07, and Corsi ratio for 2007-08).

During this period, there were 120 season-pairings in total. For each pairing, I subtracted each team's Corsi/EV shot ratio in one season from that same team's Corsi/EV shot ratio in the following season, and ranked the differences in descending order. Presented below is a table showing the ten largest differences.

Turnarounds similar in magnitude to that exhibited by this year's Coyotes are a relative rarity. In the post-lockout period, only the 2007-08 Capitals and 2006-07 Leafs have shown a larger improvement in terms of EV shot metrics than the 2009-10 Coyotes.

The 2007-08 Capitals showed the largest swing. Although much of the credit for Washington's improvement has been attributed to the coaching change, the data suggests that the praise for Boudreau is misplaced. While it's true that the team struggled in terms of results early on, they were an outshooting team from opening day forward.

For the record, the coaching replacement occurred between games 20 and 21.

The Capitals weren't the only team to display a large improvement at EV in 2007-08. The Bruins also increased their Corsi ratio by a sizable margin. It's worth mentioning, however, that the difference in underlying play is probably overstated -- there's evidence that the Boston shot recorder is biased against the Bruins in terms of recording shots on goal, but impartial when it comes to recording shots directed at the net. (Keep in mind that the data for 2006-07 strictly includes EV shots on goal, whereas for 2007-08 all shots directed at the net at EV are included).

Even so, the Bruins were a much better team at EV in 2007-08 than in 2006-07. They also appear to have improved as the season progressed. As is typical of Julien-coached teams, they looked to have played to the score to a strong degree. (Note that the Bruins outscored the opposition at EV in the first half of the year, and were themselves outscored in the second half).

The 2006-07 and 2005-06 Leafs present an interesting contrast. While the two teams were fairly similar in terms of roster composition, the 2006-07 team was a substantially better team at EV. I tend to attribute this to the coaching change from Quinn to Maurice -- whereas Maurice's teams have historically been pretty good at outshooting the opposition at EV, Quinn's teams have not.

Of course, the Leafs' improvement at EV was nearly entirely offset by poorer special teams performance, which explains why the two teams finished at about the same place in the standings.

Finally, the Panthers brief post lockout improvement warrants some attention. The 2005-06 Panthers were actually a relatively decent team at EV -- they marginally outshot the opposition and fared even better in terms of goal differential (158 GF, 143 GA), largely on account of their goaltending. However, they were absolutely murdered on special teams (-35), and they missed the playoffs as a result.

The 2006-07 Panthers were even better at outshooting at EV -- their EV shot ratio of 1.17 was 3rd best in the league that year, behind only Detroit and Toronto. However, their special teams were again quite poor and, when combined with below average goaltending, they missed the playoffs yet again.

Interestingly, the Panthers would revert to their pre-lockout ways in the two subsequent seasons. Both the 2007-08 and 2008-08 Panthers were decidedly below average with respect to their EV Corsi ratio (0.94 and 0.87, respectively). I'm not quite sure as to the cause of the dropoff, although it's probably something worth investigating in the future.

EDIT: All statistical figures quoted do not include empty net goals.

Scoring Chances for Game Number 20436 : Wild @ Coyotes

2010-01-04T16:46:00.000-08:00

Scoring Chances for NHL Game Number 20436

Team	Period	Time	Note	MIN						Opponent
PHX	1	15:51		3	6	9	14	32	36	4	11	16	19	30	55	5v5
PHX	1	13:29		9	15	20	32	34	55	4	29	30	34	38	55	5v5
PHX	1	5:25		5	16	32	51	55		3	15	17	19	30	33	4v5
PHX	1	2:18		3	6	14	15	16	32	2	4	14	19	20	30	5v5
MIN	2	18:51		11	25	32	34	51	55	2	8	15	18	30	88	5v5
MIN	2	18:37		11	25	32	34	51	55	2	8	15	18	30	88	5v5
PHX	2	17:39		3	6	9	15	20	32	4	11	16	17	30	55	5v5
PHX	2	17:32		3	6	14	16	25	32	4	11	16	17	30	55	5v5
PHX	2	15:28		3	6	9	15	20	32	2	14	18	19	30	38	5v5
PHX	2	14:39		5	11	25	32	34	51	3	14	19	20	30	33	5v5
PHX	2	14:24		5	11	25	32	34	51	3	14	19	20	30	33	5v5
MIN	2	14:01		3	9	14	15	20	32	4	30	34	38	55		5v4
MIN	2	13:37		5	11	14	25	32	48	11	18	29	30	33		5v4
MIN	2	12:14		9	15	20	32	34	55	4	11	15	17	30	55	5v5
PHX	2	11:16		9	15	20	32	34	55	4	11	15	17	30	55	5v5
MIN	2	10:29		5	11	14	16	26	32	3	8	15	30	33	88	5v5
MIN	2	10:13		5	14	16	26	32	36	2	18	29	30	34	38	5v5
PHX	2	9:30	Goal	11	25	32	34	51	55	3	8	15	30	33	88	5v5
PHX	2	8:46	Goal	5	6	12	21	32	48	3	14	19	30	33	38	5v5
MIN	2	7:04		3	9	12	32	55		3	11	17	30	33		4v4
PHX	2	5:50		6	11	16	26	32		3	8	15	19	30	33	4v5
PHX	2	5:34		6	11	16	20	26	32	3	8	15	30	33	88	5v5
PHX	2	5:33		6	11	16	20	26	32	3	8	15	30	33	88	5v5
MIN	2	4:23		3	5	12	21	32	48	2	18	29	30	34	38	5v5
PHX	2	18:01		5	9	15	20	26	32	4	11	16	17	30	55	5v5
PHX	3	14:49		3	6	14	16	32	48	4	8	15	30	55	88	5v5
MIN	3	11:40		3	9	14	15	20	32	11	18	29	30	33		5v4
PHX	3	10:06		6	12	16	32	34	51	4	14	19	20	30	55	5v5
PHX	3	5:25		14	16	32	34	48	55	3	18	29	30	34	38	5v5
PHX	3	0:38		3	9	14	15	20	48	4	11	16	17	30	55	5v5

#	Player	EV			PP			SH
3	M. ZIDLICKY	16:03	2	7	4:19	2	0	3:52	0	0
5	K. JOHNSSON	18:06	3	4	3:34	1	0	1:45	0	1
6	G. ZANON	16:01	0	10	0:56	0	0	4:09	0	1
9	M. KOIVU	14:10	2	7	4:41	2	0	1:45	0	0
11	O. NOLAN	9:53	3	5	3:45	1	0	1:39	0	1
12	C. KOBASEW	12:43	2	2	0:31	0	0	0:21	0	0
14	M. HAVLAT	10:28	2	6	6:25	3	0	0:17	0	0
15	A. BRUNETTE	12:34	1	7	4:18	2	0	0:00	0	0
16	A. EBBETT	9:34	2	7	0:25	0	0	2:33	0	2
20	A. MIETTINEN	13:45	1	8	4:18	2	0	1:23	0	0
21	K. BRODZIAK	11:23	1	1	0:22	0	0	1:53	0	0
25	E. BELANGER	11:06	2	4	3:39	1	0	1:44	0	0
26	J. SIFERS	12:17	2	3	0:00	0	0	0:16	0	1
32	N. BACKSTROM	44:02	7	17	8:34	3	0	6:35	0	2
34	S. HNIDY	12:43	3	7	1:49	0	0	0:42	0	0
36	J. SCOTT	4:13	1	1	0:00	0	0	0:00	0	0
48	G. LATENDRESSE	12:03	1	4	3:43	1	0	0:07	0	0
51	J. SHEPPARD	10:50	2	4	0:03	0	0	1:29	0	1
55	N. SCHULTZ	13:46	4	4	0:02	0	0	2:26	0	1

Period	Totals		EV		PP		5v3 PP		SH		5v3 SH
1	0	4	0	3	0	0	0	0	0	1	0	0
2	9	12	7	11	2	0	0	0	0	1	0	0
3	1	4	0	4	1	0	0	0	0	0	0	0
4	0	0	0	0	0	0	0	0	0	0	0	0
Totals	10	20	7	18	3	0	0	0	0	2	0	0

Scoring Chances for Game Number 20589 : Wild @ Ducks

2010-01-04T14:34:00.000-08:00

Scoring Chances for NHL Game Number 20589

Team	Period	Time	Note	MIN						Opponent
ANA	1	18:50		5	9	15	20	36	37	1	9	11	27	34	42	5v5
ANA	1	16:08		5	6	21	24	37	51	1	4	10	20	28	53	5v5
MIN	1	14:27		5	9	15	20	36	37	1	13	22	27	34	50	5v5
ANA	1	12:52	Goal	3	6	21	24	37	51	1	9	11	27	34	42	5v5
MIN	1	9:38		9	15	20	34	37	55	1	9	11	19	21	42	5v5
MIN	1	5:28		6	11	22	25	34	37	1	4	22	39	50	53	5v5
MIN	1	4:20		5	9	15	20	36	37	1	4	28	39	50	53	5v5
MIN	1	4:19	Goal	5	9	15	20	36	37	1	4	28	39	50	53	5v5
ANA	1	3:44	Goal	3	6	14	16	37	48	1	9	11	27	34	42	5v5
ANA	2	10:52		3	6	9	15	20	37	1	9	11	27	34	42	5v5
ANA	2	1:51		5	9	37	55			1	9	10	11	19	27	3v5
ANA	2	1:29		3	6	9	37			1	9	10	11	19	27	3v5
ANA	2	1:17	Goal	3	6	9	25	37		1	9	10	11	19	27	4v5
MIN	3	13:25		5	6	15	16	20	37	1	9	11	27	34	42	5v5
MIN	3	11:08		5	15	16	20	36	37	1	9	11	19	21	42	5v5
MIN	3	6:53	Goal	5	9	14	15	37	48	1	17	20	27	34		5v4
MIN	3	5:27		5	6	16	20	37	48	1	4	10	20	28	53	5v5
MIN	3	0:49		3	9	14	15	20	34	1	4	11	21	22	27	5v5
MIN	3	0:48		3	9	14	15	20	34	1	4	11	21	22	27	5v5
ANA	3	0:09	Goal	3	9	14	15	20	25	1	11	22	27	34		5v4

#	Player	EV			PP			SH
3	M. ZIDLICKY	19:02	2	3	3:32	0	1	1:29	0	1
5	K. JOHNSSON	19:34	6	2	2:37	1	0	1:20	0	0
6	G. ZANON	20:32	3	4	0:00	0	0	1:29	0	1
9	M. KOIVU	13:01	6	2	3:21	1	1	0:53	0	1
11	O. NOLAN	13:44	1	0	2:04	0	0	0:22	0	0
14	M. HAVLAT	15:42	2	1	3:12	1	1	0:05	0	0
15	A. BRUNETTE	13:58	8	2	3:21	1	1	0:00	0	0
16	A. EBBETT	15:36	3	1	1:07	0	0	0:35	0	0
20	A. MIETTINEN	14:52	9	2	3:15	0	1	0:00	0	0
21	K. BRODZIAK	9:19	0	2	0:24	0	0	1:45	0	0
22	C. CLUTTERBUCK	13:12	1	0	0:14	0	0	1:15	0	0
24	D. BOOGAARD	5:32	0	2	0:10	0	0	0:00	0	0
25	E. BELANGER	13:06	1	0	2:42	0	1	0:43	0	1
34	S. HNIDY	14:25	4	0	0:47	0	0	0:00	0	0
36	J. SCOTT	6:54	4	1	0:10	0	0	0:00	0	0
37	J. HARDING	49:38	8	5	4:56	1	0	2:49	0	1
48	G. LATENDRESSE	15:05	1	1	2:10	1	0	0:00	0	0
51	J. SHEPPARD	5:47	0	2	0:24	0	0	0:00	0	0
55	N. SCHULTZ	19:49	1	0	0:28	0	0	1:20	0	0

Period	Totals		EV		PP		5v3 PP		SH		5v3 SH
1	5	4	5	4	0	0	0	0	0	0	0	0
2	0	4	0	1	0	0	0	0	0	1	0	2
3	6	1	5	0	1	1	0	0	0	0	0	0
4	0	0	0	0	0	0	0	0	0	0	0	0
Totals	11	9	10	5	1	1	0	0	0	1	0	2

Shot Recording Bias: Florida and New Jersey

2009-12-31T16:04:00.000-08:00

Earlier this year, I made a post that examined whether certain NHL arenas systematically undercount or overcount shots on goal. My methodology involved comparing each team's seasonal home and road splits from 1995 until 2008 in terms of shots on goal . More particularly, the total number of shots taken by both teams in a given team's road games was compared to the total number of shots taken by both teams in that same team's home games.

Where the home-road split revealed a discrepancy in recorded shots, I then looked at the shooting percentage data to determine whether there was, in fact, a recording bias. I reasoned that if a discrepancy was due to bias, rather than randomness or other factors, there ought to a concomitant increase (in the case of undercounting) or decrease (in the case of overcounting) in the shooting percentage of both teams in games played in the arena in question.

Since that time, others, such as Sunny Mehta, Vic Ferrari, Chris Boersma and Tom Awad, have also examined the issue through work of their own, all of which I would recommend reading.

Two of the arenas that I suspected might be overcounting shots were Bank Atlantic Center in Sunrise, the home of the Panthers, as well as Continental Airlines Arena (and, perhaps, the Prudential Center as well) in New Jersey. While the data on shooting percentage suggested that shots were likely undercounted in New Jersey, the same was not true of Florida.

The purpose of this post is to take a somewhat more refined look at the topic so as to properly determine the existence of bias. While my initial post looked at overall shot totals and overall shooting percentage, it failed to consider the influence of specific game states, such as special teams play and the playing to the score effect. As both of these factors are known to influence shots on goal as well as shooting and save percentage, merely examining the data in aggregate can be more misleading than illuminating. In order to mitigate these concerns, the data below has been broken down according to game situation.

Firstly, the data for Florida. Presented below is a table comparing the number of shots taken by both teams in Florida road games versus Florida home games, broken down by game state and season. Shots that resulted in an empty net goal have been excluded. This essentially confirms what was already known -- that more shots are recorded in Sunrise than elsewhere. Interestingly, the putative bias appears to be confined to even strength, with no effect on special teams.

I've also prepared a similar table that compares the shooting percentage (again, for both teams) in Florida road and home games. As with the previous table, the percentages do not include empty net goals.

Looking at the data, it's difficult to argue for any sort of shot recording bias. The aggregate shooting percentage in Florida home games is identical to the aggregate shooting percentage in Florida road games. The same is essentially true at even strength with the score tied. If shots were, in fact, being overcounted, then one would expect to to observe a lower shooting percentage in Florida home games. But such is not the case.

In the comment thread of this post made by the Contrarian Goaltender, Vic Ferrari surmised that some of the apparent shot recording biases are not biases at all, and that some arenas really do consistently feature more or fewer shots than average, perhaps due to team style, strategy or some other like factor. I think that's probably the best explanation in this case. The Panthers, for whatever reason, seem to play a more exciting style of hockey at home, which serves to increase the shots on goal numbers while leaving the shooting percentage data unaffected. This is consistent with the shot discrepancy being restricted to even strength.

The data for New Jersey tells a different story. Unlike in Florida, New Jersey home games have featured a deficit of shots, rather than an excess.

More significantly, however, this deficit in shots has been accompanied by an increase in the shooting percentage in Devil home games. This implies that the deficit is due to recording bias, rather than some other factor.

Looking solely at even strength play, the shooting percentage in Devil road games from 2003-04 to 2008-09 has been nearly an entire percentage point lower than the shooting percentage in Devils home games during the same period. While the difference may not seem large, it is greater than what one would expect to observe through chance alone. I've included a separate table below that shows a range of expected shooting percentage values, expressed in the form of confidence intervals, for both EV play with the score tied as well as for EV play in general.

This table shows the range in values where one would expect the overall shooting percentage for New Jersey home games to be found, during the period under review (2003-04 to 2008-09), if it is assumed that:

There is no shot recording bias
The 'true' shooting percentage in Devils home games is equivalent to that observed in Devils road games.

As a specific example, consider the Devils home-road splits at EV. The Devils and their opponents had a combined EV shooting percentage of 0.072 in Devils road games played between 2003-04 and last season. Thus, it is assumed that the underlying shooting percentage in Devils home games is 0.072. Making the further assumption that shots are recorded accurately in New Jersey, the table shows the range in the 'expected' shooting percentage for Devils home games. So, for example, if the above assumptions are true, one would expect to see the shooting percentage in Devils home games fall between 0.067 and 0.0777 95% of the time, and between 0.0654 and 0.0795 99% of the time. The observed value was 0.081, which lies outside both confidence intervals.

One final comment: some will have noticed that more shots were recorded in New Jersey home games than road games for both 2007-08 and 2008-09. I take this to mean that the shot recording bias is likely no longer in existence. While it is true that the shooting percentage in Devils home games continues to be higher than in Devils road games, the difference is probably meaningless in the absence of an actual difference in recorded shots. Perhaps the switch to a different arena was accompanied by a change in shot recorders.

Scoring Chances for Game Number 20262 : Wild @ Capitals

2009-12-26T12:48:00.000-08:00

Scoring Chances for NHL Game Number 20262

Team	Period	Time	Note	MIN						Opponent
MIN	1	18:10		8	21	22	36	37	67	2	4	16	17	40	85	5v5
MIN	1	13:29		3	6	11	14	25	37	3	9	21	28	40	89	5v5
WSH	1	5:30		3	6	9	25	37		9	14	19	22	40	52	4v5
WSH	1	5:14		3	6	9	25	37		9	14	19	22	40	52	4v5
WSH	1	5:00		3	6	9	25	37		9	14	19	22	40	52	4v5
WSH	1	3:38		3	6	14	25	37		2	3	17	21	28	40	4v5
WSH	1	3:37		3	6	14	25	37	55	2	3	17	21	28	40	5v5
WSH	1	3:29		3	6	11	14	25	37	3	10	39	40	53	89	5v5
MIN	1	0:09		3	8	9	11	14	37	3	39	40	53			5v3
MIN	2	18:29	Goal	6	8	21	22	37	67	9	17	21	26	40	52	5v5
WSH	2	17:03		5	11	14	37	51	55	3	9	21	28	40	89	5v5
WSH	2	14:58		6	8	9	21	37		9	17	21	28	40	52	4v5
WSH	2	14:21	Goal	5	22	25	37	55		9	14	21	28	40	52	4v5
MIN	2	13:41		3	6	11	14	37	51	2	4	14	16	19	40	5v5
WSH	2	13:05		8	11	14	36	37	51	2	4	10	39	40	53	5v5
MIN	2	12:49		5	9	15	20	37	55	3	9	21	28	40	89	5v5
WSH	2	3:50		3	6	9	20	37		3	14	19	28	40	52	4v5
WSH	2	3:07		8	11	14	25	36	37	3	16	17	21	40	89	5v5
WSH	2	0:57		6	8	9	20	37	67	2	4	14	17	19	40	5v5
WSH	2	0:26		3	6	20	25	37	67	9	21	26	28	40	52	5v5
WSH	3	18:00	Goal	8	21	24	36	37	38	2	4	16	40	53	85	5v5
MIN	3	15:29		8	21	22	36	37	67	2	4	16	39	40	53	5v5
MIN	3	15:05		3	6	9	15	20	37	3	16	40	53	85	89	5v5
WSH	3	14:10		5	11	14	25	37	55	2	4	9	21	28	40	5v5
WSH	3	9:36		8	15	20	21	36	37	3	10	14	19	40	89	5v5
MIN	3	8:38		3	6	11	14	37	51	2	4	17	21	40	85	5v5
MIN	3	6:39		3	14	21	36	37	51	3	10	39	40	53	89	5v5
WSH	3	5:36		5	8	9	11	15	37	9	21	26	28	40	52	5v5
WSH	3	4:16		8	11	14	37	51	55	3	10	39	40	53	89	5v5

#	Player	EV			PP			SH
3	M. ZIDLICKY	16:46	5	3	3:16	0	0	3:00	0	5
5	K. JOHNSSON	19:52	1	3	2:58	0	0	1:14	0	1
6	G. ZANON	20:11	5	4	0:01	0	0	3:43	0	6
8	B. BURNS	16:27	3	7	2:32	0	0	1:43	0	1
9	M. KOIVU	14:07	2	2	2:30	0	0	2:49	0	5
11	O. NOLAN	16:24	3	7	2:53	0	0	0:39	0	0
14	M. HAVLAT	16:53	4	7	2:37	0	0	0:12	0	1
15	A. BRUNETTE	14:14	2	2	2:08	0	0	0:00	0	0
20	A. MIETTINEN	14:12	2	3	2:24	0	0	2:13	0	1
21	K. BRODZIAK	11:51	4	2	0:01	0	0	1:14	0	1
22	C. CLUTTERBUCK	12:48	3	0	0:01	0	0	0:51	0	1
24	D. BOOGAARD	5:30	0	1	0:00	0	0	0:00	0	0
25	E. BELANGER	12:01	1	5	2:31	0	0	1:56	0	5
36	J. SCOTT	8:56	3	4	0:00	0	0	0:00	0	0
37	J. HARDING	49:07	9	12	5:02	0	0	4:57	0	7
38	R. EARL	5:21	0	1	0:00	0	0	0:00	0	0
51	J. SHEPPARD	12:35	3	3	0:00	0	0	0:00	0	0
55	N. SCHULTZ	17:04	1	4	1:17	0	0	0:14	0	1
67	B. POULIOT	12:53	3	2	0:01	0	0	0:00	0	0

Period	Totals		EV		PP		5v3 PP		SH		5v3 SH
1	3	6	2	2	0	0	1	0	0	4	0	0
2	3	8	3	5	0	0	0	0	0	3	0	0
3	4	5	4	5	0	0	0	0	0	0	0	0
4	0	0	0	0	0	0	0	0	0	0	0	0
Totals	10	19	9	12	0	0	1	0	0	7	0	0