The Percentages Revisited: 5-on-4 Shooting Percentage

A while back, I wrote about the effect of randomness on even strength* shooting percentage. For those who didn't have an opportunity to read that post, I'll briefly summarize the findings:


1. It would appear that a large portion of the inter-team variation in EV shooting percentage can be accounted for by random variation.

2. The spread among NHL teams is very slightly broader than what would be expected by chance alone. Therefore, it would appear that teams do in fact exert some influence on their EV shooting percentage.

* I actually only looked at 5-on-5 shooting percentage. I assume that the results are generalizable to even strength play as a whole, although that may not be the case.

In making my playoff predictions this year, I looked very closely at each team's shot rate (both SF and SA) in each of the main game situations (that is, 5-on-5, 5-on-4, 4-on-5). I also looked at how often each team had played in each game situation over the course the season. My method of determining the 'better' team basically revolved entirely around these two factors.

My method of evaluation didn't really accord much weight to the percentages, regardless of game state. I did this under the -- somewhat faulty -- assumption that most of the inter-team variation in the percentages is due to randomness. If true, there wouldn't be much point in taking the percentages into account when attempting to predict future results.

As it happens, that really isn't true at all. It appears to largely be true in terms of EV shooting percentage. However, this finding isn't necessarily generalizable to other game states. For one, it doesn't seem to be case for EV save percentage. More on that later.

It also doesn't seem to apply to 5-on-4 shooting percentage. While I began my analysis under the expectation that the majority of the inter-team variation in 5-on-4 shooting percentage could be explained through randomness, that doesn't appear to be true.

My methodology was basically identical to that used in my analysis of 5-on-5 shooting percentage, with one obvious difference -- instead of looking at 5-on-5 play, my focus this time was on 5-on-4 play. Here's a quick explanation of my method.

Firstly, I looked at how many shots each team took at 5-on-4 during the 2008-09 regular season. The values can be viewed at behindthenet. I then figured out the average 5-on-4 shooting percentage in the league (~0.128). I then simulated 100 'seasons'. In each 'season', the number of shots taken by each team was the number of 5-on-4 shots taken by that team during the 2008-09 season. However, the percentage of scoring a goal on each shot for every team was 0.128 -- the league average 5-on-4 shooting percentage. That is, each team was assigned the exact same shooting percentage. This is significant as, in any particular 'season', any deviation from the mean is strictly due to randomness, thus allowing one to determine how the spread in 5-on-4 should appear through the impact of randomness alone.

The results:

The first graph is fairly straightforward. The blue distribution is the 'predicted' distribution. It represents the spread in 5-on-4 shooting percentage over the course of the 100 simulated seasons. Thus, it's an approximation of what the spread among teams in 5-on-4 shooting percentage would look like if each team had the exact same underlying 5-on4 shooting percentage.

The red distribution is the 'actual' distribution. It represents the spread in 5-on-4 shooting percentage among NHL teams for the 2008-09 regular season. That mini-peak on the far right of the graph represents Philadelphia, who led the league with a gaudy 5-on-4 shooting percentage of 0.181.


This graph is a 'smoothed' version of the above graph. The blue distribution required no smoothing and is therefore identical to the one above.

However, the red distribution did require smoothing. Thus, the red distribution in this graph is simply a normal distribution with a mean of ~0.128 and standard deviation of 0.02. Why 0.02? That was the standard deviation in 5-on-4 shooting percentage among NHL teams during the 2008-09 season.

Here's the raw data. It's more or less self-explanatory.

The first two columns are the start and end points for the percentage 'ranges' (it's hard to make sense of non-discrete data). The 'actual' column -- the third one from the left -- shows the numerical distribution in 5-on-4 shooting percentage for the 2008-09 season. So, for example, one team in the NHL had a shooting percentage between 0.18 and 0.185 this season. The 4th column merely shows the relative frequency of the third column values.

In terms of the predicted values, the 5th column shows the frequency of each percentage range for the 100 simulated seasons, while the 6th column expresses those values as a relative frequency. So, for example, out of the 3000 simulated team-seasons (100 seasons * 30 teams = 3000 team-seasons), two teams had a shooting percentage falling between 0.165 and 0.170.

The final column merely shows the numerical distribution in shooting percentage in a hypothetical 30 team league where each team has the same underlying shooting percentage. This allows for a comparison to be made with the actual distribution, shown in the 3rd column.

Finally, the supplemental data. For each of the 100 simulated seasons, I calculated the standard deviation in shooting percentage among the teams. 'PREDICTED ST DEV MEAN' is the average standard deviation over the 100 seasons. 'PREDICTED ST DEV MIN' is the minimum standard deviation for the 100 seasons. 'PREDICTED ST DEV MAX' is the maximum standard deviation for the 100 seasons. 'ACTUAL ST DEV' is the standard deviation in 5-on-4 shooting percentage among NHL teams for the 2008-09 regular season.

The fact that the actual standard deviation is larger than the maximum standard deviation for any of the simulated seasons is fairly conclusive proof that randomness alone cannot account for the inter-team variation in 5-on-4 shooting percentage. For what it's worth, when I did my analysis on the effect of randomness on EV shooting percentage, some of the simulated seasons had a larger standard deviation than the actual standard deviation.

Lastly, the final row shows the inter-year correlation -- that is, for 0708 and 0809 -- in 5-on-4 shooting percentage at the team level. The value is non-trivially positive, which lends support to my above finding that teams can reliably influence their 5-on-4 shooting percentage.* Not surprisingly, the Flyers were tied for the league lead in 5-on-4 shooting percentage last season.

*On the other hand, Tyler at mc79hockey, in a post examining this type of thing at the start of the 2008-09 season, found an inter- year correlation that was somewhat lower, on the order of ~0.30.

EDIT:

Also relevant and of interest:

Vic Ferrari, in the comments section of this post -- in which he examines the ability of individuals player to effect PK SV% --, reports that individual Oilers had a substantial effect on powerplay shooting percentage while on the ice. This tends to support the idea that powerplay shooting percentage is highly non-random in its distribution.

Playoff Predictions -- Western Conference

(1) San Jose vs Anaheim (8)

This is a tough matchup for the Sharks. Out of all of the teams that the Sharks could have potentially drawn (NSH, CBJ, MIN, STL, EDM), Anaheim is probably the strongest.

The Sharks started the season on a tear, outshooting and outplaying the opposition like it was nobody's business. Since that time, they've cooled down a bit. They're still consistently outplaying the other team, but not to the degree that they were at the beginning of the year. I'm not sure how important this is, but I know that Matt at Battle of Alberta has been an advocate of excluding a team's first 20 games of the year when assessing each team's chances of playoff success. Perhaps there's something to that.

Anaheim has a formidable powerplay and I think that if they're going to win this series, they're going to have do it on that basis, considering that San Jose is clearly the more dominant team at ES. There are two problems with this, however:

1. If this series sees a lot of special teams play, it might actually benefit the Sharks more, as the Sharks are a much more disciplined team than Anaheim and have a much better PP/PK ratio.

2. The Sharks have the better PK and have a pretty good PP in their own right.

This series won't be an easy win for San Jose by any means, but at the same time it's hard to pick against them.

Sharks in 6.


(2) Detroit vs Columbus (7)

Having browsed through the picks of other bloggers and media personalities, Columbus seems to be a popular pick as an underdog.

From what I've seen, some of the rationale behind the pick is that Columbus will be able to exploit Detroit's weak goaltending situation.

I don't necessarily agree with this reasoning.

Firstly, Detroit has had poor goaltending all season, yet they've still managed to post a much better goal differential than Columbus. That's important.

Secondly, I have a hard time believing that Chris Osgood is as bad as his save percentage would imply. This is same goaltender that posted a 0.914 SV % in the regular season last year and 0.930 SV % in the playoffs. A lot of that had to do with playing behind the league's best team -- his expected save percentage based on shot quality in the playoffs last year was something like 0.94, according to hockeynumbers. However, this years Wings are as good or almost as good as last years squad. True, Osgood is getting up there in age, but I doubt that any age-related decline would be so marked. Save percentage is at least partly random in its distribution and I would expect Osgood's save percentage to gravitate towards the league average in the foreseeable future (i.e. the playoffs).

Thirdly, even if Osgood actually is terrible, then the Wings have the option of playing Conklin in his stead, who's actually been fairly competent this season.

Detroit in 5.


(3) Vancouver vs St. Louis (6)

There isn't a great deal that can be said about this series, but it's obvious to me that Vancouver is the better team and I expect them to advance without too much difficulty.

Not only is Vancouver the better team on paper, and they're also better by virtue of conventional metrics of team strength, like goal differential. Vancouver's underlying numbers are pretty average, although one of the benefits of having a goaltender like Luongo is that it generally allows you to be an EV outscorer without having the shot differential to match.

St. Louis has played well in the second half of the season, but so have the Canucks. Therefore, picking St. Louis on account of their second half play isn't overly logical.

Canucks in 5.


(4) Chicago vs Calgary (5)

A lot of people are discounting the Flames -- even Flames fans themselves, it seems.

One of my earlier posts addressed the fact that the Blackhawks are an interesting team. They have an excellent shot differential, an excellent goal differential, yet are marginally above average in terms of the expected goals numbers at hockeynumbers. I'm not sure how to account for this but I'm thinking that it might have something to do with the "shoot liberally and prevent shots against at all costs" strategy, as historically employed by Joel Quenneville.

As Kent notes, Chicago is a territorially dominant team at even strength, with an aggregate team corsi of 655. However, Calgary has an even better corsi at 778. Thus, both teams perform well here, with there being no clear advantage to either of them.

The difference between these two teams largely relates to goaltending. Whereas Chicago's has been excellent, Calgary's has been below average, even though for some reason I keep hearing Kiprusoff's name brought up when discussing the Vezina. While this will likely work to Chicago's advantage over the course of the series, I'm not sure how sustainable their team save percentage is, considering that they tend to give up such high quality shots against on average.

While I'm not necessarily convinced that Chicago is the better team, their advantage in goal differential is hard to ignore. That, coupled with the Flames injury problems and the fact that they'll be starting this series on the road, tilts the scales in their favor.

Blackhawks in 7.

Playoff Predictions -- Eastern Conference

(1) Boston vs Montreal (8)

I've written before about how I think that the Bruins are not as good as either their goal differential or record would suggest. Now that the season is over, my opinion hasn't really changed. That Boston has managed to post a goal differential of +80, despite having a negative 43 shot differential, suggests that they've been at least somewhat fortunate, and I don’t think that any reasonable person would deny that. Since my original post back in January, it appears that I've been somewhat vindicated. As per timeonice, the Bruins' EV shooting percentage had been 10.3% up to that point, but has only been 7.6% since then. However, their team EV save percentage has remained excellent and, considering that they also excelled in that regard last year, I think that they're the type of team that's going to reliably post a high EV save percentage over the large sample of games. Whether this is due to good goaltending, coaching/team strategy, or some combination thereof, I can't say. Interestingly, it seems that the Bruins have not been any better than the average team in terms of shot quality against this season, which implicates good goaltending as the causal factor (see here, for example).

While the difference between these two teams is not as large as the gap in goal differential would suggest, the Bruins still appear to be the superior club. Boston’s underlying numbers aren't impressive by any stretch of the imagination, but Montreal’s are even worse. A comparison:

For those that value the underlying numbers more than the results, special teams are a wash. But at even strength, the Bruins are much better any way you look at it.

The Habs were actually playing pretty well throughout the first part of the season, but since then they’ve fallen off the proverbial cliff. Both their goal and shot differential have dropped precipitously. I’d be inclined to attribute this to injuries, but they were also missing some guys during the first half and it didn’t seem to have too great of an impact upon their play.

Although I wouldn't necessarily be shocked if Montreal were to win this series, I just can't think of a compelling reason to pick them. The fact that they'll be without the services of Markov -- who is arguably their best player -- doesn't help matters either.

Bruins in 5.


(2) Washington vs New York Rangers (7)

The Rangers are another team that I've written about over the course of the season. In hindsight, my appraisal may have been a tad harsh. I seemed to have overlooked the fact that the Rangers had given up a tonne of shorthanded goals at the time, which tends to suggest bad luck. Since then, the Rangers have undergone a coaching range which, like in the case of the Penguins, seems to have helped them to some degree -- though perhaps moreso in terms of their results than their actual play.

Even though the Rangers are respectable, the Capitals seem to be the better team. They're better than the Rangers at EV strength and much better on the powerplay. The Rangers appear to have the penalty kill but the advantage is too small for it to make up for their other deficiencies. Some may point out that the Rangers have the better goaltending, and while this probably true, goaltending is only really important to the extent that it contributes to goal differential. The Capitals have a much better GD than the Rangers. I realize that there's a tendency in the hockey world to treat goaltending as more important in the playoffs, but I've never seen any evidence that would support that notion. I suspect that it's neither more nor less important than during the regular season.

Capitals in 6.


(3) New Jersey vs Carolina (6)

A fairly strong argument can be made that the Devils are the class of the East. Their underlying numbers are fantastic, especially at EV and on the powerplay. Additionally, it's difficult on paper to find any source of weakness with the team.

In that sense, I think that Carolina was a bit unfortunate to draw the Devils as a first round opponent. Assuming that the Canes are competent at distinguishing between the good teams from the not-so-good ones, they probably would have preferred to play Washington or Boston, and would much rather preferred Philadelphia. I don't think Carolina is a weak team by any stretch of the imagination. They're a reasonably dominant team territorially at EV, and have the best penalty differential in the league ( they've been among the league leaders in this category for several years running). If their special teams were better, I wouldn't hesitate to classify them as one of the best teams in the conference.

I realize that some might pick the Hurricanes on account of the fact that they’ve been ‘hot’ down the stretch, with the reverse being true for the Devils. However, I don’t think that there’s much value in this approach, considering that a team’s results will vary naturally over the course of a season. I prefer to look at how a team has performed over the season as a whole, rather than isolating recent stretches of games and attempting to infer team quality on that basis. The exception is when there’s a compelling reason to do so, such as in the event of a major trade, an injury to a star player, or a coaching change. Otherwise, it’s a dangerous practice.

Although there’s some evidence that Carolina’s play has improved over the course of the season, it’s not enough to confidently identify a genuine trend. There’s been some talk that Carolina has been a different team since the Cole trade. However, their EV shooting numbers prior to the trade are more or less identical to their post-trade numbers. It’s the percentages that have changed. Thus, picking the Canes on the basis of their recent play would seem to be a bit misguided.

My choice, therefore, is not a difficult one, and while Carolina could certainly advance, there's no logical reason for anyone to expect that outcome.

Devils in 6.


(4) Pittsburgh vs Philadelphia (5)

I've been meaning to make a post about the turnaround that the Pens have experienced since their coaching change. Not only have they substantially improved their record, but -- and more importantly -- their underlying numbers as well. Observe:

I realize that this might appear a bit contradictory, given what I wrote above. However, unlike in the case with Carolina, there is a compelling reason to focus on the post-Therrien Pens, that being the coaching change (although it is perhaps arguable that the player personnel changes have contributed as well). The change in underlying numbers is sufficiently marked for one to make the argument that the current Pens are a different team then the one that was iced from October to Valentines Day.

The Flyers, on the other hand, I have a hard time accepting as legitimate. For a 4th seed team with +28 goal differential, their underlying numbers are awfully poor. The percentages have been very kind to the Flyers in nearly every game situation (EV, PP, PK). As far as I can tell, the Penguins are fundamentally the better team. The fact that they’ll be starting the series at home makes this pick that much easier.

Penguins in 5.

The Blackhawks

The Blackhawks have been an interesting team this year.

First of all, there's plenty of evidence which suggests that the Blackhawks are a pretty solid team. They've accrued one of the best goal differentials in the league up to this point in the season, despite playing in the league's toughest division in the better of the two conferences. They've also soundly outshot the opposition, both at even strength and in general. In these respects, it would be difficult to argue that the Blackhawks are not one of the league's best teams.

What I find unusual, then, is that the Blackhawks expected goal differential, as calculated at hockeynumbers, is only slightly positive. The Blackhawks have allowed some 20 fewer goals than what would be predicted on the basis of shot quality, while having scored some 20 more. Given that their shot ratio is more or less in line with their goal ratio, the implication is that Chicago has been below average in both shot quality for and shot quality against. Indeed, if the expected goals numbers are translated to yield a shot quality index for each team, the Blackhawks do in fact fare quite poorly.

The fact that the Blackhawks tend to allow high quality shots against is not surprising. Firstly, shot quality is repeatable on a year-to-year basis, with Chicago having ranked 27th in the league in that regard last year.

Secondly, teams coached by Joel Quenneville tend to allow high quality shots against on average. Outside of 1999-00, for every year that Quenneville has been a head coach in the NHL, his team has ranked in the bottom half of the league in terms of save percentage, which implies that his teams were surrendering high quality shots against. While it's perhaps true that Quenneville was burdened with poorer than average goaltending during his tenure in both St. Louis and Colorado, shot quality has been directly measured from the 2002-03 season onward, with the results tending to support the argument that Quenneville-coached teams are poor in terms of shot quality against.

The Contrarian Goaltender has also found evidence that the effect of Quenneville's coaching in St.Louis was to reduce the save percentages of his own goalies, who tended to have better save percentages prior to playing under Quenneville (see, for example, the comments section of this post).

With a team save percentage of 0.912, the Blackhawks goaltending has been nothing short of superb this season. However, the fact that the team apparently allows such high quality shots against, not to mention the fact that save percentage is at least partially a product of random statistical variation, inevitably leads to the question of sustainability. Of course, It's true that both Khabibulin and Huet have proven track records, and both goaltenders are certainly better than anything Quenneville had to contend with in St. Louis and Colorado. Nonetheless, I think that it's a potential cause for concern and, at the very least, something that one ought to be mindful of in evaluating the team's prospects for the postseason.

As for the team in general, I'm inclined to think that they're still pretty good, the shot quality numbers notwithstanding. As I intimated in the above paragraph, both Huet and Khabibulin are above average netminders and the Blackhawks team save percentage is in that sense somewhat sustainable. And while it is true that the Blackhawks have exceeded their expected goals for, I'm reluctant to ascribe the difference to luck considering their plethora of offensively talented and creative players. Furthermore, even if I happen to be wrong on these points, their tendency to convincingly outshoot the other team is, if nothing else, encouraging.

Home Recording Bias: Shots on Goal

In previous posts, it was shown how some of the statistics that are recorded by the NHL are subject to a home arena bias. Home arena bias seems to be most pronounced with respect to the RTSS data, which includes statistics like hits, takeaways, giveaways, blocked shots, and so forth.

However, this bias is also observed with less subjective statistics, such as shots on goal. Below is a chart showing how the recording of shots on goal has varied on a site-by-site basis over the last 13 NHL seasons, with the more interesting information highlighted. The values contained in each cell were derived as follows:

[ (Home shots for/60 minutes played + Home shots against/60 minutes played) - (Road shots for/60 minutes played + Road shots against/60 minutes played) ]

Basically, the formula boils down to this: the total shots on goal (by both teams) in games played by a particular team at home, minus the total shots on goal in games played by that particular team on the road, with ice time controlled for. Empty net situations were not included, both in terms of shots on goal and minutes played. I should also mention that the ice time data for 1994-95 to 1997-98 is approximate.


While the home recording bias for shots on goal is not large, it is nonetheless clear that not all NHL arenas record shots equally. The recorders in Vancouver have over the years been very conservative in their shot counting, although the effect appears to have been moderated in the last couple seasons. There were more shots/60 in Colorado and Anaheim home games than there were in road games played by those two teams for every single season analyzed. Shot recording in Nashville has been generous ever since their inaugural season (although I'm not sure what happened in 2003-04), whereas the reverse has been true in Minnesota. In both New Jersey and Dallas, shots have been harder to come by since around the turn of the millennium. Finally, a bias towards overcounting seems to have materialized in Sunrise over the last couple years.

Of course, the above values are not necessarily demonstrative of a bias; they are merely suggestive of it. They ought to be supplemented with data on shooting percentage in order to allow for a more confident interpretation of the effect.

Why shooting percentage? Well, if an arena does in fact undercount or overcount shots on goal, the bias should concern saves rather than goals. The reasoning here is not difficult. Each shot on goal that results in a goal is necessarily a shot on goal -- there is no room for the exercise of discretion on the part of the shot recorder. However, in the case of a shot on goal that does not result in a goal, the shot recorder is permitted a modicum of discretion, and what constitutes a shot for some may not constitute a shot for others. Undercounting shots should have a positive effect on shooting percentage, whereas overcounting would be expected to have a positive effect on save percentage.

Therefore, it can be seen how accompanying data on shooting percentage will shed light on the extent to which a true bias is present. For the teams for which a bias is suspected -- Florida, Dallas, New Jersey, Nashville and Minnesota, I've included information below on the shooting percentage in games played by those teams, broken down into road and home situations. The data in the left column is the shooting percentage in road games played by the team indicated in the upper left hand corner. The data in the right column is the shooting percentage in that team's home games. It is important to stress that these figures do not merely represent the road and home shooting percentages of the team in question. Rather, the figures represent the overall shooting percentage (that is, both for the team in question as well as their opponents) in road or home games played by that team during the season indicated.

In terms of New Jersey, it seems that the tendency for undercounting shots at Continental Airlines arena began during the 2001-02 season. In every subsequent year, the shooting percentage in New Jersey home games has been higher than in New Jersey road games. Indeed, this bias has had some negative effect on the home save percentage of Devils goaltenders during the period in question (keeping in mind that the average home save percentage for NHL teams tends to be 0.003 to 0.007 higher than the average road save percentage).

The Devils led the league in shot quality against from 2002-03 to 2006-07. They also surrendered the fewest powerplays against during each of these seasons. While the Devils' road save percentage during the period in question reflects this fact, their home save percentage does not. At least part of the discrepancy can be accounted for by recording bias.

The shooting percentage data for Dallas games suggests that the bias emerged during the 1998-99 season. The effect appears to be large.

The data for Minnesota is less clear. The difference is in the predicted direction for four of the seasons (2001-02, 2002-03, 2003-04, 2005-06), the opposite direction for two of them (2006-07, 2007-08), with there being no difference in 2000-01. It's possible that:

a. The Wild simply play more conservatively at home.
b. The bias has lessened over time.
c. The results can be explained through some combination of the above factors.

The data on Nashville reveals that the bias is genuine, or at least was genuine prior to 2006-07 and 2007-08. The results for the last two seasons, taken together, indicate that the bias may no longer persist.

Finally, the data on Florida implies that there exists no recording bias at the BankAtlantic Center. The shooting percentage in Panther road games is largely indistinguishable from the shooting percentage in Panther home games. The fact that Florida goaltenders (Luongo, Anderson, Vokoun) have placed among the league leaders in save percentage in each of past several seasons (outside of 2006-07) have led some to conclude that their must be something amiss, given that the Panthers do not employ any type of defensive system and have not been an otherwise successful hockey team during that period. However, the most probable explanation is that the Florida has merely benefited from having a series of good goaltenders -- indeed, both Luongo and Vokoun have posted very impressive numbers elsewhere (granted, the data on Nashville suggests that the latter's save percentage may have been somewhat inflated by recording bias during his stay in the Music City).

Team Rankings and Playoff Probabilities

The first chart shows how each team in the league has fared thus far in terms of adjusted winning percentage. Adjusted winning percentage is essentially each team’s Pythagorean Expectation, with the exception that, instead of goals for and goals against, I use adjusted goals for and adjusted goals against. In computing each team’s adjusted GF and adjusted GA, I simply take each team’s actual GF and GA, subtract shootout goals and empty netters, and then make a second order correction for schedule difficulty. In determining schedule difficulty, oppositional strength is determined through the goal differential of the opponent, the location of the game (i.e. whether it’s a home or away game), and the circumstances of the game – namely, whether or not it’s the second half of a back-to-back for the road team.

If you compare these rankings to the actual standings, most teams are similarly positioned. There is, however, one notable outlier.

The Rangers are currently 9^th in the league in points per game, yet 26^th by this metric. Not surprisingly, they’ve had a ton of success in the shootout so far (record: 9-4), which is basically equivalent to sheer luck. While some may point to the Rangers shot differential, especially at EV, as evidence of them being not that bad of a team, I’m inclined to disagree. Reason being: they're in the red in terms of expected goals, which suggests that they’ve been below average in terms of shot quality for, shot quality against, or both.

Of course, there are a few teams who can be labeled as either lucky or unlucky in general – notwithstanding the fact that that these rankings aren’t too different from the standings. In other words, teams who are either better or worse than these rankings would suggest.

In terms of teams that probably aren’t as good as their adjusted winning percentage would indicate, I’m thinking of BOS, FLA, and PHI. These teams have all been greatly aided by the percentages this year. I think that the success that each of these teams has experienced thus far is unlikely to continue during the remainder of the regular season and the playoffs. Granted, the Flyers outperformed their underlying numbers last season as well. As the sample size in games played increases, it becomes increasingly difficult for one to point to randomness in an attempt to account for success with the percentages. On the other hand, I find it very difficult to look at a team that’s scored 15 shorthanded goals and conceded none and say that they haven’t been at least somewhat fortunate. I just don’t think that they're an inherently good hockey team.

And for teams in which the opposite is true, I’m thinking of OTT, LAK, COL, and TOR. These teams have all been – for lack of a better term – utterly screwed by the percentages this season, to the point where none of them have a realistic shot at making the playoffs. This is unfortunate in the sense that, if you were to compare this group of teams with the three listed above, I don’t think that there’s much to choose between them. Hell, I think that one could make a reasonable argument for the Kings being the best team of the seven – at least, looking at it in terms of which team is most likely to experience success from this point forward.

Anyway, here the playoff probabilities for all 30 teams (updated on 02/19/09). The left hand column contains seeds 1-15 in each conference, with the corresponding column for each team showing the probability of finishing the season in that position, expressed as a percentage. So, for example, the Blackhawks have an (approximately) 1% chance of finishing in 1st place in the West. The final two rows contains each team's probability of making the playoffs (in the second last row) and each team's probability of winning the division (in the last row). Future game probabilities are based on the respective adjusted winning percentages of the involved teams, game location, and whether or not the game is the second half of a back-to-back for the road team.

Coming off a Win/Loss: The effect of Prior Results

I’ve often wondered if the outcome of a team’s previous game has any affect on the result of that team’s subsequent game. Intuitively, I wouldn’t expect there to be much of an effect. The outcome of any given game is determined by many different factors, some of which are known to have a large effect.

While the result of the previous game could conceivably be one of these factors, it would probably rank pretty far down the list in terms of importance. In other words, if there is such an effect, I would expect it’s magnitude to be small.

That said, I’ve heard it argued before that the previous game does in fact have an effect on a team’s performance in the following game, so it’s something worth examining, I think.

On the one hand, some have suggested that the momentum of winning the previous game carries over to the next game, thus enhancing a team’s chance of success. According to this line of reasoning, the average team should do slightly better when coming off a win than when coming off a loss.

Conversely, others have suggested that winning breeds complacency, with losing having the opposite effect. This approach predicts that teams should do better when coming off a loss, on average.

I don’t think that either of these arguments have much merit. Both are based on the idea that psychological factors have a measurable effect on game outcomes, a premise with which I personally disagree. While casual fans often resort to folk psychology when discussing success and failure at the NHL level, its relevance has never, to my knowledge, been demonstrated through actual evidence.

In any event, I attempted to determine if the preceding game has any effect on following game results. My methodology was pretty straightforward. The sample included all regular season games played during the seasons of 2005-06, 2006-07 and 2007-08. Each game played was classified as a win, a loss, or a tie for both of the involved teams. For the sake of simplicity, any game that went past regulation was considered to be a tie. I then looked at whether that team won, lost or tied in its next game. Here are the results for 2007-08. The teams that had a better record when coming off a win compared to coming off a loss are shaded green. Teams for which the opposite was true are shaded orange.

Below is a chart of the average winning percentages of all 30 teams in each situation (coming off a win, coming off a loss, and coming off a tie) for all three seasons. The left hand column shows the average winning percentage for all 30 teams in games played after a win. The middle and right hand columns do the same, only for games where the team was coming off a loss and tie, respectively. It’s necessary to look at the average winning percentages rather than the aggregate winning percentages for one simple reason: better teams, by virtue of winning more games, tend to play a higher percentage of their games when coming off a win. For example, the Thrashers played a mere 18 games coming off a win last season; Detroit played 46. It needn’t be explained as to how this could confound the results.

Also included is a chart that breaks down the number of teams that had a better record after winning vis-à-vis their record after losing, and vice-versa.

The results are pretty consistent with my expectation in that the effect of the preceding game appears to be fairly small. In the 90 ‘team-seasons’ analyzed, 41 teams had a better record after winning, whereas the other 49 had a better record after losing. The average winning percentage for teams coming off a win was slightly less than 0.49. For teams coming off a loss, that figure was approximately 0.505. Therefore, it can be said that teams have, since the lockout, done slightly better after losing their previous game than they have when coming off a win. Of course, the margin is quite small and well within the potential range of random variance. Even supposing that the results are statistically significant, the influence of a team’s preceding game upon the outcome of its following game appears to be limited.