Wednesday, April 28, 2010

2nd Round Playoff Predictions and Probabilities

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


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.


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.


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.


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.

Tuesday, April 27, 2010

The Repeatability of Special Teams Performance

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%.

Wednesday, April 14, 2010

Corrected Playoff Probabilities

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

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.


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.

Tuesday, April 13, 2010

Playoff Predictions


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.


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.


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.


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.


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.


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.


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.


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

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.

Friday, April 9, 2010

The Leafs, Scoring Chances and Corsi

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.