Thursday, April 28, 2011

2nd Round 1011 Playoff Probabilities and Predictions

[ For an explanation, see here ]


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.


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.


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.


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

Thursday, April 14, 2011

Playoff Outcome Probabilities

Self Explanatory. Based on each team's expected winning percentage, as shown here.

Wednesday, April 13, 2011

1st Round 1011 Playoff Predictions


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.


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.


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


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.


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.


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.


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.

1st Round 1011 Playoff Probabilities

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:

  1. 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.
  2. 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
  3. 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.
  4. 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.

Tuesday, April 12, 2011

Cumulative Score Tied Corsi

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.

Thursday, April 7, 2011

Loose Ends - Part III B: The Power Play

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.


Loose Ends - Part III A: The Power Play

[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.]


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.