Tuesday, April 13, 2010

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.

Tuesday, March 9, 2010

Shot Recording Bias: Part n

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

Saturday, February 20, 2010

The Relationship Between Outshooting and Outscoring over Time

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

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.

Monday, January 4, 2010

Scoring Chances for Game Number 20436 : Wild @ Coyotes

Scoring Chances for NHL Game Number 20436

TeamPeriodTimeNoteMINOpponent
PHX115:51 369143236411161930555v5
PHX113:29 91520323455429303438555v5
PHX15:25 516325155 315171930334v5
PHX12:18 361415163224141920305v5
MIN218:51 11253234515528151830885v5
MIN218:37 11253234515528151830885v5
PHX217:39 369152032411161730555v5
PHX217:32 3614162532411161730555v5
PHX215:28 369152032214181930385v5
PHX214:39 51125323451314192030335v5
PHX214:24 51125323451314192030335v5
MIN214:01 3914152032430343855 5v4
MIN213:37 511142532481118293033 5v4
MIN212:14 91520323455411151730555v5
PHX211:16 91520323455411151730555v5
MIN210:29 5111416263238153033885v5
MIN210:13 51416263236218293034385v5
PHX29:30Goal11253234515538153033885v5
PHX28:46Goal5612213248314193033385v5
MIN27:04 39123255 311173033 4v4
PHX25:50 611162632 38151930334v5
PHX25:34 6111620263238153033885v5
PHX25:33 6111620263238153033885v5
MIN24:23 3512213248218293034385v5
PHX218:01 5915202632411161730555v5
PHX314:49 361416324848153055885v5
MIN311:40 39141520321118293033 5v4
PHX310:06 61216323451414192030555v5
PHX35:25 141632344855318293034385v5
PHX30:38 3914152048411161730555v5


#PlayerEVPPSH
3M. ZIDLICKY16:03274:19203:5200
5K. JOHNSSON18:06343:34101:4501
6G. ZANON16:010100:56004:0901
9M. KOIVU14:10274:41201:4500
11O. NOLAN9:53353:45101:3901
12C. KOBASEW12:43220:31000:2100
14M. HAVLAT10:28266:25300:1700
15A. BRUNETTE12:34174:18200:0000
16A. EBBETT9:34270:25002:3302
20A. MIETTINEN13:45184:18201:2300
21K. BRODZIAK11:23110:22001:5300
25E. BELANGER11:06243:39101:4400
26J. SIFERS12:17230:00000:1601
32N. BACKSTROM44:027178:34306:3502
34S. HNIDY12:43371:49000:4200
36J. SCOTT4:13110:00000:0000
48G. LATENDRESSE12:03143:43100:0700
51J. SHEPPARD10:50240:03001:2901
55N. SCHULTZ13:46440:02002:2601


PeriodTotalsEVPP5v3 PPSH5v3 SH
1040300000100
291271120000100
3140410000000
4000000000000
Totals102071830000200

Scoring Chances for Game Number 20589 : Wild @ Ducks

Scoring Chances for NHL Game Number 20589

TeamPeriodTimeNoteMINOpponent
ANA118:50 591520363719112734425v5
ANA116:08 562124375114102028535v5
MIN114:27 5915203637113222734505v5
ANA112:52Goal362124375119112734425v5
MIN19:38 9152034375519111921425v5
MIN15:28 6112225343714223950535v5
MIN14:20 591520363714283950535v5
MIN14:19Goal591520363714283950535v5
ANA13:44Goal361416374819112734425v5
ANA210:52 36915203719112734425v5
ANA21:51 593755 19101119273v5
ANA21:29 36937 19101119273v5
ANA21:17Goal3692537 19101119274v5
MIN313:25 561516203719112734425v5
MIN311:08 5151620363719111921425v5
MIN36:53Goal5914153748117202734 5v4
MIN35:27 561620374814102028535v5
MIN30:49 391415203414112122275v5
MIN30:48 391415203414112122275v5
ANA30:09Goal3914152025111222734 5v4


#PlayerEVPPSH
3M. ZIDLICKY19:02233:32011:2901
5K. JOHNSSON19:34622:37101:2000
6G. ZANON20:32340:00001:2901
9M. KOIVU13:01623:21110:5301
11O. NOLAN13:44102:04000:2200
14M. HAVLAT15:42213:12110:0500
15A. BRUNETTE13:58823:21110:0000
16A. EBBETT15:36311:07000:3500
20A. MIETTINEN14:52923:15010:0000
21K. BRODZIAK9:19020:24001:4500
22C. CLUTTERBUCK13:12100:14001:1500
24D. BOOGAARD5:32020:10000:0000
25E. BELANGER13:06102:42010:4301
34S. HNIDY14:25400:47000:0000
36J. SCOTT6:54410:10000:0000
37J. HARDING49:38854:56102:4901
48G. LATENDRESSE15:05112:10100:0000
51J. SHEPPARD5:47020:24000:0000
55N. SCHULTZ19:49100:28001:2000


PeriodTotalsEVPP5v3 PPSH5v3 SH
1545400000000
2040100000102
3615011000000
4000000000000
Totals11910511000102