Saturday, August 1, 2009

Defenseman's Impact (cont'd...)

I was initially only going to look at the performance of replacement level defensemen to see if their inclusion in the lineup had any additional negative impact relative to that of losing a #1 or #2 defenseman. But I ended up pulling the "With or Without You" data for every defenseman over the last four seasons who played between 10 and 70 games in a season. That ended up being 502 in all.

I looked at two quantities: Even-Strength Save Percentage For and Even-Strength Save Percentage Against, both when the player was in the lineup and when he was out. I then regressed against average TOI. What we get is essentially this, with the coefficients varying slightly depending on how I weight the data:

Opponent's Save Percentage Delta vs Avg TOI = -0.44 * (TOI - 15)
Own Team's Save Percentage Delta vs Avg TOI = +0.44 * (TOI - 15)

TOI isn't a perfect proxy for a defenseman's ability (or for a team's performance when he's in the lineup), so we end up with R^2 in the range of 0.3 to 0.5. Nonetheless, replacing a good defenseman with a bad one tends to decrease your team's shooting percentage and increase your opponent's.

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Wednesday, July 29, 2009

Defenseman's impact on Offense

I might as well re-run the previous post on the offensive end of the ice:

N=28 Better +/- 1610 1.89 21.77 913.3 686 1.71 21.16 919.1 5.8
N=25 Worse +/- 1229 1.81 21.76 916.9 821 1.81 21.32 914.9 -2.0

Again, the "Better +/-" group had a significant impact on scoring when they were in the lineup: +14.5 goals per 82 games. The "Worse" group generated more shots on goal, but scored less often, resulting in no increase in scoring.

As a whole, here are the offensive and defensive contributions in and out of the lineup:

Offense/GF 2839 1.86 21.77 914.9 1507 1.77 21.25 916.8 1.9
Defense/GA 2839 1.86 21.79 914.5 1507 1.95 21.97 911.0 3.5

So we get what we expect when the players are in the lineup: the expected record of a large number of teams is .500. When a top D-man is out of the lineup, both offensive and defensive shot volume and quality suffer to varying degrees, resulting in a .450 team in the aggregate. The difference between these two teams is approximately 8.66 points in the standings, or a little more than four wins. This seems like a reasonable estimate of the value of the average #1 or #2 defenseman.

If we look purely at the change in goals allowed due to not having one good defenseman in particular in the lineup, it accounts for approximately six goals per season. The difference in expected save percentage between the best and worst defensive teams using a simple shot quality model (see: translates to approximately 20-25 goals per 82 games. If we assume that having neither a #1 or #2 defenseman on your team costs you twelve goals on shooting percentage alone, it seems unlikely that much more than half of this 20-25 goal difference is due to a weak defensive corps.

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Do Defensemen influence Save Percentage?

[Note: this methodology is similar to a previous analysis of replacement level: It is obvious that teams do worse when their top players are out of the lineup, but it's not clear what suffers.]

In order to answer this question, I made a list of defensemen over the last four seasons who averaged more than 22 minutes per game and played between 20 and 70 games in a given season. 22 minutes of TOI corresponds approximately to the 60th-best defenseman, which means that the group of subjects includes mostly 1st and 2nd defensemen.

I then counted up the number of even-strength goals and shots against when each defenseman was in the lineup and when he was not dressed. I further split the defensemen into those whose +/- was better than the team's overall +/- (on a per minute basis). Presumably the group with the "Better +/-" would have more of an impact on even-strength defensive zone play.

The results:

N=28 Better +/- 1610 1.85 21.48 914.0 686 2.04 21.94 907.2 5.8
N=25 Worse +/- 1229 1.89 22.20 915.1 821 1.89 22.00 914.2 0.9

The assumption here is that during a given season, a player's aggregate group of teammates, including the goalie, will be basically unchanged whether he's in the lineup or not. Similarly, his team's aggregate group of opponents is assumed to be the same whether he's in the lineup or not.

While the defensive difference with the "Worse +/-" defensemen out of the lineup was negligible, the teams of the "Better +/-" defensemen allowed 15.5 fewer goals per 82 games when they were playing. One-quarter of this change was due to reducing the volume of shots allowed, but the rest is due to better save percentage.

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Monday, June 2, 2008

Replacement-Level Redux: Goals vs Wins

In the comments section for my previous post, Tom Tango pointed out that it would be interesting to see the breakdown of goals for and against when defensemen and forwards are missing from the lineup. For 2002-2008, we get the following:

In In In Out Out Out
+/- GF GA +/- GF GA
D 2.22 2.816 2.788 -9.67 2.707 2.825
F 3.21 2.833 2.794 -5.13 2.776 2.839

The results seem a little counterintuitive. Goal prevention drops the same amount when a forward and a defenseman are out of the lineup, while goal scoring drops much more when the defenseman is out. And the gap, 11.9 goals/82 lost defensive games to 8.3 for forwards, is nowhere near the almost 3:1 difference we saw when we just looked at wins and losses.

It's possible there's a problem with the ESPN GF/GA data - such things have cropped up before. Or including SO and OT goals is skewing the results. It's hard to say, but I'll take a closer look at the numbers.

Here's some yearly detail:

Forwards (~19 mins TOI or more)

Per 82 Games

Year +/- +/-GF +/-GA
2002-03 0.79 -5.88 -5.10
2003-04 10.73 -3.21 7.52
2005-06 13.83 -4.07 9.76
2006-07 8.34 -2.34 6.00
2007-08 8.15 -3.70 4.45

Average 8.34 -4.70 3.64

Defensemen (~21 mins TOI or more)

Per 82 Games

Year +/- +/-GF +/-GA
2002-03 5.84 -8.44 -2.60
2003-04 7.18 -5.89 1.29
2005-06 19.05 -11.46 7.59
2006-07 8.47 -5.963 2.51
2007-08 18.02 -14.40 3.62

Average 11.89 -8.93 2.96


Thursday, April 17, 2008

Replacement level: how many wins do injuries cost?

Replacement level can be a bit difficult to define in hockey. Unlike baseball, where Derek Jeter gets hurt and all his playing time goes to a guy who has yet to prove he can hit AAA pitching, an NHL player's minutes get spread around to other NHL players (aka his teammates) while he's hurt. So the Yankees can see the difference between Jeter and true replacement level, while an NHL team might shift every line and give nine low-leverage minutes to a guy who only dresses half the time, obscuring the difference between top players and the 21st guy on the roster.

I'm not going to try to compute replacement level here. Instead, I want to look at how many wins it costs a team when one of their top players is injured. For the last five seasons, I looked at forwards who averaged 19 minutes or more per game and defensemen who averaged 21 minutes or more - and who played between 52 and 74 games with a single team. This roughly corresponds to a team's top two forwards and top two defensemen. I compared their team's record with them in the lineup to its record with them out of the lineup. Here are the results:

Forwards (~19 mins TOI or more)

Games Games Pts
Played Wpct* Missed Wpct Delta/82GP
Total 6540 0.502 1619 0.484 3.07
2007-08 1292 0.508 348 0.487 3.39
2006-07 1331 0.491 309 0.479 2.03
2005-06 1344 0.510 296 0.483 4.48
2003-04 1240 0.505 360 0.474 5.19
2002-03 1300 0.492 296 0.441 8.37

Defensemen (~21 mins TOI or more)

Games Games Pts
Played Wpct Missed Wpct Delta/82GP
Total 6610 0.498 1546 0.447 8.44
2007-08 1325 0.486 315 0.443 7.08
2006-07 1322 0.505 318 0.447 9.64
2005-06 1318 0.503 322 0.429 12.27
2003-04 1300 0.492 296 0.441 8.37
2002-03 1345 0.505 295 0.478 4.47

The overall winning percentage when players were in the line-up was close to .500 for both datasets, which we would expect since playing time is evenly distributed across good and bad teams. And for both forwards and defensemen, there was a clear difference in winning percentage when these players were out of the lineup. However, the difference was much greater for defensemen overall, and in four out of five seasons for which we have ice time data. Teams can expect to lose four extra games if one of their top two blueliners goes down for the season, while losing a first-line forward appears to cost just one and a half losses. The error bars on these estimates are large, but it's clear that losing a defenseman is a bigger deal than losing a forward.

* - Winning percentage was calculated assuming SO and OT games were ties.


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