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overpass 10-05-2009 12:06 PM

With or Without You: Mario Lemieux
 
2012 edit: There were a couple of small errors in the data. Post 37 contains corrected results.

With or Without Mario Lemieux

The "With or Without You" method of player evaluation is simple. It looks at a team's record with a player and without a player, and estimates the player's impact based on the difference. The method has one main problem; it requires the player to have missed a number of games in multiple seasons to get a good estimate. The With or Without You method was developed for baseball by Tom Tango, and applied to hockey by Gabriel Desjardins in this article.

Mario Lemieux is a prime candidate for this method. He had a famously injury-plagued career. Despite being perhaps the most talented hockey player ever, his NHL accomplishments were limited by his injuries. Lemieux’s fragility was a great loss for hockey fans. However, it does allow the “With or Without You” method of player evaluation to be used.

Lemieux missed 10 or more games in 12 seasons. I used all of those seasons, with the exception of 1995/96. In this season, Lemieux was not missing games randomly. Instead the games he missed were the second half of back-to-backs, in order to rest his body. Since the games he missed were games in which the team could be expected to perform poorly, I left this season out of the calculation.

First, what is Lemieux’s estimated impact over his whole career?

Estimated impact: Mario Lemieux (career)

+0.120 Win% (or 20 standings points over an 82 game season)
+0.56 GF/G (or 46 goals added over an 82 game season)
-0.05 GA/G (or 4 goals prevented over an 82 game season)

Lemieux had a significant impact on winning percentage and goals scored. The impact on goals scored is large, but not as large as one might imagine.

Oddly enough, Lemieux’s impact on wins was larger than his impact on goals for and against. His impact on Pythagorean winning percentage (an estimated winning percentage based on goals for and against) was only +0.082, considerably lower than the actual winning percentage increase of 0.120. This suggests that Lemieux was a clutch player, stepping up his play in close games (or slacking off in blowouts).

While Mario's impact wasn't as large as we might have thought, we know that much of Mario’s career was spent playing hurt. Also, his last few seasons, while not bad, were hardly “Mario Lemieux” seasons. The next step will be to calculate Mario’s impact when he was in his prime and healthy. The seasons selected will be: 1986-87, 1989-90, 1991-92, 1992-93, and 2000-01. 1990-91 and 1993-94 were seasons in which every game he played was a struggle, and he wasn't able to perform at close to his peak level of play in the regular season. I determined this not by the results of this statistical exercise, but by scanning through old game recaps from the seasons in question.

Estimated impact: Mario Lemieux (prime)

+0.203 Win% (or 33 standings points over an 82 game season)
+1.16 GF/G (or 95 goals added over an 82 game season)
-0.01 GA/G (or 1 goal prevented over an 82 game season)

Lemieux's offensive impact is far greater now that his prime seasons are isolated. While this is expected, another interesting point is that his defensive impact appears to be neutral. This shows that he wasn't hurting his team defensively by focusing on scoring.

Again, Lemieux appears to have a clutch element to his game. The estimated increase in Pythagorean winning percentage, based on goals for and against, was only 0.157.

Finally, while Lemieux was arguably in his prime during the seasons in the previous sample, he was still at less than full speed in some of them. The final step is to select three seasons where, while he missed games, he was still at peak effectiveness, or as close as he ever got. These seasons are 1989-90, 1991-92, and 1992-93.

Estimated impact: Mario Lemieux (peak)

+0.256 Win% (or 42 standings points over an 82 game season)
+1.40 GF/G (or 115 goals added over an 82 game season)
-0.04 GA/G (or 3 goals prevented over an 82 game season)

These numbers are absolutely remarkable. The sample is only based on three seasons, so these estimates have a higher variance than the earlier ones, but Mario Lemieux’s impact on his team when he was playing was incredible. He added almost a goal and a half per game, and his team won at a far improved rate while he was on the ice.

Finally, here are the raw numbers for each one of the seasons in question.

Year Team GP W L T GF GA W% GF/G GA/G
1986-87 WithMario 63 28 28 7 246 230 0.500 3.90 3.65
1986-87 WithoutMario 17 2 10 5 51 60 0.265 3.00 3.53
1989-90 WithMario 59 27 27 5 248 264 0.500 4.20 4.47
1989-90 WithoutMario 21 5 13 3 70 95 0.310 3.33 4.52
1990-91 WithMario 26 14 9 3 112 100 0.596 4.31 3.85
1990-91 WithoutMario 54 27 24 3 230 205 0.528 4.26 3.80
1991-92 WithMario 64 35 22 7 291 234 0.602 4.55 3.66
1991-92 WithoutMario 16 4 10 2 48 68 0.313 3.00 4.25
1992-93 WithMario 60 45 10 5 292 195 0.792 4.87 3.25
1992-93 WithoutMario 24 11 11 2 75 73 0.500 3.13 3.04
1993-94 WithMario 22 11 9 2 74 79 0.545 3.36 3.59
1993-94 WithoutMario 62 33 18 11 225 206 0.621 3.63 3.32
1995-96 WithMario 70 44 24 2 331 257 0.643 4.73 3.67
1995-96 WithoutMario 12 5 5 2 31 27 0.500 2.58 2.25
2000-01 WithMario 43 26 14 3 168 134 0.640 3.91 3.12
2000-01 WithoutMario 39 16 17 6 113 122 0.487 2.90 3.13
2001-02 WithMario 24 10 12 2 63 66 0.458 2.63 2.75
2001-02 WithoutMario 58 18 34 6 135 183 0.362 2.32 3.16
2002-03 WithMario 67 22 40 5 160 215 0.366 2.38 3.21
2002-03 WithoutMario 15 5 9 1 29 40 0.367 1.93 2.67
2003-04 WithMario 10 3 4 3 20 29 0.450 2.00 2.90
2003-04 WithoutMario 72 20 47 5 170 274 0.313 2.36 3.81
2005-06 WithMario 26 6 13 6 65 93 0.346 2.50 3.58
2005-06 WithoutMario 56 16 33 8 179 220 0.357 3.20 3.93

pitseleh 10-05-2009 12:16 PM

Awesome work overpass.

Adding 0.256 to winning percentage is insane. Assuming he performs at that average over a season, 82 games of Lemieux would have taken the Islanders of last season from 30th in the NHL to 5th. A replacement level team would easily be a playoff team if they added Lemieux.

overpass 10-05-2009 12:18 PM

I'll repost the Al MacInnis and Peter Forsberg numbers that I ran for the Top-100 project. The final estimates are slightly different than the original ones I posted, as I improved the weighting method.

Al MacInnis
Year Player GP W L T GF GA W% GF/G GA/G
1993-94 WithAl 75 40 24 11 279 224 0.607 3.72 2.99
1993-94 WithoutAl 9 2 5 2 23 32 0.333 2.56 3.56
1995 WithAl 32 20 7 5 133 87 0.703 4.16 2.72
1995 WithoutAl 16 8 8 0 45 48 0.5 2.81 3
1996-97 WithAl 72 33 31 8 209 210 0.514 2.9 2.92
1996-97 WithoutAl 10 3 4 3 27 29 0.45 2.7 2.9
1997-98 WithAl 71 42 24 5 224 167 0.627 3.15 2.35
1997-98 WithoutAl 11 3 5 3 32 37 0.409 2.91 3.36
1999-00 WithAl 61 38 13 9 181 117 0.697 2.97 1.92
1999-00 WithoutAl 21 13 6 2 67 48 0.667 3.19 2.29
2000-01 WithAl 59 36 17 6 191 128 0.661 3.24 2.17
2000-01 WithoutAl 23 7 10 6 58 67 0.435 2.52 2.91
2001-02 WithAl 71 35 28 8 188 163 0.549 2.65 2.3
2001-02 WithoutAl 11 8 3 0 39 25 0.727 3.55 2.27

Estimated Impact: Al MacInnis
+0.132 W% (22 standings points over 82 games)
+0.40 GF/G (32 goals added over 82 games)
-0.47 GA/G (39 goals prevented over 82 games)


Year Player GP W L T GF GA W% GF/G GA/G
1996-97 WithPeter 65 37 21 5 219 162 0.608 3.37 2.49
1996-97 WithoutPeter 17 12 3 4 58 43 0.824 3.41 2.53
1997-98 WithPeter 72 36 19 17 217 180 0.618 3.01 2.50
1997-98 WithoutPeter 10 3 7 0 14 25 0.300 1.40 2.50
1999-00 WithPeter 49 28 13 7 161 124 0.643 3.29 2.53
1999-00 WithoutPeter 33 14 15 4 72 77 0.485 2.18 2.33
2000-01 WithPeter 73 46 13 10 240 167 0.699 3.29 2.29
2000-01 WithoutPeter 9 6 3 0 30 25 0.667 3.33 2.78
2002-03 WithPeter 75 40 15 12 240 182 0.613 3.20 2.43
2002-03 WithoutPeter 7 2 4 1 11 12 0.357 1.57 1.71
2003-04 WithPeter 39 23 13 3 119 84 0.628 3.05 2.15
2003-04 WithoutPeter 43 17 16 10 117 114 0.512 2.72 2.65
2005-06 WithPeter 60 35 25 0 213 187 0.583 3.55 3.12
2005-06 WithoutPeter 22 10 12 0 54 72 0.455 2.45 3.27

Estimated Impact: Peter Forsberg
+0.109 W% (18 standings points over 82 games)
+0.68 GF/G (56 goals added over 82 games)
-0.17 GA/G (14 goals prevented over 82 games)

overpass 10-05-2009 12:25 PM

Quote:

Originally Posted by pitseleh (Post 21435954)
Awesome work overpass.

Adding 0.256 to winning percentage is insane. Assuming he performs at that average over a season, 82 games of Lemieux would have taken the Islanders of last season from 30th in the NHL to 5th. A replacement level team would easily be a playoff team if they added Lemieux.

Thanks pitseleh.

You could almost be describing the 1988-89 Penguins...

I should say that these estimates are comparing the player to an in-season replacement, and the team is probably shuffling lines to compensate. As a result, this method has a very low replacement level. If Lemieux misses the full season the team should be able to do a better job of replacing him.

But even with those caveats, the change in his teams performance when he missed games at his peak was incredible.

Dark Shadows 10-05-2009 12:26 PM

Great work as usual overpass. I look forward to seeing the Mark Howe and Ray Bourque's:)

seventieslord 10-05-2009 02:04 PM

Although I am very impressed with Lemieux's results, the results looked just a little less impressive when it was shown that MacInnis and Forsberg fared almost as well.

overpass 10-05-2009 03:38 PM

Quote:

Originally Posted by seventieslord (Post 21437669)
Although I am very impressed with Lemieux's results, the results looked just a little less impressive when it was shown that MacInnis and Forsberg fared almost as well.

To be fair to Lemieux, I don't think the career estimate I made properly evaluates his career. Of the seasons used to calculate his career estimate, a disproportionate number are seasons in which he was clearly past his prime or playing hurt. It was for this reason that I calculated the prime estimate and the peak estimate, although I may not have made that clear.

In 1990-91 and 1993-94, Lemieux was barely able to get on the ice, and was relatively ineffective. While these season are part of his career, they are only 5% of his regular season games, but are given 20% of the weight in the career estimate.

Second, 27% of the career estimate comes from post-2001 seasons which are past his prime. These represent only 18% of his regular season games. For comparisons sake, Peter Forsberg has no past-prime seasons included in his estimate.

Also, Lemieux's excellent 1988-89 season and his 1995-96 season are given no weight in the career estimate.

I'd rather use the prime estimate, while realizing that he wasn't playing at that level at the end of his career or for those two seasons in which he was playing hurt.

MacInnis and Forsberg don't need this kind of detailed breakdown, as they were fairly healthy for the games they played and neither played much past their prime (2005-06 was the last season I used for Forsberg).

foame 10-05-2009 04:29 PM

This is really great work. One thing to note about MacInnis/Forsberg is that they never played on a weak team like Penguins 86/87.

What players are you going to look at next?

popo 10-14-2009 03:06 PM

Drastic difference in Lemieux's contribution from his peak years to his post 2001 comeback years.

It would be interesting to see the comparison for Gretzky in 87-88, and 92-93.

Ilya Kovalchoke* 10-14-2009 03:18 PM

Wonder what Orr or Richards numbers would have been like.

Hockey Outsider 07-09-2012 02:36 PM

Not sure how I missed this thread when it was first made - excellent work.

Quick question. Based on this analysis, both MacInnis and Forsberg added roughly the same number of goals to their respective teams (+32 goals scored and -39 goals allowed for MacInnis = +71 overall; and +56 goals scored and -14 goals allowed for Forsberg = +70 overall). However, MacInnis apparently had a larger impact on his team's ability to win games (+22 standing points compared to +18 for Forsberg).

There are three possible interpretations:

1. This could be evidence that MacInnis was more of a clutch player than Forsberg. Not to take anything away from MacInnis, but, despite Chopper winning the Conn Smythe, Foppa generally has the stronger reputation as a clutch player.

2. This could simply be a result of fluke variances over small sample sizes.

3. I suspect that Forsberg generally played on stronger teams than MacInnis. I think there are "diminishing returns" to additional goals scored/prevented for a really strong (or weak) team. Thus, even though Forsberg contributed the same amount as MacInnis, it had a smaller impact on his team since the Avalanche were such a dominant team without him (i.e. even if Forsberg scorers/saves a few more goals, it doesn't necessarily translate into more wins since the Avalanche won so many games already). A quick calculation shows that the point increase per goal differential is +0.26 for Forsberg (i.e. each additional goal scored or saved added 0.26 points to his team's standings), +0.31 for MacInnis and +0.40 for Lemieux.

seventieslord 07-09-2012 03:05 PM

Quote:

Originally Posted by Hockey Outsider (Post 52342907)
Not sure how I missed this thread when it was first made - excellent work.

Quick question. Based on this analysis, both MacInnis and Forsberg added roughly the same number of goals to their respective teams (+32 goals scored and -39 goals allowed for MacInnis = +71 overall; and +56 goals scored and -14 goals allowed for Forsberg = +70 overall). However, MacInnis apparently had a larger impact on his team's ability to win games (+22 standing points compared to +18 for Forsberg).

There are three possible interpretations:

1. This could be evidence that MacInnis was more of a clutch player than Forsberg. Not to take anything away from MacInnis, but, despite Chopper winning the Conn Smythe, Foppa generally has the stronger reputation as a clutch player.

2. This could simply be a result of fluke variances over small sample sizes.

3. I suspect that Forsberg generally played on stronger teams than MacInnis. I think there are "diminishing returns" to additional goals scored/prevented for a really strong (or weak) team. Thus, even though Forsberg contributed the same amount as MacInnis, it had a smaller impact on his team since the Avalanche were such a dominant team without him (i.e. even if Forsberg scorers/saves a few more goals, it doesn't necessarily translate into more wins since the Avalanche won so many games already). A quick calculation shows that the point increase per goal differential is +0.26 for Forsberg (i.e. each additional goal scored or saved added 0.26 points to his team's standings), +0.31 for MacInnis and +0.40 for Lemieux.

I'm guessing it is almost entirely #2.

However, there may be another factor at play. Without looking at the actual numbers, I think Forsberg's Avs would have been a higher offense team in total GF+GA than MacInnis' Blues. Which means that it would take more of a positive swing in goal differential to make the same impact. I don't have numbers that prove this but it makes sense in my head...

Czech Your Math 07-09-2012 03:16 PM

This is very interesting, and the pythagorean portion is similar to what I've been looking at with even strength data (instead of overall data).

Unfortunately, when I click the link provided, the article seems to be in French. Given your usual diligence, I think I can make a fair guess at the methodology, but what exponent was used in the pythagorean estimation? From what I read of Ryder's (?) pythagorean study, it seemed there various alternatives, many of which were dependent on GF & GA levels (such as exponent = [GFPG * GAPG] ^ 0.285 ). One of the problems I ran into while using even strength data, was which exponent to use, given that ES GF & GA levels would naturally be lower than overall levels. Additionally, the levels with and without the player may be significantly different (in the case of deducting all or some of player's role at ES, without will always be lower). Also, I assume you are calculating the effect for each season separately and then summing the results, can you verify this?

When I did so with a very limited sample, I found large effects for players such as Jagr, Lemieux, Messier, Forsberg and Lindros. I would be interested in seeing the effects for Jagr, Messier, and Lindros verified.

Blargh 07-09-2012 04:00 PM

This thread made me think of Igor Larioniv. I remember one year reading a newpaper article supporting him for the Hart Trophy since he was "most valuable to his team" than any other player that year. Looking back it had to 1994-95.

With Larionov
Sharks were 30-20-10, 3.25 GFA, 2.93 GAA
Without Larionov
Sharks were 3-15-6, GFA 2.375, 3.708 GAA

For 1993-94, Larionov, in his first season with the Sharks, had a +.333 Win Pct, + .875 GFA, -0.775 GAA.

Czech Your Math 07-09-2012 04:09 PM

Quote:

Originally Posted by Blargh (Post 52346925)
This thread made me think of Igor Larioniv. I remember one year reading a newpaper article supporting him for the Hart Trophy since he was "most valuable to his team" than any other player that year. Looking back it had to 1994-95.

With Larionov
Sharks were 30-20-10, 3.25 GFA, 2.93 GAA
Without Larionov
Sharks were 3-15-6, GFA 2.375, 3.708 GAA

For 1993-94, Larionov, in his first season with the Sharks, had a +.333 Win Pct, + .875 GFA, -0.775 GAA.

Wow, it even inspired you to make your first ever post on HFB.

Now that's an impact! ;)

Hobnobs 07-09-2012 04:48 PM

The with or without you stat is probably very flawed. Team strength? What about teams that rallies because the star is gone? Who else was gone at the same time? Who was gone when they played? Would be funny to look at this stat for a guy like Komisarek or Lebda :laugh:

MadLuke 07-09-2012 05:07 PM

Quote:

Originally Posted by Hobnobs (Post 52348839)
The with or without you stat is probably very flawed. Team strength? What about teams that rallies because the star is gone? Who else was gone at the same time? Who was gone when they played? Would be funny to look at this stat for a guy like Komisarek or Lebda :laugh:

Context is important of course (did another star's came back when you were gone (like Malkin winning hart when Crosby was hurt would impact a lot Crosby with or without you).

Psycho Papa Joe 07-09-2012 05:16 PM

From a Habs perspective, I'd like to see one done for andrei Markov.

Czech Your Math 07-09-2012 09:37 PM

I think you should verify your win-loss data for Lemieux, in particular the 1990, 1992, and 1994 seasons. A small change can have large effects, of course, over a small sample of games. This why I prefer the weighted-average by games missed, since it negates disproportional effects of changes in sample size from season to season.

Hardyvan123 07-09-2012 10:04 PM

Quote:

Originally Posted by MadLuke (Post 52349581)
Context is important of course (did another star's came back when you were gone (like Malkin winning hart when Crosby was hurt would impact a lot Crosby with or without you).

While reading this thread I was thinking about how the Penguins actually seemed to come together and did rather well in 11 after Crosby went down.

I have no idea on how the Pens do with and without Sid numbers wise but in 11 could it be simple variance or chance or is it possible in a more defensive era that teams can compensate for the loss of a superstar like Mario or a guy like Orr perhaps?

I remeber something vaugely about King Clancy and his team perfomance both with and without him as well that helped his case in the top 60 Dman project.

overpass 07-09-2012 11:30 PM

Quote:

Originally Posted by Czech Your Math (Post 52361745)
I think you should verify your win-loss data for Lemieux, in particular the 1990, 1992, and 1994 seasons. A small change can have large effects, of course, over a small sample of games. This why I prefer the weighted-average by games missed, since it negates disproportional effects of changes in sample size from season to season.

I just did a quick check of Mario's 1990 game log at HR. You're right, it appears the Pens were 27-28-4 with him, not 27-27-5.

I was working from newspaper archives at the time to cover those seasons, because HR didn't have game logs yet and the HSP wasn't complete for those seasons. Guess I made a couple of errors. I'll update the calculations using HR's game logs when I get a chance.

I actually did use a weighted average by games missed.

overpass 07-09-2012 11:34 PM

Quote:

Originally Posted by Hobnobs (Post 52348839)
The with or without you stat is probably very flawed. Team strength? What about teams that rallies because the star is gone? Who else was gone at the same time? Who was gone when they played? Would be funny to look at this stat for a guy like Komisarek or Lebda :laugh:

Ideally you'd want to control for factors like teammates injuries, etc. I haven't done that - it would be a lot more work. Basically just hoping it washes out over a career. I'll admit these are no more than rough estimates. The underlying data isn't detailed enough to go further.

overpass 07-09-2012 11:40 PM

Quote:

Originally Posted by Hockey Outsider (Post 52342907)
Not sure how I missed this thread when it was first made - excellent work.

Quick question. Based on this analysis, both MacInnis and Forsberg added roughly the same number of goals to their respective teams (+32 goals scored and -39 goals allowed for MacInnis = +71 overall; and +56 goals scored and -14 goals allowed for Forsberg = +70 overall). However, MacInnis apparently had a larger impact on his team's ability to win games (+22 standing points compared to +18 for Forsberg).

There are three possible interpretations:

1. This could be evidence that MacInnis was more of a clutch player than Forsberg. Not to take anything away from MacInnis, but, despite Chopper winning the Conn Smythe, Foppa generally has the stronger reputation as a clutch player.

2. This could simply be a result of fluke variances over small sample sizes.

3. I suspect that Forsberg generally played on stronger teams than MacInnis. I think there are "diminishing returns" to additional goals scored/prevented for a really strong (or weak) team. Thus, even though Forsberg contributed the same amount as MacInnis, it had a smaller impact on his team since the Avalanche were such a dominant team without him (i.e. even if Forsberg scorers/saves a few more goals, it doesn't necessarily translate into more wins since the Avalanche won so many games already). A quick calculation shows that the point increase per goal differential is +0.26 for Forsberg (i.e. each additional goal scored or saved added 0.26 points to his team's standings), +0.31 for MacInnis and +0.40 for Lemieux.

Diminishing returns should apply in theory to a small degree.

But I'd lean towards random variation. A single blowout might explain the difference.

overpass 07-09-2012 11:45 PM

Quote:

Originally Posted by Czech Your Math (Post 52344933)
This is very interesting, and the pythagorean portion is similar to what I've been looking at with even strength data (instead of overall data).

Unfortunately, when I click the link provided, the article seems to be in French. Given your usual diligence, I think I can make a fair guess at the methodology, but what exponent was used in the pythagorean estimation? From what I read of Ryder's (?) pythagorean study, it seemed there various alternatives, many of which were dependent on GF & GA levels (such as exponent = [GFPG * GAPG] ^ 0.285 ). One of the problems I ran into while using even strength data, was which exponent to use, given that ES GF & GA levels would naturally be lower than overall levels. Additionally, the levels with and without the player may be significantly different (in the case of deducting all or some of player's role at ES, without will always be lower). Also, I assume you are calculating the effect for each season separately and then summing the results, can you verify this?

When I did so with a very limited sample, I found large effects for players such as Jagr, Lemieux, Messier, Forsberg and Lindros. I would be interested in seeing the effects for Jagr, Messier, and Lindros verified.

Don't worry about the French article, it was just a general presentation of the concept, not a detailed example of my method. Going from memory of what I did over 2 years ago...

I used the exponent 2. You raise some interesting points there, but I kept it simple.

Yes, I calculated the effect for each season, I weighted each season's effect by the square of either GP (with) or GP (without), whichever was lower. So seasons in which the player played roughly half the team games are weighted the most, and seasons where they played almost all or almost no games receive a very low weight.

Czech Your Math 07-09-2012 11:50 PM

Quote:

Originally Posted by Hardyvan123 (Post 52362929)
While reading this thread I was thinking about how the Penguins actually seemed to come together and did rather well in 11 after Crosby went down.

I have no idea on how the Pens do with and without Sid numbers wise but in 11 could it be simple variance or chance or is it possible in a more defensive era that teams can compensate for the loss of a superstar like Mario or a guy like Orr perhaps?

I remeber something vaugely about King Clancy and his team perfomance both with and without him as well that helped his case in the top 60 Dman project.

I don't have changes in GF-GA for Crosby, since it's much more time-consuming. I do have the weighted "expected win%" and actual win% for the games he has missed in his career. In his case it is complicated by shootout wins/losses and whether to consider those W/L or ties for the purposes of the study. Since the data for individual players only contains W/L and does not indicate OT or SO, these W/L are treated like any other in the interest of saving time (and with no clear consensus as to how they should be treated).

Crosby
-------------
Career
Expected win% w/o (EW%): .617
Actual win% w/o (AW%): .579
Difference: .057 (6.2% decrease)

2006-2011
EW% .602
AW% .556
Diff: -.046 (8.7% decrease)

Of course, the cause can always be variance. Crosby's 2012 season is additionally complicated by the fact that he only played 22 games, and these 22 games are what is used to calculate the "expected win%" and "expected wins" (EW% * games) for each season (which is then summed and divided by games missed to obtain a weighted average). In such cases, the individual season data is particularly useful. Let's look at the 3 seasons in which he missed by far the most games:

2008: 19 games w/o, .585 with, .552 w/o (5.7% decrease)
2011: 41 games w/o, .634 with, .561 w/o (11.5% decrease)
2012: 60 games w/o, .636 with, .617 w/o (3.1% decrease)

I don't think the defensive era is the cause for the small decrease in win%. This is because some of the other forwards studied also played within the past 20 years when it also a defensive era, but most showed significantly larger efffects (the exception being Sakic):

Sakic '97-04
-----------------
91 games missed
EW% .592
AW% .593
Diff: +.001 (0.2% increase)

Selanne '94-01
--------------------
68 games missed
EW% .414
AW% .353
Diff: -.061 (17.2% decrease)

Forsberg '97-04
---------------------
123 games missed
EW% .634
AW% .533
Diff: - .101 (16.0% decrease)

Lindros '93-00
-----------------
134 games missed
EW% .623
AW% .541
Diff: -.082 (13.2% decrease)

Messier '88-97
---------------------
76 games missed
EW% .573
AW% .414
Diff: -.159 (27.7% decrease)

Lemieux '88-97
-----------------
including '91 & '94
201 games missed
EW% .605
AW% .502
Diff: -.103 (16.9% decrease)

not including '91 & '94
87 games missed
EW% .620
AW% .414
Diff: -.206 (33.3% decrease)

Jagr '97-01
----------------
45 games missed
EW% .534
AW% .389
Diff: -.145 (27.2% decrease)


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