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 injuryplagued 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 backtobacks, 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: 198687, 198990, 199192, 199293, and 200001. 199091 and 199394 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 198990, 199192, and 199293. 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.

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. 
I'll repost the Al MacInnis and Peter Forsberg numbers that I ran for the Top100 project. The final estimates are slightly different than the original ones I posted, as I improved the weighting method.
Al MacInnis
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)
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) 
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You could almost be describing the 198889 Penguins... I should say that these estimates are comparing the player to an inseason 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. 
Great work as usual overpass. I look forward to seeing the Mark Howe and Ray Bourque's:)

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.

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In 199091 and 199394, 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 post2001 seasons which are past his prime. These represent only 18% of his regular season games. For comparisons sake, Peter Forsberg has no pastprime seasons included in his estimate. Also, Lemieux's excellent 198889 season and his 199596 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 (200506 was the last season I used for Forsberg). 
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? 
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 8788, and 9293. 
Wonder what Orr or Richards numbers would have been like.

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. 
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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... 
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. 
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 199495.
With Larionov Sharks were 302010, 3.25 GFA, 2.93 GAA Without Larionov Sharks were 3156, GFA 2.375, 3.708 GAA For 199394, Larionov, in his first season with the Sharks, had a +.333 Win Pct, + .875 GFA, 0.775 GAA. 
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Now that's an impact! ;) 
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:

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

I think you should verify your winloss 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 weightedaverage by games missed, since it negates disproportional effects of changes in sample size from season to season.

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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. 
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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. 
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But I'd lean towards random variation. A single blowout might explain the difference. 
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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. 
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Crosby  Career Expected win% w/o (EW%): .617 Actual win% w/o (AW%): .579 Difference: .057 (6.2% decrease) 20062011 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 '9704  91 games missed EW% .592 AW% .593 Diff: +.001 (0.2% increase) Selanne '9401  68 games missed EW% .414 AW% .353 Diff: .061 (17.2% decrease) Forsberg '9704  123 games missed EW% .634 AW% .533 Diff:  .101 (16.0% decrease) Lindros '9300  134 games missed EW% .623 AW% .541 Diff: .082 (13.2% decrease) Messier '8897  76 games missed EW% .573 AW% .414 Diff: .159 (27.7% decrease) Lemieux '8897  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 '9701  45 games missed EW% .534 AW% .389 Diff: .145 (27.2% decrease) 
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