How injuries affect performance

by James Mirtle on Mar 22, 2009 4:02 PM CDT in Statistics Comment 20 comments

I had some great stuff sent into me on the heels of this post earlier in the week on the man games lost to injury totals, including this chart from Kyle Joecken, a graduate student in mathematics at The Ohio State University:

Injury_chart_medium

Essentially what this shows is the performance of teams and their injury totals from 2005-06 to 2007-08 (he did not include this season's projections). On average, teams during this period that had 100 man games lost to injury finished with about 10 more points than those that had 300.

And it's been virtually impossible to have a great season with more than 300 man games lost to injury. (This season's Capitals team will likely be only the second to top 100 points postlockout.)

Here's some geek speak from Kyle on this: "The equation for the line was y = -.0528x + 103.19. The R^2 value is .1018."

His conclusion based on this data (and ignoring the fact that some injuries are much, much more devastating than others)?

"Basically, you lose one point for every 20 man-games lost."

Of course, that's all depending on averages, etc., and the correlation isn't that high, but if you apply that conclusion to a team rocked by injuries like the Islanders (on pace for an insane 566 man games lost to injury), they'd finish the season with about 28 more points than they're on pace for.

Or right about eighth or ninth in the Eastern Conference.

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Did he test the correlation coefficient for statistical significance? I don’t see a p-value listed. Shame on you, Kyle. The correlation isn’t a strong negative value, but I’d be curious about the p-value. It would likely need to be a non-parametric test, but I don’t have my stats texts with me so I don’t remember which one. Dang.

Seriously, cool graph. Score one for the math nerds. :)

"A vacuum is a hell of a lot better than some of the stuff that nature replaces it with." -- Tennessee Williams

by Baroque on Mar 22, 2009 5:45 PM CDT reply actions 0 recs

"Of course, that’s all depending on averages, etc., and the correlation isn’t that high, but if you apply that conclusion to a team rocked by injuries like the Islanders (on pace for an insane 566 man games lost to injury), they’d finish the season with about 28 more points than they’re on pace for.

Or right about eighth or ninth in the Eastern Conference. "

Yes, but the alternative you’re comparing to here would be zero man-games lost, which is an absurd scenario. The more true comparison would be to an average number of man games lost. That would probably be closer to 13 or 14 points lost due to injury, rather than 28, which is still a huge amount, but far from putting them in the playoff picture.

In fact, one might be inclined to say the Isles are actually lucky to have been hit by such a crazy number of injuries in this, a year when they were gonna be near the bottom anyway, rather than in a year where they would have competed. Little PR is lost going from really bad to the worst in the league, and they get the best possible draft situation as a bonus.

by Costa24 on Mar 22, 2009 6:13 PM CDT reply actions 0 recs

All good points. Teams have finished with as few as about 50 man games lost, so maybe what we should say is that, best injury case scenario possible, the Isles could make up 25 points in the standings and finish in 10th or whatever.

by James Mirtle on Mar 22, 2009 7:43 PM CDT up reply actions 0 recs

In fact, one might be inclined to say the Isles are actually lucky to have been hit by such a crazy number of injuries in this, a year when they were gonna be near the bottom anyway, rather than in a year where they would have competed.

That’s certainly the argument I’ve been going with. They weren’t going to fix injuries by making trades anyway, so this has provided: 1) a chance at a good pick, 2) PR cover for a bad season, and 3) a chance to see more of their kids than they otherwise would have even in this rebuilding season.

Lighthouse Hockey: SBN's New York Islanders blog with hip issues.

by Dominik on Mar 23, 2009 11:15 AM CDT up reply actions 0 recs

Cum hoc ergo propter hoc -man games lost to injuries is not a sufficient condition to explain performance-too many other factors including relative performance of replacement players(Steve Mason for Pascal LeClaire etc), injury status of opponents (see above) etc,etc

by Big Picture Guy on Mar 22, 2009 7:07 PM CDT reply actions 0 recs

There’s definitely a low correlation, but a non-existent one? I don’t think so.

by James Mirtle on Mar 22, 2009 7:44 PM CDT up reply actions 0 recs

-0.10 is pretty close to non-existent. Look at it without the line and it looks like someone fired some birdshot at the monitor.

SNN Sports - A theoretical Oilers blog (i.e. theoretically, I write stuff there)

by Doogie2K on Mar 22, 2009 8:12 PM CDT up reply actions 0 recs

Not exactly correct, but a very, very common error. That was why I asked if he did a non-parametric test to determine statistical significance.

A correlation coefficient of -0.10 is definitely weak, in terms of explanatory power – a (very) rough way of thinking of it is that the variability in points is the product of many factors, all of which add up to 1.00 (or 100). Variation in the number of man-games lost to injury “explains” roughly 0.10 (or 10) of the variability in the points aquired. This is not a negligible proportion – a drug that was 10% better at treating a disease might be worth prescribing, all other things (cost, side-effects, ease of use, etc.) being equal, but iff the difference when compared to comparable treatments was statistically significant.

Without a p-value, it really can’t be evaluated properly. Statistical significance and it is an interesting (although minor) part of the picture. If it is statistically insignificant, however, it might even be more interesting because it would mean that the number of man-games lost, despite everything that seems logical at first glance, doesn’t have a substantial effect on the points a team has by the end of the season.

I hope that makes sense to non-stats people. Statistical significance of a weak correlation, or statistical insignificance of a strong correlation, are probably some of the most difficult ideas to get a brain around, because it seems intuitively obvious that a weak relationship can’t really matter, and a strong one simply must be important, and that isn’t always the case.

"A vacuum is a hell of a lot better than some of the stuff that nature replaces it with." -- Tennessee Williams

by Baroque on Mar 22, 2009 8:26 PM CDT up reply actions 0 recs

edit

Please put a percent sign after the 100 and 10 in parentheses in the second paragraph. Don’t know what happened there.

And the “iff” is an abbreviation for “if and only if.” I had no intention of being intentionally obtuse.

"A vacuum is a hell of a lot better than some of the stuff that nature replaces it with." -- Tennessee Williams

by Baroque on Mar 22, 2009 8:29 PM CDT up reply actions 0 recs

You caught me; you’d think I’d remember that subtle distinction having just taken a research methods class last semester. It’s a (very) weak correlation, but I guess it can still theoretically be statistically significant. Still, I’ve found that r2 values that low seldom wind up holding statistical significance, at least in the data I’ve worked with, though I’ll grant that the samples I’m working with might just be too small: I’ve never had an n greater than about 30, whereas this is an n of 90.

SNN Sports - A theoretical Oilers blog (i.e. theoretically, I write stuff there)

by Doogie2K on Mar 22, 2009 11:11 PM CDT up reply actions 0 recs

Hah! :)

It’s not very common, but I mentioned it because I have seen data sets with a weak, but statistically significant correlation. But biology can be weird beyond belief like that sometimes.

"A vacuum is a hell of a lot better than some of the stuff that nature replaces it with." -- Tennessee Williams

by Baroque on Mar 23, 2009 5:58 AM CDT up reply actions 0 recs

I didn’t think there’d be much of a correlation at all, to tell you the truth. The man games lost figures are just too random the way they’re calculated.

by James Mirtle on Mar 22, 2009 8:46 PM CDT up reply actions 0 recs

Would it improve the correlation/calculation if the man games lost figures were weighted by the line of the the person in question? I don’t know what the weight would be, but that would reflect the fact that your first line center’s injury is a bit more valuable than your 8th best defenseman. I realize this isn’t a perfect measure, but it refine the current calculations and possibly reduce the appearance of buckshot on a screen (kudos to whoever used that terminology, I like it).

Anyway, just a thought from a huge nerd.

John Madden told me 90% of the game was half-mental...

by TheK-GunNeedsReloaded on Mar 22, 2009 11:33 PM CDT up reply actions 0 recs

Good luck quantifying 1,000+ individual players like that though. It’s just too tough.

by James Mirtle on Mar 22, 2009 11:52 PM CDT up reply actions 0 recs

Aside from sheer scale, theres also the stickier issues of exactly how to figure that stuff out too. For example, is Crosby Pittsburgh’s first or second line center? Obviously, he and Malkin should have a similar weight, being similar caliber players. Does Pitt just not have a second line weighting then, and go straight to a third? Other problems would be that there are players who may move around lines a lot, or coaches who change the lines a lot, and there is the fact that some teams use a really good defensive group for a 4th line and use them consistently, while other teams may not have as good a quality of line. Thus their 4th line isn’t worth as much. Isn’t Sami Pahlsson worth more than whoever is skating 4th line for the Thrashers?

If you were to do something where you took a players career pts/game and then multiplied that by games missed to find a value of some sort for that player, that would be a step in the right direction, but leaves out any other contribution, like defensive play, faceoffs, etc. etc. It would presumably be possible to assign values to all of these contributions, if you could come up with stats to rate these various contributions (like Mirtle has done with the Rod Langway award), and then combine all of this stuff into some sort of cumulative formula to spit out a total value on a per game basis for the loss of a certain player.

Taking a stab at creating such a formula would be a pretty messy deal, but it wouldn’t surprise me if Mirtle or MC79 or someone tried it. Even an attempt though would probably give more meaningful numbers than a straight man-games missed state though.

by IAmJoe on Mar 23, 2009 1:08 AM CDT up reply actions 0 recs

Just to add on to this- maybe weighing it by ice time would be more helpful?

John Madden told me 90% of the game was half-mental...

by TheK-GunNeedsReloaded on Mar 23, 2009 1:05 PM CDT up reply actions 0 recs

Maybe weighting by salary. There are a lot of other variables, but at least it has the virtue of being a known quantity, and in most cases if a guy making $5 million a year is out of commission it impacts the team more than a $1 million player on the shelf for the same amount of time.

It’s still sloppy, but otherwise it would be so subjective that I can’t see how it would work at all.

"A vacuum is a hell of a lot better than some of the stuff that nature replaces it with." -- Tennessee Williams

by Baroque on Mar 23, 2009 6:02 AM CDT up reply actions 0 recs

But then you have guys like Briere, whose salary (and subsequent LTIR credit) was actually beneficial to Philadelphia, especially considering the players that were called up.

It comes down to a simple question: were Briere’s replacements better than having Briere?

Shut up when you're talking to me!

by Afino on Mar 23, 2009 10:12 AM CDT up reply actions 0 recs

Mentioned above

But the error bars on this line look to big to make heads-or-tails of this. I hate criticizing anyone from tOSU (my alma matter), but if you’re going to do a curve fit, like this one, you need error bars/error lines and a ± kind of rating. Someone with 390 man-games lost could have anywhere between 57 and 101 points. That’s not much of a trend.

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by Jibblescribbits on Mar 23, 2009 1:29 AM CDT reply actions 0 recs

Nerds

Every last one of you. And I love it ;)

Sorry for the half-post just above. Accidentally hit Enter.

by ShaneG on Mar 23, 2009 1:07 PM CDT reply actions 0 recs

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