Saturday, April 24, 2010

Statistics in Hockey

Note: more of a philosophy piece, and re-posted from Japers' Rink (I claim authorship on J.R. as well).

Statistics is no doubt an important field in sports nowadays. Baseball probably got the head start, as almost every situation can be individualized, but now increasingly in hockey too, we're trying to objectify the game, via statistics. Gabriel Desjardins, for example, runs Behind the Net (blog, stats), a must read. Puck Prospectus also does some good work with statistics, identifying interesting trends.
Gone are the days when goals, assists, and points were the only statistics. Now, not only do we have +/-, shots, faceoffs, and much more via the NHL stats engine, but single game and season Corsi and Fenwick numbers among others.
But how much can we read into statistics?
What exactly is the point of statistics, and how does it relate to the Caps this season? For one, it helps us to determine how much a player should be payed. As an example, I use our favorite Double-Nickel.
I think we can all agree Jeff Schultz, current salary $715k, is a steal, considering his defensive prowess and season-long improvement in all facets of his game. We also all know, however, that plus-minus is heavily misleading, and thus his +50 shouldn't be taken for what it's worth. What should his +/- actually be? +25? +35? And, for negotiating and arbitration purposes, how does this compare to other "comparable" players around the league (for whom plus-minus also needs to be adjusted)?
Schultz's BtN RATING (+/- relative to the team) is second on the Caps, behind Alex Ovechkin, and when you look up and down the list of all players sorted by RATING, Schultz seems to do pretty well (names of note above him are essentially Daniel Sedin and Mark Fistric, but I'm not complaining about Dallas choosing the latter between Washington 2004 late first-round draft choices). Then you could look at his QualTeam, and see he plays with strong teammates (only Ovechkin, Nicklas Backstrom, and Mike Knuble have higher QualTeam's on the Caps), which diminishes the effect of his season achievements no doubt; but on the other hand, his QualComp means he's not exactly playing against fourth lines all the time (and Alex Ovechkin has some pretty stiff competition). And then there's this:
'Quality of Competition' is a flawed statistic because it penalizes good players who play against other good players.
This is definitely a flaw in a "first-order" Quality of Competition calculation. When people calculate Power Rankings in football (or Chess ratings) they run a recursive algorithm so that good players or teams aren't penalized when they play against others with the same skill level. We could calculate a recursive version of Quality of Competition that would solve this problem, but it's computationally cumbersome. Quality of Competition still gives us a lot of insight, particularly into the NHL's few checking lines.
QualComp, like as is quoted, is helpful in assessing players who play similar roles, even on different teams. We hope (and assume) that small differences like system and goaltending will all cancel out. But what happens if a player isn't played in a role that is really comparable to others?
Of course, I'm speaking of the Caps in particular. It's well-known that, while Bruce Boudreau is always cognizant of which line the other team puts on the ice, rarely, if ever, matches forward and defense lines based on what line the other team plays. As such, Schultz probably has a lower QualComp and much higher QualTeam than our eyes--judging him for defensive play--would tell us. The same is true of Mike Green, who continues to receive all kinds of crap about his being a "defensive liability," though luckily from the mass media this has died down (and in fact, some statistics even last season suggested otherwise).
And then we go into the mechanics of some of these +/- based statistics--when you face a guy like Ilya Kovalchuk, it'll likely show up as lesser competition than, say, Alexander Semin, because Kovalchuk has a much lower plus minus and his team is flat out worse. That, however, doesn't mean facing Kovalchuk is any easier.
I know I'm being nit-picky, but it feels like once we start relying on statistics, especially more advanced metrics, too much, then that in itself is being nit-picky and thus nullifies the advantage of metrics that try (and do an excellent, but imperfect) job of accounting for nuances from team-to-team. Why? My theory is that these advanced metrics have to be based on simpler metrics, which are flawed as well. So what do we have to do? Subjectively judge the value of these statistics, because we know they're not 100% accurate (or else we could just use a simulating engine to go through the season, and the NHL could be EA Sports' NHL GM).
Why do we use statistics in hockey, at the end of the day? I get the feeling that we use statistics to try and objectively judge what we see on the ice, and judge what we don't see as well (case in point: Schultz at his best when invisible), especially to the more untrained hockey mind --basically anyone not currently coaching/playing professionally. So, in other words, are we using statistics as replacements for our eyes? To remove subjectivity, especially in what we see? There is some involved in judging statistics, and some in judging play on television or at a game. So we're back at square one.
I'm not arguing that statistics are worthless--they're quite helpful, since we can't see everything, and the teams feel the same way, so statistics are not crap by any means--but they're also not all-encompassing. They cannot account for "intangibles" or, quite simply, for players being human. They are prone to external effects just as we are. We hope that over time (larger sample size) these effects cancel each other out, but not always. Is it so ridiculous that San Jose does feel some extra pressure, notwithstanding what the players, coaches, and management say?
That takes us into small sample size issues as well. You could say Jaroslav Halak's not-up-to-par play in Capitals-Canadiens, Games 2 and 3, was a fluke of only two games (small sample size). That it was luck. Or, that, through a combination of unseen factors, it is reality. The same applies to the Caps' struggling power play in the 2010 postseason, as of this writing. Could they be trying to be too cute? Is Montreal's PK just well suited to disrupt the Caps' power play? And how about that Montreal road power play which, during the regular season, was north of 27%, more than 10% better than at Centre Bell? Is that a fluke of a single season, or is there some unforeseen factor.
I have to think that it's the latter--some factor that occurs maybe just this season, or maybe just over two seasons, but nevertheless occurs. While this factor could be considered a fluke, it's not unreasonable to think that, if Montreal (to go with the power play question) played this season thousands of times, with the same external factors, then the same result would occur. These things may not "regress to the mean" instantly, or even at all. The same is true of "intangible" assets we commonly refer to like maturity, experience, leadership, and so on. While statistical production could be all over the place, will these intangibles ever go away? I doubt it. There's a reason they are "intangible" because they are what they are--unmeasurable. We can only see correlations (like the Caps' record with Ovechkin as captain) but cannot see causation through statistics. That brings us back to the eyes.
To head back to Schultz--so far we've judged the following: Schultz's basic stat line is pretty solid. His advanced stat line (linked to above) is pretty decent too. He's unquestionably doing his job out there every shift on the ice--keeping pucks out of his net and helping to put them into the other net, one way or another. How much though are his stats caused by his teammates/system/goalies, and how much does he contribute in terms of goals for and against? What intangibles does he have, and how much are they worth? The stats probably point to something more than he's getting now. How much is a guy like Alexander Semin, maddeningly inconsistent (until the playoffs, two of the last three seasons) but with comparable upside to Ovechkin offensively and Datsyuk defensively, worth? Maybe less than the $6 million he will get next season. And despite our best efforts to judge a guy like Semin, we really just base his play on our eyes, right? And while Tom Poti probably isn't worth his $3.5 million cap hit, he does have some "special powers" at even strength, even though our eyes tell us otherwise, right? And Bruce Boudreau, better hockey mind than any of us, must have some reason we can't see--statistically or visually--for having him play so much on the PK when his PK numbers are worth "grilling," right?
My message to George McPhee and every other GM, and every hockey fan: go right ahead and use statistics. In many cases they are clear enough that any fluke reasonably fathomable will not change the result--that Mike Green and Jeff Schultz are a strong even strength defense pairing, for example. But make sure you do a thorough visual analysis of the player as well. Otherwise, you could miss statistical "flukes" (that are actually recurring, unquantified factors) that lead to a player having a statistic unrepresentative of his actual playing ability, and hence not only do you read too much into statistics and begin to miss the realities of hockey, but your analysis also comes across as mathematical hubris.
It is difficult to assess every player visually, in fact impossible I'd say, and often times, for the sake of one discussion, watching hours of highlights or spending hours watching hockey every day and night to simply be able to comment on a one-time discussion is probably not time well spent. The solution? Field trips. Reading about other teams. Judging situations for yourself with as objective an eye as possible, not simply going by what the "experts" say. See this comment history (no wonder he knows so much about the Caps and can comment intelligently, or even stick up for a much-maligned player (and again) on his "second" team). Of course, to hold intelligent discussions about any topic will still be difficult, but at least it won't be embarrassing (notice to whose comments many of those are replying). And that's what GMGM's task is this offseason--judge every potential free agent on the market and see if they can fit on the Caps. Quite difficult indeed.
Imperfect analogy, I realize, but as an online translator will translate words from one language to another, but imperfectly, statistics translate a sport into a page of numbers...imperfectly. Just as each online translator comes with a disclaimer--"is not a substitute for a real (human) translator" or something similar--statistics are not a substitute for a real hockey mind (again, something which most, and maybe all, of us are not). They are most valuable to assess trends you miss, but when, later, you look for these trends (like Jeff Schultz's invisibility), you see them. So statistical analysis must go hand in hand with visual analysis. Always.
At the end of the day, the only statistic that truly matters is team wins. Everything else simply builds to that ultimate goal, of sixteen wins between the end of the regular season and mid-June.
Here's to thirteen more of those. Go Caps.

(My apologies for jumping around with ideas in this FanPost. If it's difficult to follow, outline in the comments and I'll try to restructure to clear it up)

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