Friday, October 31, 2008

The Worst Statistic In Sports

Could any statistic in sports be less useful than the plus-minus system in hockey?

Editorial Note: Season stats used in this article are for the 2007-08 season. Career stats are current as of October 31, 2008.
For those who aren’t familiar: when a hockey player scores a goal (not counting power-play goals), everyone on the ice at the time receives a “plus one”. When a goal is scored against his team, everyone receives a “minus one”. In other words, a player on the ice for every goal in a 3-2 victory would be +1 for the game. If he was on the ice for every goal of a 6-2 loss, he would be -4.

Hockey, like other sports, has a hard time translating defensive superiority into statistical excellence. It has no sacks, steals or put-outs. So, until stats like “hits” and “takeaways” were introduced a couple of years ago, a player’s plus-minus rating was the gold standard for evaluating his defensive play.

But is plus-minus really a reflection of a player’s defensive skill? Here are three reasons to think not:

1) Typically, the league’s top players face off against one another throughout the game. First lines are often matched against first lines, especially on balanced squads like San Jose and Detroit. This spells plus-minus disaster for players like Ilya Kovalchuk (-12) and Olli Jokinen (-19), who have few high-scoring teammates. In a typical Coyotes game, Jokinen will be expected to carry his team offensively at the same time that the opposition’s highest-scoring players are on the ice; naturally, Jokinen will end up on the losing end of that equation most of the time.,. regardless of how well or poorly he plays.

2) Plus-minus reflects team play, not individual play. Teams like Tampa Bay (-46) and Los Angeles (-33) are horrid on defense, and players for those squads will naturally have low plus-minus ratings. But are we truly to believe that these teams’ defensive stalwarts are inferior to their counterparts playing for the division leaders? That is, can Jack Johnson (-19) really be that much worse Doug Murray (+20)?

3) The Dan Cloutier Effect. No matter how the defense plays, not all goalies are created equal.

What does all of this mean in real-life terms? Well, let’s look at the past few winners of the Selke Trophy, awarded to the league’s best defensive forward. I’ve matched them up with a defensively-challenged teammate for the sake of illustrating how dramatically a player’s +/ is affected by circumstances (such as defensive assignments, offensive opportunity, line selection, etc.):

Kris Draper (Selke winner): +2 vs. Valtteri Filppula: +16
Jere Lehtinen (3-time Selke winner): +9 vs. Mike Ribeiro: +21
Rod Brind’Amour (2-time Selke winner): even vs. Chad LaRose +6
Michael Peca (Selke winner): -1 vs. Sergei Fedorov (2-time Selke winner): -2 vs. Curtis Glencross: +5

Last season, of course, Pavel Datsyuk won the Selke with a remarkable +41. Datsyuk has an aggregate +110 since 2005... the previous season he was -2.

And lest we believe that these numbers are the result of statistical flukes or oddball circumstances, check out these CAREER +/ totals for a few suprises:
Wayne Gretzky: +518
Slava Kozlov: +122
Henrik Sedin: +74
Martin Straka: +67
Paul Kariya: +36
Pavel Bure: +42
Erik Cole: +9
Rod Brind’Amour: +8
Chris Drury: +7
Jay Bouwmeester: -26
Shane Doan: -29
Ed Jovanovski: -46
Trevor Linden -64
Olli Jokinen: -70

It’s pretty clear what the guys at either end of the list have in common -- their defensive ability has an inverse relationship with their career +/-.

The stats bear it out: The +/- is useless for any player-to-player comparison, even within the same pool of teammates. Career +/- is not even worth recording, because it is absolutely arbitrary.

Until the NHL can conceive of a more complex, "adjusted" statistic (the QB Rating being an example), it’s time for the NHL to ditch this dinosaur and replace it with meaningful defensive statistics such as hits, blocked shots, and takeaways.

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The Bastahd said...

The problem is, with hits and takeaways they are a purely subjective statistic. What qualifies as a hit is left to the discretion of the arena game monitor and therefore has considerable variance. For instances, last season Dustin Brown of the Kings led the league with 311 hits, 60 ahead of Trent Hunter (NYI) and 90 ahead of Zdeno. Are we really to believe this Kings player had so many more hits than everyone else? Or was his total merely padded by a generous game monitor in LA? Statistically speaking, you can adjust the values to make his hit total 251 which puts him closer to Hunter's 246 and Zdeno's 232.

To further illustrate the problem, consider that the top two teams in hits were Montreal (2007) and NYR (2137), miles ahead of tough teams like Anaheim (1619) and Boston (1593)... are we really to believe MONTREAL outhit two very physical teams by over 400 hits last season?

dstaples said...

You may be interested in this, another attack on plus/minus, from a different angle . . .

Anonymous said...

great work, have you seen the Corsi numbers that Stanley Cup of Chowder dug up?

Nuuuuugs said...

Thought you might like this one from

Question No. 2: Which is the dumbest stat in hockey - the fact that assists have the same value as goals, giveaways, plus/minus or shooting percentage?

John Tortorella: Plus/minus. It's probably the most talked-about stat and probably the most useless stat. Too many variables come into play here with coaches putting players into different situations in a game, other players making mistakes that cost you, or bad goals. There's so many different things that come into play. It's a useless stat.