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June 28, 2006

Lies, Damned Lies

We are Elo?

by Nate Silver

I’m one of those people that likes to feign knowledge about pretty much any topic that might come up in a conversation. A lot of the time, this requires nothing more than an Ozzie Guillen-like shamelessness for talking myself into and out of trouble. But a little bit of research goes a long way. In this spirit, I stumbled across this website, which applies an Elo Rating system to football… err, soccer teams. This is some pretty cool stuff. Not only is every national team in the world rated, but you can find its rating for any date in the past century. If you wanted to know, say, whether Qatar or Bahrain would have been favored in a match played in August, 1971, you could find that out (answer: Qatar, but only by a hair).

Elo Ratings (apparently pronounced E-L-O, as in the band that has inspired so many hapless karaoke renditions over the past thirty years) will be familiar to those of you who have played chess, backgammon, or Scrabble competitively. Their goal is very simple: to provide an objective and reliable measure by which the strength of two opponents can be compared. A backgammon player with a 1900 Elo Rating, for example, would be expected to beat a backgammon player with a 1700 rating around 76% of the time.

Naturally, if an Elo Rating system can be applied to soccer, then it can be applied to baseball as well. Just as naturally, you might ask why do we need another way to rate baseball teams, when we already have cool features like the Adjusted Standings Report? For one thing, Elo Ratings are extremely elegant. They are able to incorporate a lot of information--things like strength of schedule and run differential--and boil it down to one simple number. More substantively, however, Elo Ratings strive to answer a different question than something like Pythagorean records. Pythagorean records and their brethren give us an assessment of how well a team has played over a given time frame (usually the span of one particular baseball season). Elo Ratings, on the other hand, are designed to give an assessment of how strong a team is today, right now, at this very moment–or at any other moment in time throughout history.

This is a distinction that comes more or less naturally to soccer fans. National soccer clubs don’t really have seasons; they play in various tournaments like the World Cup and the Olympics, but otherwise it’s a big hairy mess of "friendlies" (one-off matches), qualifiers, and various minor regional tournaments. It’s assumed that a team’s form changes organically over time, as various players age, retire, get injured, or are brought up from the junior ranks.

Baseball fans, meanwhile, are rather hung up on the concept of the season. But the season is not sacred. Roster composition changes over the course of the year as players are injured, acquired in trade, promoted from the minor leagues, and so forth. A young team like the Marlins can reasonably be expected to be stronger in the latter part of the year than the earlier, while the opposite is true for a veteran club. And, perhaps, there are some karmatic factors at work. The Orioles played .457 ball last year--but would you really stake them at those odds in a game played last September? Can we acknowledge, perhaps, that the 2002 A’s really were playing better baseball during their 17-game winning streak in August and September than they were in April? Team strength is more dynamic than it’s usually made out to be.

You can find the formula for the soccer Elo Ratings system here. Although the math behind the Elo Ratings system is not complicated in itself, it quickly became apparent that some of the parameters included in the soccer version of the ratings would need to be tweaked for baseball. In particular, the following questions need to be resolved: