23 March 2009

Basketball, Chess, Scrabble, WoW, and Arpad Elo

Ranking the relative skill and performance of people who play a game is an interesting problem. Physicist and Chess enthusiast Arpad Elo invented a system of ranking the relative skills that is both simple and flexible. Variation of the Elo rating system are used for Baseball, Basketball, Backgammon, Football (American rules and Soccer), Go, Pokemon, Scrabble, World of Warcraft, and many others.

The basis of the system is very simple: Players start with an arbitrary number of points (generally 1000) representing that players' rating. For each scored game played, there is a "trade" of points, with the loser giving some number of points to the winner. The amount traded is scaled so that winning against a higher rated player (one with more points) is worth more than a lower rated player, and vice-versa. Beat a player rates higher than you and you gain more points, and less for a lower rated player. Over repeated games, wins and losses against many opponents, players tend to accumulate points that reflect their ability relative to other players.

March Madness SI Sports Illustrated VaultIf you have any interest in the NCAA Basketball Championship and March Madness, and have ever wondered how they come up with the team ratings, the Elo system is a big part of it. You can find Jeff Sagerin's Basketball (and other) rankings at USAtoday.com, and more rating from Jeff Sagarin at his site.
[Image SI Vault]

A fair criticism of the Elo system is that it is better at rating past performance than it is at predicting games yet to be played. It's good information, but don't count on it to win the office pool for you. For that, you might need a bit of luck.
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