How a Hungarian Physicist Ranked Every Chess Player

Arpad Elo was a physics professor at Marquette and a strong chess player who got tired of arguing about who was better than whom. The US Chess Federation's existing rating method was a mess of subjective tiers. In 1960 Elo proposed something cleaner: model each player as a normal distribution of performance, predict the expected result of any matchup from the gap between their means, and after each game move both ratings by the difference between expected and actual.

The formula sits inside one line. If your expected score against an opponent is 0.7 and you win (actual = 1), your rating goes up by K × 0.3, where K is a tuning constant. Lose, and you drop by K × 0.7. The two players' rating changes are equal and opposite, so the system conserves total rating points. No central authority decides what you're worth. Your last 30 games do.

FIDE adopted it in 1970. From there it spread far past chess: tennis, Scrabble, video-game matchmaking, the original Facemash that became Facebook, the early dating site OkCupid. Anywhere two entities compete head-to-head and someone wants a single number, an Elo variant is probably running underneath.

The weakness is the same as the strength. Elo treats every game as independent and assumes a player's strength is roughly stable. It doesn't know about hot streaks, fatigue, or the fact that you only play opponents inside your bubble. Modern systems — Glicko, TrueSkill, Microsoft's matchmaking math — patch in uncertainty and time decay. They are still arguing with the ghost of a 1960 paper.