{"id":2342,"date":"2014-01-27T09:57:05","date_gmt":"2014-01-27T14:57:05","guid":{"rendered":"http:\/\/2d823b65bb.nxcli.io\/?p=2342"},"modified":"2014-01-27T09:57:05","modified_gmt":"2014-01-27T14:57:05","slug":"first-move-advantage-in-chess","status":"publish","type":"post","link":"https:\/\/www.robweir.com\/blog\/2014\/01\/first-move-advantage-in-chess.html","title":{"rendered":"First Move Advantage in Chess"},"content":{"rendered":"

The Elo Rating System<\/h3>\n

Competitive chess players, at the amateur club level all the way through the top grandmasters, receive ratings based on their performance in games.\u00a0\u00a0 The ratings formula in use since 1960 is based on a model first proposed by the Hungarian-American physicist Arpad Elo<\/a>.\u00a0 It uses a logistic equation to estimate the probability of a player winning as a function of that player’s rating advantage over his opponent:<\/p>\n

$latex E = \\frac 1 {1 + 10^{-\\Delta R\/400}}&s=3$<\/p>\n

So for example, if you play an opponent who out-rates you by 200 points then your chances of winning are only 24%.<\/p>\n

After each tournament, game results are fed back to a national or international rating agency and the ratings adjusted.\u00a0 If you scored better than expected against the level of opposition played your rating goes up.\u00a0 If you did worse it goes down.\u00a0 Winning against an opponent much weaker than you will lift your rating little.\u00a0 Defeating a higher-rated opponent will raise your rating more.<\/p>\n

That’s the basics of the Elo rating system, in its pure form.\u00a0 In practice it is slightly modified, with ratings floors, bootstrapping new unrated\u00a0 players, etc.\u00a0 But that is its essence.<\/p>\n

Measuring the First Mover Advantage<\/h3>\n

It has long been known that the player that moves first, conventionally called “white”, has a slight advantage, due to their ability to develop their pieces faster and their greater ability to coax the opening phase of the game toward a system that they prefer.<\/p>\n

So how can we show this advantage using a lot of data?<\/p>\n

I started with a Chessbase database of\u00a0 1,687,282 chess games, played from 2000-2013.\u00a0\u00a0 All games had a minimum rating of 2000 (a good club player).\u00a0 I excluded all computer games.\u00a0\u00a0 I also excluded 0 or 1 move games, which usually indicate a default (a player not showing up for an assigned game) or a bye.\u00a0 I exported the games to PGN<\/a> format and extracted the metadata for each game to a CSV file via a python script.\u00a0 Additional processing was then done in R.<\/p>\n

Looking at the distribution of ratings differences (white Elo-black Elo) we get this.\u00a0 Two oddities to note.\u00a0 First note the excess of games with a ratings difference of exactly zero.\u00a0 I’m not sure what caused that, but since only 0.3% of games had this property, I ignored it.\u00a0\u00a0 Also there is clearly a “fringe” of excess counts for ratings that are exactly multiples of 5.\u00a0 This suggests some quantization effect in some of the ratings, but should not harm the following analysis.<\/p>\n

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The collection has results of:<\/p>\n