Computer Analysis of Chess Champions

Understanding Distributions of Chess Performances

“…This mode is similar to how Guid and Bratko [5] operated the program CRAFTY to depth (only) 12, and how others have run other programs since. Game turns 1-8, turns where RYBKA reported a more than 3.00 advantage already at the previous move, and turns involved in repetitions are weeded out.…”

“…The errors over a game or player-performance or an entire tournament are summed and divided by the number of moves (those not weeded out) to make the "Average Error" (AE) statistic. Besides including moves 9-12 and using Rybka depth 13 with a [−3.00, +3.00] evaluation range rather than Crafty depth 12 with a [−2.00, +2.00] range, our statistic differs from [5] in not attempting to judge the "complexity" of a position, and in several incidental ways.…”

“…Their main difference from [5][6][7] is the use of Multi-PV analysis to obtain uthoritative values for all reasonable options, not just the top move(s) and the move played. Thus each move is evaluated in the full context of available options.…”

“…-A version, called AE for "average error," of the "average difference" (AD) statistic used by Guid and Bratko [5] (see also [6,7]) to compare world championship matches. An important scaling discovery leads to Scaled Average Error (SAE).…”

Skill rating by Bayesian inference

“…the 'opening' or 'endgame', • the relative skill of contemporary players in different leagues, • the relative skill of players of different eras, • whether a match or game was won by good play or lost by bad play, • whether a player is playing abnormally, suspiciously well and perhaps cheating. In contrast, a few systems have been proposed to assess, rank and rate absolute chess skill [6], [15], [7], [16]. Authors in [15] and in [16] use only the 'error' of move-decisions to calculate mean-error: they do not use the full move-context of the decisions.…”