Understanding Distributions of Chess Performances

Abstract

Abstract. This paper studies the population of chess players and the distribution of their performances measured by Elo ratings and by computer analysis of moves. Evidence that ratings have remained stable since the inception of the Elo system in the 1970's is given in several forms: by showing that the population of strong players fits a simple logistic-curve model without inflation, by plotting players' average error against the FIDE category of tournaments over time, and by skill parameters from a model that employs computer analysis keeping a nearly constant relation to Elo rating across that time. The distribution of the model's Intrinsic Performance Ratings can hence be used to compare populations that have limited interaction, such as between players in a national chess federation and FIDE, and ascertain relative drift in their respective rating systems.Note.

A Comparative Review of Skill Assessment: Performance, Prediction and Profiling

“…The last caveat on the AD method anticipates a key finding by Regan [14,22] that average-difference correlates with the absolute value of the position, see Figure 1. This may be because (a) humans are only sensitive to the relative values of moves, (b) humans with an advantage tend to avoid the risk associated with the sharpest tactical plans, and/or (c) engines see the win more clearly when the position is relatively decisive already.…”

“…No information about the clock-regime, move number, material, relative ELO difference or clock-times is considered, although there is evidence of the errorinducing zeitnot effect as players approach move 40 under classic conditions [14].…”

“…Table 1 highlights some games analysed with STOCKFISH 3.0. [14,22,23] identifies the BP i which best fits the observed play: it is essentially frequentist. The probability of BP(c i ) playing moves m 1 -m k is p(c i )  q j,i and c i is found to maximize p(c i ).…”

Measuring Level-K Reasoning, Satisficing, and Human Error in Game-Play Data

“…These values are scaled as described and justified in [20], [21], [26]; the details do not concern us here. The difference in optimality of m i at depth d is denoted by…”

Psychometric modeling of decision making via game play

“…This could be done with any set of chess positions used as a test, but having them come from one side in one game increases the popular element of "being in the game" and executing strategies across positions. The technical results of this and previous papers [1], [2] can be viewed as furnishing scientific scoring based on actual games played by grandmasters, masters, experts and so on, for evaluating moves made under real competition rather than "solitaire" or in simulations.…”