Anyone for chess? Analysing chess ratings above high thresholds

TL;DR

This paper develops statistical models to analyze the distribution of top chess ratings, focusing on the extreme upper tail of the rating distribution among active players.

Contribution

It introduces new models and tools for analyzing high-threshold data and applies them to FIDE chess ratings to understand the distribution of top players.

Findings

Different models are needed for analyzing the top percentile of ratings.

Small differences in variance can explain rating gaps among the very best players.

The study provides insights into the distribution of elite chess ratings.

Abstract

Suppose some cleverness score parameter is sufficiently interesting to be defined and then measured, perhaps for different strata of specialists or for the broader population. Such phenomena could have Gaussian distributions, when it comes to all players in a stratum, but when interest focuses on the very tails, for the top few percent, those above certain high thresholds, different models are called for, along with the need to analyse such based on the listed top scores only. In this note I develop such models and tools, and apply them to the top-100 and above 2100 points lists for regular chess ratings, for the currently active 14671 men and 753 women, as given by the FIDE, January 2026. It is argued that even when two or more distributions have close to identical expected values, or medians, even smaller differences in variance may explain gaps for the few very best ones.