On the ranking of a Swiss system chess team tournament

TL;DR

This paper proposes a family of scoring procedures for ranking Swiss system chess team tournaments, highlighting the advantages of the least squares method over official rankings through case studies and various evaluation metrics.

Contribution

It introduces a new ranking approach based on paired comparison methods, especially advocating for the least squares method, and demonstrates its effectiveness with real tournament data.

Findings

Least squares ranking shows higher retrodictive accuracy.

Ranking results are more stable and robust.

Differences from official rankings are systematically analyzed.

Abstract

The paper suggests a family of paired comparison-based scoring procedures for ranking the participants of a Swiss system chess team tournament. We present the challenges of ranking in Swiss system, the features of individual and team competitions as well as the failures of the official rankings based on lexicographical order. The tournament is represented as a ranking problem such that the linearly-solvable row sum (score), generalized row sum, and least squares methods have favourable axiomatic properties. Two chess team European championships are analysed as case studies. Final rankings are compared by their distances and visualized with multidimensional scaling (MDS). Differences to the official ranking are revealed by the decomposition of the least squares method. Rankings are evaluated by prediction power, retrodictive performance, and stability. The paper argues for the use of least squares method with a results matrix favouring match points on the basis of its relative insensitivity to the choice between match and board points, retrodictive accuracy, and robustness.