Using simulations to compare the current Davis Cup ranking system to Elo

TL;DR

The paper compares the Davis Cup ranking system to the Elo rating system using simulations and finds that the Davis Cup method performs well, especially in responsiveness.

Contribution

The study introduces an alternative optimization method for the Elo K-factor that matches the Davis Cup ranking system's performance.

Findings

The Davis Cup ranking system outperforms Elo in responsiveness, a key performance criterion.

An alternative K-factor optimization method for Elo can match the Davis Cup ranking system's performance.

The current Davis Cup ranking system is not outperformed by a typically optimized Elo system.

Abstract

The Davis Cup is the premier men’s team event in tennis, run by the International Tennis Federation and in which over 130 nations compete. It uses a merit-based ranking system that allows nations to gain a pre-determined number of points when they win. The rankings are integral to the competition structure and used in the draws of every round. Therefore, it is essential that the ranking method performs well with respect to required performance criteria of the International Tennis Federation. The Elo rating method is a commonly used method of rating and ranking participants in a competitive exercise and is used by FIFA for the ranking of male and female national teams. The performance of the current Davis Cup ranking method and Elo rating were compared using a simulation of the Davis Cup competition structure. Four criteria were used for the comparison: Finishing Order Correlation, Skill Level Correlation, Responsiveness, and Protection. Such a comparison has not previously been published. The two methods were comparable across three of the criteria, with the Davis cup easily outperforming Elo in responsiveness. Indeed, the Elo method had such poor responsiveness that improved performance may not be fully recognised within a player’s career. An alternative method of optimising the Elo K-factor parameter was developed and this improved the performance of Elo to match the current Davis Cup method. In conclusion, the current Davis Cup ranking method is performing at a standard that cannot be matched by typically optimised Elo but can be matched when an alternative optimisation method is used. Therefore, no evidence was found to suggest that the current Davis Cup ranking method could be improved upon by using Elo. However, alternative K-factor optimisation methods should be considered when applying Elo to a competition.

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