# Introducing Fairness and Diversification in WTA and ATP Tennis Tournaments Generation

## TL;DR

This paper proposes a novel approach to generate fair and diversified tennis tournament schedules by optimizing seed placement and match distribution, reducing early H2H encounters and unbalanced pairings.

## Contribution

It introduces a clustering optimization model and a hybrid algorithm to improve fairness and diversity in tournament scheduling, validated on real Grand Slam data.

## Key findings

- The approach reduces early H2H matches.
- It balances first-round pairings among unseeded players.
- The hybrid algorithm performs efficiently on real data.

## Abstract

Single-elimination tournaments are the standard paradigm both for the main tennis professional associations. Schedules are generated by allocating first seeded and then unseeded players with seeds prevented from encountering each other early in the competition. Besides, the distribution of pairings in the first round between unseeded players and seeds for a yearly season may be strongly unbalanced. This provides often a great disadvantage to some "unlucky" unseeded players in terms of money prizes. Also, a fair distribution of matches during a season would benefit from limiting in first rounds the presence of Head-to-Head (H2H) matches between players that met in the recent past. We propose a tournament generation approach in order to reduce in the first round "unlucky" pairings and replay of H2H matches. The approach consists in a clustering optimization problem inducing a consequent draw within each cluster. A Non-Linear Mathematical Programming (NLMP) model is proposed for the clustering problem so as to reach a fair schedule. The solution reached by a commercial NLMP solver on the model is compared to the one reached by a faster hybrid algorithm based on multi-start local search. The approach is successfully tested on historical records from the recent Grand Slams tournaments.