Statistical analysis of the effect of the current, potential and proposed rules of a game in tennis

TL;DR

This paper uses mathematical modeling to analyze how different tennis rules affect game outcomes, proposing a modification to increase unpredictability and spectator excitement.

Contribution

It introduces formulas based on random walk models to evaluate rule impacts and suggests a specific rule change to enhance game unpredictability.

Findings

Proposed a rule modification limiting second serves after faults.

Quantified how rule changes affect winning probabilities and break point occurrences.

Validated models against ATP statistics for top players.

Abstract

With the aid of mathematical modelling (basic tool is the random walk with absorbing barriers) we derive subsequent formulas to study the effect of different versions of possible rules. For different rules the probability of winning a game, the probability of break point occurrence, the mathematical expectation of the number of rallies (points) and, the mathematical expectation of the number of break points in a game are expressed. We check these rules against ATP statistics for the Top-200 men players. In conclusion, we suggest a slight but essential modification for the rule of a tennis game, namely , second service ( in case of a first service fault) is to be allowed only at the first three points (rallies). This would partially preserve the traditions (server has an advantage in the modern game) and at the same time it would reduce the predictability of the game, significantly increasing in this way the excitement for the spectators.