Probabilistic models comparing Fast4 and traditional tennis

Abstract

Tennis matches are hierarchies made up of sets containing games which, in turn, contain points. Traditional tennis games and tiebreakers could theoretically be infinite in length because a player needs to be at least 2 points ahead of the opponent to win. Fast4 tennis is a newer format of tennis that has been used at a number of levels of the sport including professional tennis where it has been used in Next Generation Finals events since 2017. The purpose of the current investigation is to compare the traditional tennis format to Fast4 tennis in terms of the probability of different players winning matches and the duration of matches. Probabilistic models of Fast4 tennis games and tiebreakers were developed. These models allowed the probability of winning games and tiebreakers to be compared between the two formats of tennis for a range of probabilities of players winning points. The models were then used within a series of simulations to determine the probability of winning sets and matches as well as the durations of games, tiebreakers, sets and matches in the two formats. Each component of the two formats of tennis was simulated 100,000 times revealing a reduced impact of serve, greater chance of upsets and shorter matches in Fast 4 tennis than in traditional tennis. The probability of players of differing abilities winning matches as well as the duration of tennis matches should be considered by those making decisions on the format of matches to be applied in tennis tournaments as well as by those preparing to compete in such tournaments.

Probability of winning and match length in Tiebreak Ten tennis

“…Equation (3) represents the probability that Player A wins their own service game in Fast4 tennis (Simmonds, & O'Donoghue, 2018). Equation (3) only differs from equation (1) for traditional tennis by replacing pA 2 / (1 -2pAqA) with pA because only one point will be played after the score reaches 3-3.…”

“…Equation ( 4) represents the probability of Player A winning a tiebreak in Fast4 tennis where they serve first in the tiebreak (Simmonds, & O'Donoghue, 2018). As in traditional tennis, both players serve during a Fast4 tiebreak.…”

“…The probability of Player A winning the Tiebreak Ten match is compared with the probability with which they win a best of three traditional sets match (with tiebreaks to 7 at the end of each set if required) and the probability of winning a best of five Fast4 sets match. This comparison used the models of Croucher (1986) for winning traditional games, Newton and Keller (2005) for winning a tiebreak to 7 points and Simmonds and O'Donoghue (2018) for winning Fast4 games and tiebreaks to 5. This was done for a range of pA values from 0.5 to 0.9 in steps of 0.01 and pB values of 0.5, 0.6 and 0.7.…”

“…Fast4 tennis has now been introduced at the Next Generation Finals by the Association of Tennis Professionals (ATP) and International Tennis Federation (ITF). The probability of winning and the duration of Fast4 tennis matches has been investigated (Simmonds, & O'Donoghue, 2018). It is important to continue this research as further developments take place in tennis.…”

“…Therefore, there is no value in comparing the durations of these different forms of tennis within the current investigation. Furthermore, the duration of traditional tennis matches and Fast4 tennis matches has already been researched (Simmonds, & O'Donoghue, 2018). However, there is still a need for information on the duration of Tiebreak Ten matches.…”