Predicting performance over time using a case study in real tennis

Abstract

It has been predicted that women marathon runners would run as fast as men by 1998, a prediction that was both incorrect and based on rather dubious logic i.e. that world records would progress in a linear manner. This led to the suggestion that a flattened S shape logistic curve was the best fit for analysing world record times but their prediction for the best possible men’s marathon performance was achieved in September 2011. This paper suggests that a simple curve may be more appropriate for most performance data. Hours on court, handicap (55 to 29.1) and world ranking (4072 to 700) were recorded for one Real Tennis player over a period of 15 months. The player’s world rank was plotted over time and hours played with a logarithmic curve proving to be the best fit. This provided an estimate for future performance, which suggested the player would achieve number one in the world after just 474 hours of play. The handicap data for all 7750 players on the Real Tennis database showed that the world ranking is not linearly related to handicap and as such not a valid measure for predicting future performance. Consequently the same procedure was applied to the handicap data and a similar logarithmic curve suggested the player could achieve a handicap of 8 after 10,000 hours of play. 95% Confidence limits were calculated to suggest that after 450 hours (three years of play) the player would achieve a handicap of between 17 and 45. It is suggested that future research should consider the optimum trade off between certainty of prediction and acceptable range for lower and upper limits of performance.