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IMA Journal of Management Mathematics Advance Access originally published online on August 25, 2008
IMA Journal of Management Mathematics 2009 20(2):147-158; doi:10.1093/imaman/dpn021
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© The authors 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

This article appears in the following IMA Journal of Management Mathematics issue: Special Issue Mathematics in Sport [View the issue table of contents]

Predicting score difference versus score total in rugby and soccer

Raymond T. Stefani{dagger}

Department of Electrical Engineering, California State University, Long Beach, CA 92630, USA

{dagger} Email: Raystefani{at}aol.com

Received on 8 August 2007. Accepted on 28 July 2008.

A common paradigm is used to show that, in rugby and soccer, score difference is more accurately predicted based on past data than is score total. Offensive and defensive ratings evolve by applying least-squares or exponential smoothing to past home scores and visiting scores, corrected for home advantage. Smoothed ratings provide a first-order prediction of score difference and score total for future matches. The average absolute error of such predictions may be minimized by employing a ‘shrinking factor’ L. If L is one, predictions are based solely on smoothed past performances. If L is zero, all predicted score differences are zero and all predicted score totals equal the average total score of past matches. L between one and zero shrinks predicted score difference towards zero and predicted score total towards average total score. Based on more than 3000 games contested in rugby union (Zurich/Guinness Premiership and Super 12/14) and soccer (English Premier League and Italian Serie A), L for score difference was more than that for score total. Thus, past performance was a better predictor of score difference than score total. It is suggested that a team focuses strategy on score difference (to win or draw) while score total is of no strategic interest, thus affecting prediction based on past data. Based on an evaluation of more than 2000 games, it was concluded that betting on score total is undesirable in contrast to score difference because of a relatively small number of possible bets and an unreliable profit.

Keywords: least squares; regression to the mean; prediction; soccer; rugby; gambling


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