International Journal of Forecasting 27 (2011) 619–630 www.elsevier.com/locate/ijforecast A Bradley-Terry type model for forecasting tennis match results Ian McHale a , Alex Morton b,∗ a The University of Salford – Centre for Operational Research and Applied Statistics, Salford, Greater Manchester M5 4WT, United Kingdom b SANSTAT LTD, 483 River Valley Road, #10-07, Singapore 248368, Singapore Abstract The paper introduces a model for forecasting match results for the top tier of men’s professional tennis, the ATP tour. Employing a Bradley-Terry type model, and utilising the data available on players’ past results and the surface of the contest, we predict match winners for the coming week’s matches, having updated the model parameters to take the previous week’s results into account. We compare the model to two logit models: one using official rankings and another using the official ranking points of the two competing players. Our model provides superior forecasts according to each of five criteria measuring the predictive performance, two of which relate to betting returns. c ⃝ 2010 International Institute of Forecasters. Published by Elsevier B.V. All rights reserved. Keywords: Bradley-Terry model; Logit; Ranking evaluation; Sport; Betting 1. Introduction Sports forecasting models are often used to inform debate on some wider aspect of research, rather than being the subject of the research themselves. In their most common application, as a tool for assessing the efficiency of betting markets, the published results of sports forecasting models have rarely been found to be successful to the extent of enabling positive returns to be made. This could be a consequence of the proprietary nature of a successful forecasting model, where neither an odds-setter nor a bettor with the ∗ Corresponding author. E-mail addresses: i.mchale@salford.ac.uk (I. McHale), sanstat1@hotmail.com (A. Morton). capacity to beat the bookmaker would be eager to release his or her formula. Attempting to win money is not the only possible use for an objective forecasting model. Such models can be used by the media (see for example Finkelstein, Graham, Morton, & Stott, 2002, or Klaasen & Magnus, 2003) to analyse the psychology of betting markets (see for example Dixon & Pope, 2004 or Graham & Stott, 2008), uncover the dynamics of a sport (see for example Dixon & Robinson, 1998, or Holder & Nevill, 1997), construct ranking systems (Macmillan & Smith, 2007), or aid in the design of tournaments (see for example Szymanski, 2003). In this paper we concentrate on forecasting tennis match results using a Bradley-Terry type model. Previous published papers on the subject 0169-2070/$ - see front matter c ⃝ 2010 International Institute of Forecasters. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.ijforecast.2010.04.004