Applied Economics

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Applied Economics Publication details, including instructions for authors and subscription information: http://www.informaworld.com/smpp/title~content=t713684000 Predicting bookmaker odds and efficiency for UK football I. Graham a; H. Stott ab a Decision Technology, Hamilton House, Mabledon Place, London, UK b Department of Psychology, University College, London, UK

Online Publication Date: 01 January 2008 To cite this Article: Graham, I. and Stott, H. (2008) 'Predicting bookmaker odds and efficiency for UK football', Applied Economics, 40:1, 99 - 109 To link to this article: DOI: 10.1080/00036840701728799 URL: http://dx.doi.org/10.1080/00036840701728799

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Hill 0.357 comparable of corresponding of probability probability is matches, assigned This 4072 average geometric these for h ai oe a i osaos20–02and 2001–2002 was seasons likelihood to log maximum fit The was 2002–2003. model basic The the Results ensure prediction model. to results prediction the odds order both bookmaker the for in and used model is we only, set so data and results found same bookmaker be league However, not could use model. matches cup the for odds in play another, divisions different one from teams which in matches, reliable. is to calibration order inter-division in the required ensure is inter-division season second allowing and The calibration. promoted divisions, are are data between teams of relegated season worth one seasons After two required. least at can parameters identified, model all be that ensure to and divisions, 26th and compete August English 2006. 5th five 820 November between the played plus comprises matches matches league league data 2036 of Our the other seasons the in leagues. in season season per three per matches matches 552 and 380 Premiership are twice. team there other 1 each Therefore plays League team Championship, Each the 2. of League and each in teams 24 and piu oe hudb eetd eueACto AIC use We selected. be should size the model optimum effect apart small. the is km 380 parameter so distance the 48.1/24.6/27.3, clubs of are for percentages and 45.1/26.2/28.8 and itnebtencus h eutgv small, gave result The of parameters clubs. distance-dependent between distance result. match each for 0.370 of maximum probability assigned the home increased to model likelihood individual the into Incorporating advantages advantage. Larger home 2. by Table ordered shown in are results The advantages. home 45.1/28.7/26.2. of percentages x ¼ natraiesrtg ol et nld cup include to be would strategy alternative An between strengths team the calibrate to order In Premiership the in teams 20 are there England, In eoemvn otednmcmdl the model, dynamic the to moving Before h ia oe dutetwst incorporate to was adjustment model final The individual of model the fit to was step next The o lb naeaedsac f10k apart km 180 of distance average an clubs For n h i/oeda ecnae are percentages win/lose/draw the and 0 d 2 ¼ 3.9 02 orsodn oa average an to corresponding 4052, 10 c 1 4 h and seEuto 3). Equation (see niae agrindividual larger a indicates c r hw nTbe1. Table in shown are .Gaa n .Stott H. and Graham I. 2 iehome/draw/away give d 1 ¼ 2.5 4100 10 h 4 Downloaded By: [Graham, I.] At: 17:07 18 December 2007 rea .2 owc .5 lhm006Bournemouth Mansfield Northampton 0.066 0.053 0.035 Weds Sheffield Oldham Tranmere 0.442 QPR 0.453 0.432 0.451 United Sheffield Millwall Norwich 1.456 Sunderland 1.514 1.824 1.714 Newcastle Liverpool United Man Arsenal Team hle .8 edn .7 Grimsby 0.370 Reading 1.382 Chelsea al .Poi oe i 2001–2003. fit model Probit 1. Table rdcin eemd o h 0320 esnfor season 2003–2004 of values the various for version. dynamic made the were to move Predictions to necessary is it model, extra the for compensate adding between to complexity. sufficient model by distance not and are caused clubs advantages home enhancements that indicate individual 3 likelihood Table in results the The model. our select ed .2 rso .5 Plymouth 0.350 Preston 1.129 Leeds lb hc ne h egeec esnare season each of league value new the the Hill. that and disadvantage enter William unknown, the which has than clubs model predictive probit not was The model less probit the for significantly that likelihood indicated match predictive like- past each of the fitting the for Bootstrapping section than this results. in smaller found 0.365 unsurprisingly of lihood and 0.350 likelihood predictive of Hill’s William to inferior slightly model. their Poisson in dynamic (1997) a Coles of and of implementation Dixon value by the in reported to days found similar is 525 as This statistic (1997). Coles likelihood and expect the Dixon would in we decay maximize longer steeper to was a data window data of the seasons If two over. only has optimum model the the after out flattens optimum is the time that shows decay 1 for Fig. used predictions. 5 further Equation all statistic likelihood predictive the lcbr .6 otmFrs .4 Brentford 0.345 Forest Nott’m 1.064 Blackburn a iy093Wmldn034Luton 0.344 Wimbledon 0.993 City Man vro .9 une .1 Barnsley 0.315 Burnley 0.991 Everton otna .6 ilnhm022Huddersfield 0.282 Gillingham 0.964 Tottenham otapo .5 rsa aae023Swindon 0.273 Palace Crystal 0.957 Southampton so il .5 afr .0 Colchester 0.203 Watford 0.955 Villa Aston etHm097Wgn019Wycombe 0.169 Wigan 0.927 Ham West uhm093Dry018Blackpool 0.168 Derby 0.903 Fulham idebr .0 adf .6 Peterboro 0.168 Cardiff 0.901 Middlesboro hrtn088Cvnr .6 otVale Port 0.163 Coventry 0.898 Charlton otn083Rtehm016NtsCounty Notts 0.156 Rotherham 0.843 Bolton imnhm078Biho .3 Stockport 0.137 Brighton 0.738 Birmingham ecse .9 rw .1 Chesterfield 0.116 Crewe 0.698 Leicester ovs060Soe007Cheltenham 0.097 Stoke 0.650 Wolves etBo .9 rdod005Rushden 0.075 Bradford 0.590 Brom West otmuh059BitlCt .7 Wrexham 0.070 City Bristol 0.549 Portsmouth pwc .1 asl .7 Hartlepool 0.070 Walsall 0.511 Ipswich rdcigbomkrod n fiinyfrU football UK for efficiency and odds bookmaker Predicting nodrt esr h rdcieeso the of predictiveness the measure to order In h rdcielklho e ac a 0.346, was match per likelihood predictive The ¼ 0 as h rdcielikelihood predictive The days. 600 n h au of value the and Team ¼ mle h model the implies c 1 0 asbecause days 600 ^ htmaximized that 2 .3 and 0.637 c 2 ^ 0.124 Team nomto sls ycnetaigo one on of odd An concentrating odds. little by Thus, lost season. bookmaker. single is between varies a does information prediction it within outcome than bookmakers season-to-season that bookmakers more and UK much similar, street be high major to by offered odds n oe(04 n Forrest and probit (2004) Pope and ordered our be can for odds their benchmark model. that a bookmaker so 1998–2003, best-performing considered period the the was in forecasting odds Hill the Forrest William for addition, reason basis main In the each our model. as street in is it high this win choosing largest and away for the UK, an of the in one and bookmakers is draw Hill a Hill William William win, match. by home offered odds a the for are use we data The model the of Description Model Forecasting Odds III. reliable make to data predictions. of seasons-worth 2 about needs h ila il prices Hills William The te okaescnb oprd u Dixon but compared, be can bookmakers Other .4 Bury 0.047 .7 Scunthorpe 0.071 .0 Rochdale 0.102 .1 Kidderminster 0.119 .7 Cambridge 0.174 .2 York 0.220 .4 Hull 0.247 .8 Torquay 0.283 .1 Lincoln 0.311 .2 Oxford 0.328 .3 Boston 0.339 .4 Macclesfield 0.340 .9 Darlington 0.394 .1 Shrewsbury 0.419 .7 Southend 0.474 .7 etnOrient Leyton 0.476 .9 Exeter 0.498 .1 Carlisle 0.511 .6 Swansea 0.560 .6 rso Rvs Bristol 0.566 ¼ eun he nt o one a for units three returns 3 Team Halifax r rsne sdecimal as presented are tal et tal et 20)fudthat found (2005) . 20)bt found both (2005) . 0.658 0.613 0.610 0.676 0.683 0.790 0.845 0.869 0.906 0.907 0.916 0.927 0.965 0.973 1.006 1.009 1.020 1.051 1.086 1.090 1.111 1.126 1.443 1.160 103 Downloaded By: [Graham, I.] At: 17:07 18 December 2007 ontsmt n eas ftetk-u rover- or take-out the of 2-to-1. because one is probabilities, of round to This to sum odd not converted 1/3. do when English of odds, traditional probability Bookmaker stake), to event unit one an equivalent the implies plus profit and units (two stake unit 104 R ie he dso ac then match a on odds three Given . 1 h Exeter Stockport Wrexham lhm0.137 0.393 0.515 Oldham Torquay United Sheffield Burnley ecse 0.770 0.606 0.396 Leicester Cheltenham Portsmouth Wimbledon otn0.883 Bolton Rvs Bristol owc .8 .7 otmFrs .4 0.225 0.243 Forest Nott’m 0.576 0.180 Southend Norwich P .4 .1 rdod0.209 0.719 Bradford 0.067 0.016 0.106 Brom West 0.715 0.040 Rochdale 0.114 0.036 Grimsby 0.052 Birmingham Peterboro 0.435 Swindon 0.253 Northampton 1.048 Swansea Derby QPR 0.157 Kidderminster 0.876 0.264 Tranmere Sunderland Chesterfield 0.376 Blackburn 0.279 0.175 0.849 Halifax Orient Leyton Everton Vale 0.798 Port Huddersfield City 0.925 Bristol Millwall Darlington Tottenham 0.330 0.340 Bournemouth 0.348 Wycombe Hull Ham West City 1.325 0.187 Man Rushden 0.354 0.741 Boston Cambridge 0.369 Stoke 0.794 York Newcastle 0.724 Preston Fulham Brentford Villa Aston Middlesboro Mansfield Team al .Idvda oeavnaemdlft2001–2003. fit model advantage home Individual 2. Table þ 1 d þ 1 a ¼ 1 þ R ’ 1 0.992 0.374 0.471 0.852 0.440 1.138 .4 .7 Barnsley 0.370 1.248 .6 .0 oety0.304 0.066 0.057 Coventry Lincoln 0.002 0.094 0.176 0.043 0.261 Oxford 0.013 0.331 0.106 0.275 Shrewsbury 0.019 0.668 0.095 1.145 1.350 0.113 0.052 Gillingham Watford 0.863 0.245 Plymouth 0.222 0.509 0.245 0.133 Brighton 0.134 0.256 1.608 Chelsea 0.258 Palace 1.229 Crystal 0.897 0.093 0.268 County 0.054 Notts 0.269 1.158 Scunthorpe Southampton 0.285 0.750 Rotherham 0.291 1.061 Blackpool 0.295 0.300 0.646 0.316 1.136 1.035 Walsall 0.046 1.077 0.349 Hartlepool 0.370 0.289 0.803 : 124 h .0 ovs0.946 1.421 1.177 Wolves Leeds Charlton 0.208 0.198 0.189 .5 uo 0.043 0.727 0.324 Macclesfield Luton Ipswich 0.155 Crewe 0.153 0.147 0.140 .3 edn 0.558 0.327 0.204 Bury Reading Weds Sheffield 0.132 Cardiff 0.131 0.102 0.091 .6 rea 1.991 Carlisle Arsenal 0.067 0.065 .2 iepo 1.671 1.871 Colchester Liverpool United Man 0.050 0.027 0.020 ð 6 Þ oe ln( effect Distance advantages home Individual Basic variants Model model of AICs and Log-likelihoods 3. Table ia 0.445 Wigan Team c 1 ^ 2 .5 and 0.650 0.791 0.492 0.975 0.170 .1 0.190 0.318 0.810 0.854 0.918 0.689 0.085 0.144 0.118 0.128 0.133 0.106 0.493 0.140 0.755 0.146 0.148 0.424 0.160 0.477 0.163 0.325 0.185 0.005 0.415 0.659 c 2 ^ 0.124 .Gaa n .Stott H. and Graham I. 089 8384 8472 8384 94 184 4098 92 4052 4100 L aaeesAIC Parameters ) h 0.455 0.569 0.549 0.548 0.573 0.381 0.444 0.422 0.399 0.312 0.372 0.337 0.326 0.292 0.297 0.290 0.287 0.269 0.262 0.254 0.244 0.243 0.232 0.220 Downloaded By: [Graham, I.] At: 17:07 18 December 2007 ac nigi naa i.Tebookmaker The and draws, win. and out wins away home on pays bet an money the in all keeps ending match a teghflosorpoi oe exactly. model strengths probit estimates our bookmaker follows The strength strength. team the relative based of of odds, compute perception rating then their predictions. a and on team make each model between of to closely, strength comparisons assumed and II are direct Bookmakers Section draw predictions can of bookmaker we follows model that model probit each so forecasting rate ordered way bookmakers bookmaker the how this The model team. can in we prices bilities, of that set regardless suggests not (2004) achieved practice. in Levitt may is outcome. profit bookmakers match same the the and h mle rbblte ecnaepoi of profit percentage a probabilities R implied the into odds decimal convert 1/ to probabilities, Thus, Hill. 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