The prices offered by the fixed-odds bookmakers in the tennis betting market are biased because of the favorite-longshot phenomenon. How to derive unbiased implied probabilities underlying the published odds is the focus of this study. This paper proposes a new normalization procedure that yields unbiased probabilities, regardless of the presence of heavy underdogs. In-sample, the proposed normalization has a superior forecasting ability than the other methods. Moreover, it enables betting strategies, which produce superior returns than those obtained from the Bradley Terry type model.
AbinzanoI., MugaL., & SantamariaR. (2016). Game, set and match: the favorite-long shot bias in tennis betting exchanges. Applied Economics Letters, 23(8), 605–608.
2.
AveryC., & ChevalierJ. (1999). Identifying investor sentiment from price paths: The case of football betting. Journal of Business, 72(4), 493–521.
3.
BrierG. W. (1950). Verification of forecasts expressed in terms of probability. Monthly weather review, 78(1), 1–3.
4.
BrownA., & YangF. (2018). The wisdom of large and small crowds: Evidence from repeated natural experiments in sports betting. International Journal of Forecasting, forthcoming.
5.
CainM., LawD., & PeelD. (2003). The favorite-longshot bias, bookmaker margins and insider trading in a variety of betting markets. Bulletin of Economic Research, 55(3), 263–273.
6.
ClarkeS. (2016). Adjusting true odds to allow for vigorish. InProceedings of the 13th Australasian Conference on Mathematics and Computers in Sport. R. Stefani and Shembri A., Eds (pp. 111–115).
7.
ClarkeS., KovalchikS., & IngramM. (2017). Adjusting bookmakers odds to allow for overround. American Journal of Sports Science, 5(6), 45–49.
8.
ColemanL. (2004). New light on the longshot bias. Applied Economics, 36(4), 315–326.
9.
CoombesR., FrazerL., JohnsonR., HockadayJ., & OttoC. (1998). A case study on the informational efficiency of markets: The market for horse racing in australia. Journal of Gambling Studies, 14(4), 401–411.
10.
DixonM. J., & ColesS. G. (1997). Modelling association football scores and inefficiencies in the football betting market. Journal of the Royal Statistical Society: Series C (Applied Statistics), 46(2), 265–280.
11.
FeddersenA. (2017). Market efficiency and the favorite-longshot bias: evidence from handball betting markets. In RodriguezP., HumphreysB. R., & SimmonsR. (Eds.), The economics of sports betting (pp. 105–117). Cheltenham, UK.
12.
FeddersenA., HumphreysB. R., & SoebbingB. P. (2017). Sentiment bias and asset prices: Evidence from sport betting markets and social media. Economic Inquiry, 55(2), 1119–1129.
13.
ForrestD., & McHaleI. (2005). Longshot bias: Insights from the betting market on men's professional tennis. In L. Vaughan Williams (Ed.),Information efficiency in financial and betting markets (pp. 215–230). Cambridge: Cambridge University Press.
14.
ForrestD., & McHaleI. (2007). Anyone for Tennis (Betting)?The European Journal of Finance, 13(8), 751–768.
15.
ForrestD., & SimmonsR. (2008). Sentiment in the betting market on spanish football. Applied Economics, 40(1), 119–126.
16.
GeyerC. J. (1994). On the asymptotics of constrained M-estimation. Annals of Statistics, 22(4), 1993–2010.
17.
GneitingT., & KatzfussM. (2014). Probabilistic forecasting. Annual Review of Statistics and Its Application, 1(1), 125–151.
18.
GrayP. K., & GrayS. F. (1997). Testing market efficiency: Evidence from the NFL sports betting market. The Journal of Finance, 52(4), 1725–1737.
19.
KahnemanD., & TverskyA. (1979). Prospect Theory: An Analysis of Decision under Risk. Econometrica, 47(2), 263–292.
20.
LahiriK., & YangL. (2013). Forecasting Binary Outcomes. In G. Elliott & Timmermann (Eds.),Handbook of economic forecasting (Vol. 2, p. 1025–1106). Elsevier.
21.
LahvickaJ. (2014). What causes the favorite-longshot bias? Further evidence from tennis. Applied Economics Letters, 21(2), 90–92.
22.
LaiT. L., GrossS. T., & ShenD. B. (2011). Evaluating probability forecasts. Annals of Statistics, 39(5), 2356–2382.
23.
LevittS. D. (2004). Why are gambling markets organised so differently from financial markets?The Economic Journal, 114(495), 223–246.
24.
McHaleI., & MortonA. (2011). BradleyA.-Terry type model for forecasting tennis match results. International Journal of Forecasting, 27(2), 619–630.
25.
NagelkerkeN. J. (1991). A note on a general definition of the coefficient of determination. Biometrika, 78(3), 691–692.
26.
PankoffL. D. (1968). Market efficiency and football betting. The Journal of Business, 41(2), 203–214.
27.
ShapiroA. (2000). On the asymptotics of constrained local M-estimators. Annals of Statistics, 948–960.
28.
ShinH. S. (1991). Optimal Betting Odds Against Insider Traders. The Economic Journal, 101(408), 1179–1185.
29.
ShinH. S. (1992). Prices of State Contingent Claims with Insider Traders, and the Favourite-Longshot Bias. The Economic Journal, 102(411), 426–435.
30.
ShinH. S. (1993). Measuring the Incidence of Insider Trading in a Market for State-Contingent Claims. The Economic Journal, 103(420), 1141–1153. doi: 10.2307/2234240
31.
SnowbergE., & WolfersJ. (2010). Explaining the favorite-long shot bias: Is it risk-love or misperceptions?Journal of Political Economy, 118(4), 723–746.
32.
SobelR. S., & Travis RainesS. (2003). An examination of the empirical derivatives of the favorite-longshot bias in racetrack betting. Applied Economics, 35(4), 371–385.
33.
ŠtrumbeljE. (2014a). A comment on the bias of probabilities derived from betting odds and their use in measuring outcome uncertainty. Journal of Sports Economics, 17(1), 12–26.
34.
ŠtrumbeljE. (2014b). On determining probability forecasts from betting odds. International Journal of Forecasting, 30(4), 934–943.
35.
ThalerR. H., & ZiembaW. T. (1988). Anomalies: Parimutuel Betting Markets: Racetracks and Lotteries. Journal of Economic Perspectives, 2(2), 161–174.
36.
VineyM., BedfordA., & KondoE. (2013). Incorporating over-round into in-play markov chain models in tennis. In15th international conference on gambling & risk-taking, Las Vegas, USA.
37.
WeitzmanM. (1965). Utility analysis and group behavior: An empirical study. Journal of Political Economy, 73(1), 18–26.
38.
WilliamsL. V. (1999). Information efficiency in betting markets: A survey. Bulletin of Economic Research, 51(1), 1–39.
39.
WilliamsL. V., & PatonD. (1998). Why are some favorite-longshot biases positive and others negative?Applied Economics, 30(11), 1505–1510.
40.
WoodlandL. M., & WoodlandB. M. (1994). Market Efficiency and the Favorite-Longshot Bias: The Baseball Betting Market. The Journal of Finance, 49(1), 269–279.
