To bet or not to bet: a reality check for tennis betting market efficiency

ABSTRACT

We present evidence that the tennis betting market appears to be much more efficient than suggested by previous studies. More specifically, we study the market efficiency by studying the forecasting performance of a diversified set of 40 betting rules in two ways: by searching for the existence of a return differential between betting rules and by analysing the profitability of betting rules. Even though individual tests provide evidence that, within our universe of betting rules, positive returns can be achieved, when data-snooping bias is taken into account, the evidence diminishes. Subsequently, we also find very little evidence of return differentials between betting rules. These results cast doubts on previous research as they suggest that when the potential detrimental effects of data-dreading are taken into account, betting markets in general might not, ultimately, be so inefficient.

KEYWORDS:

• Market efficiency
• betting
• Bradley-Terry model
• data-snooping bias
• tennis

JEL CLASSIFICATION:

• C53
• G14

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ Both types of market efficiency can arise under different information sets.

² Note that here we use average market odds, but the bets alone are based on the best possible odds on the market.

³ Let us assume we have a set of odds o_i, i = 1, 2, …, n, n ∈ ℕ and define z_i = ao_i for a ∈ ℝ⁺. With this definition, the levels of o_i and z_i are different, but the percentages of o_i and z_i from their respective means remain the same. For the variances, we get D(z_i) = a² D(o_i). For the variances in logarithms$n^{-1}\sum _{i=1}^n{\left(ln{z}_i-n^{-1}\sum _{i=1}^{n}ln{z}_i\right)}^2$$=n^{-1}\sum _{i=1}^n{\left(lna+ln{o}_i-lna-n^{-1}\sum _{i=1}^{n}ln{o}_i\right)}^2$ $=n^{-1}\sum _{i=1}^n{\left(ln{o}_i-n^{-1}\sum _{i=1}^{n}ln{o}_i\right)}^2$. Hence, the variance in the logarithms of odds does not depend on the level of odds, i.e. it is scale-invariant.

⁴ For detailed description of the performance measures used, as well as the definition of formal statistical tests for superior predictive ability, please refer to Appendix 3.

⁵ Which is difficult to assess, but the Sharpe ratios from the daily and weekly returns on the S&P 500 stock market index are 0.0135 and 0.0305, i.e. lower than those achievable while betting on tennis matches played on the grass court but higher than those achievable while betting on the clay or hard courts.

⁶ Due to the estimate issues, if one of the weightings is set to 0, it is adjusted by a small amount to be positive, i.e. 0.0001. If the match were to be played on a clay surface, wc ∈ {0.40 + r0.05, r = 0, 1, …, 12}, wh, wg ∈ {0.00 + s0.05, s = 0, 1, …., 8}, and if the match were played on a hard-court or carpet surface, wh ∈ {0.40 + r0.05, r = 0, 1, …, 12}, wc, wg ∈ {0.00 + s0.05, s = 0, 1, …., 8}.

⁷ Probably small as there are not so many players with a low number of matches.

Additional information

Funding

Lyócsa and Výrost appreciate the support provided by the Slovak Grant Agency under Grant No. 1/0392/15 and Grant No. 1/0406/17. This work was supported by the Slovak Research and Development Agency under contract No. APVV-14-0357;Agentúra na Podporu Výskumu a Vývoja [14-0357];Vedecká Grantová Agentúra MŠVVaŠ SR [1/0392/15,1/0406/17].