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Optimal Betting Under Parameter Uncertainty: Improving the Kelly Criterion

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  • Rose D. Baker

    (Centre for Sports Business, Salford Business School, University of Salford, Salford M5 4WT, United Kingdom)

  • Ian G. McHale

    (Centre for Sports Business, Salford Business School, University of Salford, Salford M5 4WT, United Kingdom)

Abstract

The Kelly betting criterion ignores uncertainty in the probability of winning the bet and uses an estimated probability. In general, such replacement of population parameters by sample estimates gives poorer out-of-sample than in-sample performance. We show that to improve out-of-sample performance the size of the bet should be shrunk in the presence of this parameter uncertainty, and compare some estimates of the shrinkage factor. From a simulation study and from an analysis of some tennis betting data we show that the shrunken Kelly approaches developed here offer an improvement over the “raw” Kelly criterion. One approximate estimate of the shrinkage factor gives a “back of envelope” correction to the Kelly criterion that could easily be used by bettors. We also study bet shrinkage and swelling for general risk-averse utility functions and discuss the general implications of such results for decision theory.

Suggested Citation

  • Rose D. Baker & Ian G. McHale, 2013. "Optimal Betting Under Parameter Uncertainty: Improving the Kelly Criterion," Decision Analysis, INFORMS, vol. 10(3), pages 189-199, September.
    • Handle: RePEc:inm:ordeca:v:10:y:2013:i:3:p:189-199
    DOI: 10.1287/deca.2013.0271
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    References listed on IDEAS

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    Cited by:

    1. Barge-Gil, Andrés & García-Hiernaux, Alfredo, 2019. "Staking plans in sports betting under unknown true probabilities of the event," MPRA Paper 92196, University Library of Munich, Germany.
    2. Michael R. Metel, 2018. "Kelly Betting on Horse Races with Uncertainty in Probability Estimates," Decision Analysis, INFORMS, vol. 15(1), pages 47-52, March.
    3. Andrés Barge-Gil & Alfredo Garcia-Hiernaux, 2020. "Staking in Sports Betting Under Unknown Probabilities: Practical Guide for Profitable Bettors," Journal of Sports Economics, , vol. 21(6), pages 593-609, August.
    4. Andrew Grant & David Johnstone & Oh Kang Kwon, 2019. "A Probability Scoring Rule for Simultaneous Events," Decision Analysis, INFORMS, vol. 16(4), pages 301-313, December.
    5. Rakesh K. Sarin, 2013. "From the Editor —Optimal Betting, Reducing Unnecessary Mammography in Breast Cancer Diagnosis, Product Line Design, and Value of Information," Decision Analysis, INFORMS, vol. 10(3), pages 187-188, September.
    6. Chu Dani & Wu Yifan & Swartz Tim B., 2018. "Modified Kelly criteria," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 14(1), pages 1-11, March.
    7. Hubáček, Ondřej & Šír, Gustav, 2023. "Beating the market with a bad predictive model," International Journal of Forecasting, Elsevier, vol. 39(2), pages 691-719.
    8. Reza Yarbakhsh & Mahdieh Soleymani Baghshah & Hamidreza Karimaghaie, 2023. "Predicting risk/reward ratio in financial markets for asset management using machine learning," Papers 2311.09148, arXiv.org.

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