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Expected Values And Variances In Bookmaker Payouts: A Theoretical Approach Towards Setting Limits On Odds

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  • Dominic Cortis

Abstract

This study summarizes the key methods of displaying probabilities as odds and provides simple mathematical derivation of a number of key statements in setting odds. Firstly it estimates the expected bookmaker profit as a function of wagers placed and bookmaker margin. Moreover it shows that odds set by bookmakers should have implied probabilities that add up to at least one, otherwise arbitrage is present. Bookmakers can increase profitability by offering more multiples, also known as accumulators, and can lower variation in payouts by maintaining the ratio of wagers and implied probability per outcome.

Suggested Citation

  • Dominic Cortis, 2015. "Expected Values And Variances In Bookmaker Payouts: A Theoretical Approach Towards Setting Limits On Odds," Journal of Prediction Markets, University of Buckingham Press, vol. 9(1), pages 1-14.
    • Handle: RePEc:buc:jpredm:v:9:y:2015:i:1:p:1-14
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    References listed on IDEAS

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    Cited by:

    1. Arne Feddersen & Brad R. Humphreys & Brian P. Soebbing, 2020. "Casual bettors and sentiment bias in NBA and NFL betting," Applied Economics, Taylor & Francis Journals, vol. 52(53), pages 5797-5806, November.
    2. Gustav Axén & Dominic Cortis, 2020. "Hedging on Betting Markets," Risks, MDPI, vol. 8(3), pages 1-14, August.
    3. Philip W. S. Newall & Dominic Cortis, 2021. "Are Sports Bettors Biased toward Longshots, Favorites, or Both? A Literature Review," Risks, MDPI, vol. 9(1), pages 1-9, January.
    4. Ge, Qi, 2018. "Sports sentiment and tipping behavior," Journal of Economic Behavior & Organization, Elsevier, vol. 145(C), pages 95-113.
    5. Hofer, Vera & Leitner, Johannes, 2017. "Relative pricing of binary options in live soccer betting markets," Journal of Economic Dynamics and Control, Elsevier, vol. 76(C), pages 66-85.
    6. Axén, Gustav & Cortis, Dominic, 2019. "Extending the price constraints of betting markets," Journal of Behavioral and Experimental Finance, Elsevier, vol. 23(C), pages 181-188.
    7. Jaume García & Levi Pérez & Plácido Rodríguez, 2017. "Forecasting football match results: are the many smarter than the few?," Chapters, in: Plácido Rodríguez & Brad R. Humphreys & Robert Simmons (ed.), The Economics of Sports Betting, chapter 5, pages 71-91, Edward Elgar Publishing.
    8. Buhagiar, Ranier & Cortis, Dominic & Newall, Philip W.S., 2018. "Why do some soccer bettors lose more money than others?," Journal of Behavioral and Experimental Finance, Elsevier, vol. 18(C), pages 85-93.
    9. Charmaine Barbara & Dominic Cortis & Roberta Perotti & Claudia Sammut & Antoine Vella, 2017. "The European Insurance Industry: A PEST Analysis," IJFS, MDPI, vol. 5(2), pages 1-20, May.
    10. Nawapon Nakharutai & Camila C. S. Caiado & Matthias C. M. Troffaes, 2019. "Evaluating betting odds and free coupons using desirability," Papers 1901.03645, arXiv.org.

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    More about this item

    Keywords

    betting markets; odds; arbitrage; multiples; accumulators; bookmakers;
    All these keywords.

    JEL classification:

    • L83 - Industrial Organization - - Industry Studies: Services - - - Sports; Gambling; Restaurants; Recreation; Tourism

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