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Modelling the probability distribution of prize winnings in the UK National Lottery: consequences of conscious selection


  • R. D. Baker
  • I. G. McHale


In the statistical and economics literature on lotteries, the problem of designing attractive games has been studied by using models in which sales are a function of the structure of prizes. Recently the prize structure has been proxied by using the moments of the prize distribution. Such modelling is a vital input into the process of designing appealing new lottery games that can generate large revenues for good causes. We show how conscious selection, the process by which lottery players choose numbers non-randomly, complicates the multivariate distribution of prize winners by introducing massive overdispersion of numbers of winners, and large correlations between the numbers of different types of prize winner. Although it is possible intuitively to reach a qualitative understanding of the data, an "a priori" model does not fit well. We therefore construct an empirical model of the joint distribution of prize winners and use it to calculate the moments of ticket value as a function of sales. The new model gives much higher estimates of ticket value moments, particularly skewness, than previously obtained. Our results will have consequences for policy decisions regarding game design. A spin-off result is that, on the basis of the results of model fitting, lottery players may increase the expected value of their ticket by strategically choosing numbers which are less popular with other lottery players. Copyright (c) 2009 Royal Statistical Society.

Suggested Citation

  • R. D. Baker & I. G. McHale, 2009. "Modelling the probability distribution of prize winnings in the UK National Lottery: consequences of conscious selection," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 172(4), pages 813-834.
  • Handle: RePEc:bla:jorssa:v:172:y:2009:i:4:p:813-834

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    Cited by:

    1. Kent Grote & Victor Matheson, 2011. "The Economics of Lotteries: A Survey of the Literature," Working Papers 1109, College of the Holy Cross, Department of Economics.
    2. Michael A. Trousdale & Richard A. Dunn, 2014. "Demand for Lottery Gambling: Evaluating Price Sensitivity Within a Portfolio of Lottery Games," National Tax Journal, National Tax Association, vol. 67(3), pages 595-620, September.

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