How to design a lottery

This chapter provides an outline to the statistical, economic, and practical considerations relevant to designing lottery games. The focus is on lotto but some of the issues apply more generally. We illustrate the analysis using an estimated statistical model of the determinants of lotto sales, that builds on recent research on horsetrack betting, to simulate the way in which changing the design of lotto games might affect their sales using data for the UK. The research complements recent lottery research that models the proximate determinants of sales, such as jackpot size, by exploiting changes induced by rollovers as a source of natural experiments. The approach pursued here assumes that what matters for sales is the shape of the prize distribution and this shape is summarized by the first three moments of the prize distribution (mean, variance, and skewness). The methodology builds on the characteristics approach to demand analysis that was pioneered by Lancaster. The approach has the advantage that it can be used to simulate the effects of hypothetical changes in the shape of the prize distribution that come about because of game design variation. We estimate the model, taking account of the endogeneity of the moments, and use the estimates to simulate how sales would evolve if game design were changed