The Dummies’ Guide to Lottery Design

This paper outlines the issues relevant to the operation of lottery games: it attempts to put some science into the art of lottery design. Our research suggests that lottery tickets sales depend positively on: the average return (i.e the proportion of revenue returned as prizes) because punters like better bets; the skewness in the prize distribution (e.g how much of the prize money goes to the jackpot) and we find that the more the better; and negatively on the variance in the prize distribution (which is a measure of the riskiness of the return – so the less the better). The sizes of these effects are important: our statistics suggest that the effect of the mean is small, as is the effect of the skewness, while the (negative) variance effect is quite important. The work suggests that good causes revenue might be higher if: the game were meaner (less of the stakes used as prize money) because, although sales would fall a little, the good causes would getter a larger share of the smaller revenue; more of the prize money was used for the jackpot, or the variance in the expected prizes were reduced. BUT, in practice, it is difficult to change one aspect of the design of the game without having a counterveiling effect on another aspect. Thus, it is difficult to make judgements about the merits of alternative game designs without looking at ALL of the parameters being proposed. However, the research suggests that there is no obvious case for not increasing the take-out (the revenue that is not returned as prizes) if the current game design is kept. If the game were changed to make the odds longer then our research suggests that other parameters of the design of the game may have to be changed to stop sales falling. While we feel that there should be a lottery (because people enjoy playing and it does little harm), we also feel that lotteries are not good vehicles for taxation because they are a larger part of the spending of the poor than the rich. Moreover, we find no compelling empirical evidence to suggest that there is any merit in having much of the take-out dedicated to good-causes – hypothecation is bad for sound investment decision-making, the best causes are already the recipients of taxpayer largesse, and adding lottery funds to these causes simply displaces Treasury dollars. That is not to say that (some, perhaps most) of the good causes are deserving – rather that they should be funded in some other way. Finally, the current “beauty contest” process of choosing an operator is fraught with risk (for the Commissioners but not the bidders) and we suggest that, if the aim is to raise good causes funds, then the license should be auctioned.