Powerball: Somebody's Gotta Win!
1 Pages Posted: 30 May 2017 Last revised: 10 Nov 2021
The case evolves around the Powerball lottery and the rule changes implemented in 2015, which, among other things, changed the chances of winning the jackpot from 1 in 175 million to 1 in 292 million. What is the impact of such rules on lottery revenues? The expected value rule is unable to explain why people play in the first place and fails to give the appropriate weight to the factors that explain the attractiveness of a lottery. This case is ideal to introduce the notion of decision weights as put forward by Kahneman and Tversky's prospect theory. By calculating decision weights, we obtain a reasonable prediction for the willingness to pay for the lottery as a function of different jackpot amounts. Using past data, we can correlate lottery revenues with predicted willingness to pay for a ticket. Quantitative-inclined audiences can then develop a simulation model of how likely it is that the jackpot grows, which, coupled with the prediction of revenues as a function of the jackpot, would give the evolution of the revenues under the new rule. The accompanying spreadsheet provides data for students to work out various scenarios to narrow objectives and maximize revenue from Powerball tickets.
Rev. Jul. 23, 2020
Powerball: Somebody's Gotta Win!
In 2015, lottery consultant Rylee Robinson was hired to examine Powerball, an interstate-run lottery, for its value, prize structure, complexity, and disappointing ticket sales. Indeed, in 2013, ticket sales had declined in all but four states, and by 2014, Powerball sales had declined across the nation by 19%. Industry insiders attributed the decline to jackpot fatigue, which meant casual players would not purchase tickets unless a huge jackpot was up for grabs. With fewer people playing, it took more time to generate jackpots large enough to get folks interested enough to buy tickets. This meant less lottery money was going to state coffers for spending on government programs such as education, economic development, mass transit, or the environmentor whatever beneficiary each state had chosen when Powerball launched.
Robinson was working with the Multi-State Lottery Association (MUSL) to address the falling revenue problems and attract new players to the game. Any rule revisions they made would affect all states that played Powerball. Several members of the MUSL committee working with Robinson believed that increasing ticket buyers' chances of winning somethingnot just the jackpotwould encourage ticket sales. A few changes to the rules would result in more prize winnersa jump from 1 in 32 to 1 in 25, but the chances of winning the jackpot would move from 1 in 175 million to 1 in 292 million. The proposed changes would make it more likely that the jackpot size increasedand history showed that the bigger the jackpot, the more tickets were sold. In a simulation run over five years, a study concluded that the chances of accumulating a jackpot worth more than $ 1 billion increased from 8.5% for the old odds (1 in 175,223,510) to 63.4% for the new odds (1 in 292,201,338).
Before getting behind the suggested rule changes, Robinson wanted to run the numbers again. Would more people really buy Powerball tickets just because the jackpot was larger? Or would the changes actually decrease the popularity of Powerball? And what effect would the new rules have on revenues?
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Keywords: revenue prediction, lotteries, decision weights, prospect theory, probability
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