The sales effects of Powerball and Mega Millions game redesign

ABSTRACT

State lottery consortia in the U.S. substantially redesigned their largest jackpot games, Powerball and Mega Millions, to stimulate sales revenue for their member states. The odds of winning the jackpot in each game were lengthened to increase the probability of larger jackpots, the minimum jackpot was raised, and ticket prices were increased from $1 to $2. This paper estimates the demand for Powerball and Mega Millions using drawing-by-drawing aggregate U.S. sales revenue and advertised jackpot data from 2010 to 2019. Each game achieved a record-breaking jackpot of about $1.5 billion during this period. We find that each game’s redesign lowered the elasticity of sales revenue of the game with respect to the size of the game’s jackpot while significantly increasing the average size of the jackpot. We also estimate the impact of each game’s redesign on sales. Finally, we estimate cross-game effects of game redesigns and jackpots.

KEYWORDS:

• Lotteries
• Powerball
• Mega Millions
• demand elasticity

JEL CLASSIFICATION:

• H27 - Other Sources of Revenue < H2 - Taxation, Subsidies, and Revenue < H - Public Economics
• L83 - Sports|Gambling|Recreation|Tourism < L8 - Industry Studies: Services < L - Industrial Organization
• H71 - State and Local Taxation, Subsidies, and Revenue < H7 - State and Local Government|Intergovernmental Relations < H - Public Economics

Acknowledgements

The authors wish to thank Marc Riemann and Saimina Weilijiang for their excellent research assistance.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

The data that support the findings of this study are available from the corresponding author, John A. Spry, upon reasonable request.

Notes

¹ Even larger jackpots have been won since our sample period ended.

² https://www.musl.com/.

³ https://www.megamillions.com/Media-Center.aspx.

⁴ https://lafleurs.com/news/2019/06/28/new-york-lottery-to-join-multi-state-lottery-association-musl/.

⁵ https://www.jacksonville.com/story/news/lottery/2021/10/13/jacksonville-man-wins-1-million-mega-millions-florida-lottery/8442793002/.

⁶ These figures describe the status of the game by the end of our sample period. Powerball has subsequently reduced its minimum jackpot and increased the number of drawings per week.

⁷ https://wyolotto.com/play/powerball/powerball-game-rules/.

⁸ https://assets-prod.mn-lottery.net/Game-Rules/Lotto/Mega-Millions-Rules-Revised-7-27-21.pdf.

⁹ The jackpot and advertised jackpot are the nominal, undiscounted sum of thirty annuity payments and are significantly larger than the one-time lump-sum payment option that most lotto winners pick.

¹⁰ For current Powerplay and Megaplier details, see https://www.megamillions.com/How-to-Play.aspx https://www.powerball.com/games/powerball.

¹¹ The actual jackpot size is the ex-post value of a jackpot that is won. The advertised jackpot is a forecast of the sum of thirty nominal payments that would be collected if there is a winner of the next drawing. The advertised jackpot of the next upcoming drawing is declared within several hours after a drawing does not result in the sale of a winning ticket.

¹² Combs and Spry (2019) use sales per adult (logged) because they specifically estimate the income elasticity of Powerball and Mega Millions. They find that the income elasticity increases as the jackpot increases. Pérez and Baker (2010) use the number of tickets sold instead of the currency value of sales.

¹³ To examine the effects of the size of the advertised Mega Millions jackpot on the sales of Powerball, we calculate the average Mega Millions jackpot in the days leading up to each Powerball drawing. The days leading up to each Wednesday Powerball drawing are Sunday, Monday, Tuesday, and Wednesday. Therefore, for Wednesday Powerball drawings, the weighted average Mega Millions jackpot is 3/4 multiplied by the Mega Millions jackpot for the Mega Millions Tuesday drawing, plus 1/4 multiplied by the advertised Mega Millions jackpot for the upcoming Friday Mega Millions drawing. The days leading up to each Saturday Powerball drawing are Thursday, Friday, and Saturday. Therefore, for Saturday Powerball drawings, the weighted average Mega Millions jackpot is 2/3 the Mega Millions jackpot for the proceeding Mega Millions Friday drawing and 1/3 the Mega Millions jackpot for the upcoming Mega Millions Tuesday drawing.

To examine the effects of the size of the advertised Powerball jackpot on the sales of Mega Millions, we calculate the average Powerball jackpot leading up to each Mega Millions drawing. The days leading up to each Tuesday Mega Millions drawing are Saturday, Sunday, Monday, and Tuesday. Therefore, for Tuesday Mega Millions drawings, the weighted average Powerball jackpot is 1/4 multiplied by the Powerball jackpot for the previous Powerball Saturday drawing, plus 3/4 multiplied by the Powerball jackpot for the upcoming Powerball Wednesday drawing. The days leading up to each Mega Millions Friday drawing are Wednesday, Thursday, and Friday. Therefore, the weighted average Powerball jackpot is 1/3 multiplied by the Powerball jackpot for the previous Powerball Wednesday drawing, plus 2/3 multiplied by the Powerball jackpot for the upcoming Powerball Saturday drawing.