The jackpot fatigue theory
The Powerball mechanics have been tweaked several times since it started in 1992. Starting in January 2012, the game had 59 white balls and 35 red balls so that a billion-dollar jackpot would happen every 10 years. No such jackpot happened until the rules changed again in 2015, but as the table below shows, the jackpot reached half a billion several times.
|Date||Jackpot ($M)||Tickets (M)|
Powerball sales dropped 19% nationally in 2014. Lottery officials suggested two explanations: the lack of a huge jackpot in 2014, and jackpot fatigue: lotteries need increasingly bigger jackpots to attract the casual players who only buy tickets when the jackpot is huge.
The table above confirms that there was only one jackpot above $300M in 2014, but it rejects the fatigue theory. For jackpots between $300M and $350M, the number of tickets sold decreased from 89M in 2012 to 51M in 2015. And for the three jackpots between $550M and $600M, the number of tickets sold went from 286M in 2012 to 191M in 2015. Sales from the biggest jackpots lost 35% in three years.
Yet, the fatigue theory made New York state lottery officials shift their focus from jackpot-driven games, where jackpots get very big too rarely, to instant scratch-off games with more frequent prizes. New York state is a major actor in the Powerball lottery: it ranks third in ticket sales, after California and Florida. So it's likely that the tweaks of October 2015 were an attempt to address jackpot fatigue.
October 2015 tweaks
In October 2015, white balls increased from 59 to 69, and red balls decreased from 35 to 26. Thus the odds of winning a prize increased from 1:32 to 1:25, but the odds of winning the jackpot decreased from 1:175M to 1:292M. Lower jackpot odds means longer streaks until the jackpot is won, ie bigger jackpots. Projections made in 2012 suggested that a billion-dollar jackpot would happen every 10 years. Data from November 2015 to January 2016 suggests that billion-dollar jackpots should now happen every year or so, and there is a 63% chance for one to show up within 5 years. This tweak is similar to the British National Lottery tweak of June 2015: 5 balls used to be picked among 49, which was raised to 59, resulting in the £58M jackpot of January 2016, the largest in the National Lottery's history.
Decreasing the odds of winning the jackpot decreases the expected value of a ticket. This expected value is plotted in the graph below, against the jackpot value. Before the rule change, the jackpot had to reach $200M for a ticket to be worth $1. Based on drawings data from 2015, $200M jackpots were expected to occur every 24 weeks. Now, after the rule change, a ticket is worth $1 when the jackpot reaches $450M, which is expected to happen every 34 weeks.
Long story short, the October 2015 tweaks increased the chance of winning a consolation prize, but decreased the chance of winning the jackpot and the expected value of a ticket. Since the expected value of a ticket estimates how much each lottery ticket costs to the organizers, their profits must have increased!