Science Reader Question: So You’d Like to Win a $1.5B Jackpot

crowd photo

The line for Powerball tickets. (Photo by Guzmán Lozano )

SS asks:

What makes statistical modeling different from, say, new age methods of trying to predict the future?

When the multi-state lottery jackpots reach staggering 10 digit totals, someone in my office will organize a lottery pool. And because I’m the closest thing we have to a statistician, they hope I’ll pick the numbers. The request is made with a dismissive chuckle, yet underlined with hope that I really can crack the lottery code. Unfortunately, expecting statistics to tell you winning numbers is asking the wrong question. Curiously, no one ever asks me the right ones.

Lottery commissions use statistical modeling to make sure there are no patterns in the winning numbers that could be used to predict the next paying sequence. They also use statistical models to determine exactly how big the jackpots should be so that the state keeps the percentage it wants to keep for revenue purposes; after all, lotteries are intended to fund government programs. On average, 60 cents of every dollar spent in the US on lottery tickets is paid out in prizes; for comparison, casinos often pay closer to 90 cents on the dollar. Note that either way, the payout is less than one dollar; the (state) house always wins.

Statistical models, when used correctly, are great at explaining what happens in large numbers of similar situations. That’s why the lottery commissions can use them productively; large numbers of people are playing the lotteries. The commission doesn’t have to predict correctly how much money it will pay out to each player; it just has to predict what the average payout will be over all the players. And since it completely controls how the lottery works, it’s not hard to make such a prediction. In fact, this jackpot is so astronomically large because the game was made less likely to produce a winner for any given drawing, leading to more rollover and bigger prizes (which attract more players and more revenue); the states haven’t gotten more generous with their payout percentage.

Statistical models can’t guarantee correct answers for singular events like the exact winning numbers of one drawing. That doesn’t lessen the demand for such answers, which is where “new age methods” and other systems try to fill the gap. And you know what? Every now and again, one of them will get it right. We take notice, because winning is so unlikely, and because we are wired to discount the vast number of incorrect ones. We start to wonder if seeing the future really is possible.

In reality, we’re back in the realm of statistics. A lot of lottery predictions are made all the time, enough to make it statistically likely that a few will be correct. After all, lotteries do have winners. When they do, we need to resist the urge to wonder “What are the odds this one specific person would have predicted this one drawing?!?!?” Instead, we should ask the statistical question: “Have enough predictions been made about enough lotteries to get positive results?”

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Andy Walsh

Andy has worn many hats in his life. He knows this is a dreadfully clichéd notion, but since it is also literally true he uses it anyway. Among his current metaphorical hats: husband of one wife, father of two elementary school students, reader of science fiction and science fact, enthusiast of contemporary symphonic music, and chief science officer. Previous metaphorical hats include: comp bio postdoc, molecular biology grad student, InterVarsity chapter president (that one came with a literal hat), music store clerk, house painter, and mosquito trapper. Among his more unique literal hats: British bobby, captain's hats (of varying levels of authenticity) of several specific vessels, a deerstalker from 221B Baker St, and a railroad engineer's cap. His monthly Science in Review is drawn from his weekly Science Corner posts -- Wednesdays, 8am (Eastern) on the Emerging Scholars Network Blog.

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