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Everyone Is Freaking Out About The $1.5 Billion Powerball, And The Stats Agree Well, this is it: the first North American lottery over$1 billion. With an advertised jackpot of $1.5 billion, and only five other Powerball lotteries1 north of a half-billion, we are far, far from home when it comes to reliably forecasting the turnout to this lottery. But the point remains: In all the trajectories of the model we’re playing around with, there’s a ballpark 95 percent chance someone wins this. Here’s where we stand: based on the old forecast — the one we used for Friday’s estimate — we’d estimate about 1.008 billion tickets will be sold for Wednesday’s jackpot. Based on that number — which is totally unprecedented and based on far too much extrapolation, keep in mind — we’d estimate a 97 percent chance of at least one winner on Wednesday’s drawing. It’s worth noting here that it’s very hard to develop a sanity test for this number. On one hand, sure, I could totally see the number of tickets sold for this lottery to be nearly double Saturday’s sales, especially given the wall-to-wall press coverage. On the other hand, a billion tickets (more than three times the population of the United States) is a ludicrous number! In the end, this lottery will be exciting not for what we’re able to guesstimate now, but rather the new data it’ll give us for next time. Still, I was eager to find the results of the new model, which recalibrates our estimates based on the Saturday drawing, when the jackpot capped out at$948 million and about 440 million tickets were sold. Since we’re in uncharted territory, my colleague Andrew Flowers and I decided to extrapolate the growth with two models, one that projects continued exponential growth and another that is more bearish on the growth rate at higher values. The new models2 say we’d estimate 1.2 billion tickets sold if the growth accelerates, and 554 million tickets if it is slower.3 If we were flying blind for Saturday’s record drawing, this is a whole other level entirely. That’s a very, very wide range, one that really hammers home how completely in the dark we are with turnout. Still, there’s anywhere from an 85 percent chance of at least one winner to a 98 percent chance4.

Well then. If historical turnout behaves the way we think it might, we’re looking at a whole lot of Powerball tickets sold. Ideally neither of these models are all that accurate, and we get new data to tweak one of them to represent reality. They’re just two ways to put a number on the upper and lower bounds.

Americans spent about $1.9 billion bringing this lottery from$40 million in November to $948 million on Saturday. The “real” jackpot — if you took the cash payout, rather than the structured annuity — was only$587 million. And while the proceeds from the lotteries theoretically go to fund state education, keep in mind that it is morally dubious in the first place to have a lottery to fund education, rather than an adequate tax system.

And while I absolutely hate that whole “the lottery is a tax on people who can’t do math” schtick — I think it’s demeaning to the undereducated, and reflects more a societal issue than a personal one — I have some legitimate questions about the 10 million tickets that get sold at $40 million or$50 million or other low jackpots. That’s not a good idea at all! Consistently participating in a lottery with a very negative expected value is a great way to lose a lot of money over a period of time. Take the Los Angeles Times’ awesome Powerball simulator interactive for a spin to get a feel for how lotteries can bleed you dry over time.5 The decision by Powerball officials in October to change the jackpot odds from 1 in 175 million to 1 in 292 million further screws over the consistent customers in an attempt to get big jackpots.

The new odds further devalue the money spent by that core base of lottery devotees who play no matter what the jackpot is. What I’m trying to say is that $1.5 billion didn’t just appear: Americans paid for it in scores of lower-stakes lotteries, and it was far from cheap. Because even now the expected value on a Powerball ticket is negative. The “expected value” tells us, based on the probability of winning and the value of the prize, how much an average individual ticket is worth. It’s a moving target with Powerball, contingent on the size of the jackpot. According to Sean Davis at The Federalist, at a$1.4 billion jackpot, after factoring in the likelihoods of multiple winners and split jackpots, as well as the certainty of federal taxation, the expected value of a Powerball ticket for which you paid $2 is only$1.32.

If you want math advice on the Powerball, there’s really not much more to go on than “You shouldn’t play with the intention of making money” and “Yes, buying a second ticket does technically double your chance of winning, however, this does not constitute a strategy.”

Think of the $2 more as buying a conversation piece to pitch how good you’d be at being rich. My friends and I talked it over and decided we would be generous winners, just, fair, financially competent and blackout drunk for no more than four consecutive months. That, or the$2 is FOMO insurance for your office pool. Because how much would it suck if everyone you work with won a damn lottery and you didn’t?

The Multi-State Lottery Association is probably pretty pleased with itself right now: Changing the Powerball jackpot odds from 1 in 175 million to 1 in 292 million did indeed lead to a billion-dollar lottery, just as I speculated last summer.

However, and this is only statistically informed conjecture, I’m personally a little worried they went too far with the odds change. Lottery turnouts are based on excitement and coverage. Powerball used to be able to get on the news with a $400 million jackpot. There’s a possibility their own success could hurt them moving forward: The folks behind Powerball should be worried that news organizations won’t bite until they see nine zeros. In that case, and it remains to be seen if this bears out, there’s a possibility it will become hard to drum up the necessary turnout to get it to a billion in the first place. It’s just a theory right now, but I’d watch the media coverage closely over the next year. ## Footnotes 1. Since the change to$2 tickets.
2. The fast-growth one is based on a second-order polynomial, which is a fancy way of saying, “a formula with a squared variable in it.” The slow-growth one is based on a cubic polynomial, which is an equally fancy way of saying, “a formula with a cubed variable as well as a squared variable in it.”
3. Since our ticket sales estimate is in serious extrapolation territory and I’m viewing it more as a guideline than a serious forecast, none of these should be taken as gospel. Last Friday, based on the $800 million jackpot, we estimated 428 million tickets sold and a subsequent 77 percent chance of the winner. Based on the eventual$948 million jackpot, there were 440 million tickets sold, which translated to a 78 percent chance of at least one winner. Just like last time, I kind of want to be wrong: more data means better understanding of how lotteries work at the upper bound, and thus better models. The hope is that the next time a billion-dollar lottery comes around, we won’t be flying blind! Any new data we get about how people behave is a blessing. The point is, we got very lucky on Saturday, since based on the actual turnout there was only a 22 percent chance of no winner. It wasn’t the likeliest scenario, but it was bound to happen about a quarter of the time based on the actual ticket sales. However, I would be gobsmacked if we don’t have a winner this time. It’s definitely possible, just highly unlikely.
4. You may notice in the following chart that the cubic model decreases at very high levels. This is the result of it being a relatively simple model, not because we’d actually expect interest to wane as the number goes up. Either way, once we obtain data for Wednesday’s lottery it shouldn’t affect the model moving forward. Just take it as demand curve that assumes the market is at capacity.
5. At least smokers get to look cool while they slowly lose thousands (and their health).

Walt Hickey is FiveThirtyEight’s chief culture writer.

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