A (Qualified) Defense of Powerball

I’ve heard variants of this argument for most of my adult life.  Many statisticians and economists love to point out that the expected value of a lottery ticket is easily calculated and almost always negative.  Hence anyone who actually purchases a lottery ticket is an innumerate rube, behaving irrationally.  My undergrad statistics professor went so far as to tell us that if he ever saw one of his students buying a lottery ticket, he would flunk them instantly.


I never fully bought that argument, and I still don’t buy it.  I’ve always found their smug disdain for the lottery rather off-putting.  Granted, I don’t think it would be wise to blow the rent money on Powerball, and any genuine expectation of riches is surely misplaced, but I also think my erstwhile professor carried things a bit too far, and that rationality isn’t always as easily calculable as some would have us believe.


As a physicist by training, I’m a quantitative sort myself, but I also understand that mathematical models can break down when pushed too far.  If these green eyeshade types genuinely lived their lives bound by such rigid calculus, none of them would ever purchase an insurance policy.  Every actuarially sound policy on the market has a negative expected value; otherwise the insurer would go out of business in short order.


But of course economists and statisticians do buy insurance, even if such a purchase can’t be strictly justified by statistics.  And they do so based on the perfectly rational consideration that a catastrophic accident or illness could easily ruin them financially, while the insurance premiums are comparatively modest, and can be absorbed with little real financial impact.


But isn’t the lottery the same thing in reverse?  Sure, buying a lottery ticket is a sucker’s bet, but the (extremely) unlikely outcome of hitting a jackpot would have life-changing consequences, whereas the buck or two you spend on the price of admission has negligible financial impact.  And none of this takes into account the less quantifiable entertainment/fantasy value of playing.
I don’t play often, but I will buy the occasional ticket, and I don’t think that warrants flunking ECON 101.  And of course the academics are right, as far as it goes, that buying lottery tickets isn’t a bankable proposition.  But when you find yourself arguing, as Alex Tabarrok does in the link above, that buying a chance on an $800 million jackpot is not rational, but paying the same price at the same odds for a chance at (say) $1.3 billion may well be?  I’d say that’s a pretty good sign that you’ve pushed your model too far.