# Powerball is a great business model but not for its players

It now takes longer for a Powerball jackpot winner to emerge. There are fewer jackpot winners, but the jackpot sizes are getting bigger. Powerball ticket revenues are way up as people are excited about the giant Powerball jackpots. What we are witnessing is the result from a redesign of Powerball game. The redesign is succeeding spectacularly for the Powerball authority. For the Powerball players, what do they get? The odds of winning the jackpot are getting longer. Should they do something else with their money instead? This post aims to highlight another side of the Powerball equation.

Prizes in the Powerball lottery are alluring. There are prizes for \$4, \$7, \$100, \$50,000, \$1 million and of course, the grand prize (the jackpot prize), which nowadays is in the hundreds of millions of dollars. The largest Powerball jackpot that was ever won (to date) is a whopping \$1.58 billion on January 13, 2016.

Even though the grand prize attracts the most attention, the smaller prizes are also designed to be attractive. With the power play option, the \$1 million prize can be turned into \$2 million and the prizes below \$1 million can be increased by up to 10x. So the \$50,000 prize could potentially become half a million dollars.

The attractiveness of Powerball is part of an overall strategy to drive ticket sales. The strategy is so successful to the detriment of the Powerball players who plunk down tens or hundreds of dollars every week in the hope of winning \$1 million or more.

The Powerball lottery has drawings twice a week, every Wednesday evening and Saturday evening. There are winners in every drawing (these are the smaller non-jackpot prizes). However not every drawing produces winner(s) of the Powerball jackpot.

Figure 1 – Most Recent 5 Powerball Drawings as of August 26, 2017

In the most recent 5 Powerball drawings, only one produced a jackpot winner with the amount of \$758.7 million. For the preceding jackpot winner, you have to go back to June 10, 2017.

The Powerball rules were revised in 2015 to make winning of the jackpot much less likely. Under the new rules, the odds for winning the Powerball jackpot are one in 292 million (1 in 292,201,338 to be exact). Since the inception in 1992, the odds for winning the Powerball jackpot had been increasing in a dramatic fashion. Prior to the most recent revision, the odds were 1 in 175 million, which are long odds for sure but are dwarfed by “1 in 292 million.” As a result, it is less and less likely that a drawing will producing a jackpot winner.

There are 292,201,338 many different 6-number Powerball combinations (5 numbers for the 5 white balls plus 1 number for the red Powerball). If all 292,201,338 combinations are chosen by the Powerball players, then there would be for sure at least one winner of the jackpot. But 292,201,338 is a huge number (see here on how the number 292,201,338 is derived).

For example, the entire population of the United States is 321.4 millions in 2015, with 248 millions of them age 18 or over. If every adult in the U.S. purchases a Powerball ticket, it is still possible that there will be no winner of the grand prize (but there could be a few \$1 million winners). Locating a person by randomly picking one person from the U.S. adult population would have easier odds than for winning the Powerball jackpot.

If the context of U.S. population is not sufficient to convince you, here’s another way to appreciate how big 292 million is. Look at this graphic from WSJ. The piece strives to illustrate how vast a quantity 292,201,338 is. Just to scroll the page over that many dots is a near impossible task.

The odds for winning the Powerball jackpot are mathematically zero (being 1 in 292 millions). That is precisely the strategy of Powerball. With no winners of jackpot over weeks and months, the excitement for Powerball is turned into a frenzy. As a result the jackpot usually keeps building until it reaches the “hundreds of millions” range or the “1 billion” range. The rules were designed to rachet up the excitement and as a result driving up sales. So the most recent jackpot winning of \$757.8 million and the \$1.58 billion in January of 2016 are no accident. They are in a sense manufactured. This point is also discussed in this piece from Washington Post.

Of course, it is not necessary for every one of 292,201,338 Powerball 6-number combinations to be purchased in order to produce a jackpot winner. Nor is it a feasible proposition (see this piece from Forbes on this point). The selection of a sufficiently large proportion of these combinations is sufficed. But for that to happen, the excitement has to be intense enough to draw people in. This is the case in the drawing on August 23, 2017 when the jackpot was over \$700 million. Who wouldn’t be excited by the prospect of winning 0.7 of a billion dollars?

The subsequent drawing on August 26, 2017 had a jackpot that was starting over (roughly \$53 million). Naturally, there was no jackpot winner in that drawing. The pattern is clear. When the jackpot is small, there is not sufficient excitement to drive ticket sales and there are usually no jackpot winners. Then the jackpot accumulates to a sizable amount (say hundreds of millions of dollars or more). Once sufficient number of people are drawn in due to the huge jackpot, a winner or winners will eventually emerge.

Looking at Data

Frequencies of Powerball jackpot winnings are hard to come by. The Powerball winning numbers are widely available. But the winning numbers by themselves do not tell you whether someone won the jackpot. A remarkable web page is found that lists all Powerball jackpot winners from 2003 to the most recent winner on August 23, 2017. There are 175 Powerball jackpot winners in this 14-year period, giving an average of 12.5 winners per year. This is not the whole picture. Let’s see how these 175 winners are distributed across the years.

Figure 2 – Frequency of Powerball Jackpot Winnings

The most telling part of Figure 2 is that there are only 7 jackpot winnings in 2016 and 5 winnings in 2017 through August. The Powerball revision occurred in October of 2015. In the years through 2015, the annual frequency of winnings ranges from 10 to 16, with an average of 12.5 a year. Then it drops off significantly to 7 a year in 2016, the first year after the Powerball redesign.

How much was paid out for the jackpot winnings in these years. The following bar graph shows the total payout for the jackpot winnings by year.

Figure 3 – Powerball Jackpot Total Payout By Year (not including non-jackpot prizes)

The total amount of winnings for the 7 jackpot prizes in 2016 is \$3,431 million or \$3.4 billion, the most telling part of Figure 3. The total payout per year for the prior years was in the 1 to 2 billion dollars range. The payout amounts are a function of the total ticket sales. So 2016 is a banner year for Powerball. Clearly the redesign is working. The rule redesign is clearly giving the sales that they were looking for. The next graph shows the average payout per jackpot.

Figure 4 – Powerball Jackpot Average Payout By Year (not including non-jackpot prizes)

Note that the average jackpot in 2016 is \$490 million (\$10 million shy of half a billion). The 2016 average is pushed up by the \$1.58 billion jackpot winning in January of 2016. Combining 2016 and 2017, the average jackpot payout would be \$440 million, way higher than the previous averages in the \$100 to \$200 million range. So in the new era of Powerball, the jackpot payouts are huge and there are far fewer jackpot winners. The following shows the jackpot prizes won in 2016 and 2017.

(2017) \$759 million, \$447 million, \$60 million, \$156 million, \$435.3 million

(2016) \$121.6 million, \$420.9 million, \$246 million, \$487 million, \$284 million, \$291.4 million, \$15.8 billion

The business model of Powerball clearly is working for the folks who run Powerball. Ticket sales are way up. Players are excited about the game. What’s in it for the players?

Playing Powerball is an excellent entertainment. With a \$2 admission price, you can dream and fantasize for a few days. Once a week habit would be about \$100 a year in entertainment cost. Buying one ticket per drawing would be a \$200 a year habit. Regular customers of Starbucks would spend more than that amount on coffee in a year. Of the regular lottery players, roughly the top 5% spend a few thousand dollars a year (a hundred thousand dollars on average in their lifetime, assuming no interest) for an illusive chance to win \$1 million or more. What if these regular players invest the money elsewhere?

If they invest the money instead on a conservative fund earning 2% a year, they would accumulate an nest egg of hundreds of thousands of dollars. Assuming a rate of returns at 2% a year, investing \$3,000 a year for 40 years would yield approximately \$185,000. In fact, if they invest in a broad base stock market index (e.g. S&P 500 index), they would do even better in the long run. The long run historical S&P 500 returns are around 10% a year (7% after inflation). Assuming a rate of returns at 7% a year, investing \$3,000 a year for 40 years would yield around \$640,000!

Playing Powerball for \$3,000 a year would mean buying 30 tickets a week, 15 tickets per drawing, assuming playing 50 weeks out of 52 weeks in a year. The top lottery spenders would pay this much or more in a year.

The number \$640,000 may seem like a pittance comparing to a Powerball jackpot or even the smaller Powerball prize of \$1 million. Even in the rare chance that someone wins \$1 million, the winning is taxed and the after tax amount could be \$600,000. Thus the rates of return of a lifetime investment in playing lottery are not as great as people imagine. Without winning, the lifetime lottery investment of a few thousands dollars a year would be money going down the drain. For a more detailed discussion, see this piece from Washington Post.

The calculation of the Powerball winning odds is a great math lesson. Rather than looking at the winning odds, perhaps it is more instructive to look at losing odds. The odds for not winning the Powerball grand prize (per \$2 bet) are 292,201,337 to 292,201,338, which are essentially 1 in 1.

Blog posts on lottery are some of the most viewed posts in our affiliated blogs. See this piece on Powerball and the lottery curse from a companion blog. It has links to other blog posts on the topics of lottery.

$\copyright$ 2017 – Dan Ma