## 27 January 2016

### Powerball lottery - Boosting jackpots to boost sales

The January 2016 jackpot reached \$1.5B because the carried-over jackpot increased faster than ever before in the streak of 19 drawings without winner. To show this, the table below compares the \$1.5B jackpot to the \$564M jackpot of February 2015, which concluded a streak of 20 drawings without winner.

StreakJackpot amount (\$M)
Jan'16Feb'15
15255208
16300230
17334261
18529289
19948317
201,500395
21-564
StreakTickets sold (M)
Jan'16Feb'15
152624
164128
175429
1817637
1944048
2063573
21-190

The February 2015 jackpot reached half a billion dollars after 20 consecutive drawings without winner. The January 2016 jackpot reached three times that amount in one drawing less. In fact, it is surprising that the January 2016 jackpot could triple from \$529M to \$1.5B in two drawings. What happened?

## Funding Powerball's jackpot

To understand how jackpots build up, we have to understand some of the inner workings of the Powerball lottery. The 2015 Powerball group rules published by the Multi-State Lottery Association (MUSL) managing Powerball are sometimes ambiguous, so this section may not be perfectly accurate. To keep it simple, the Power Play option is ignored.

Although MUSL runs Powerball, each state lottery is in charge of advertising, selling tickets, and giving non-jackpot prizes to their respective winners. Each state lottery keeps half of ticket sales, which probably directly goes into the state's budget. The other half funds MUSL's four accounts: the prize pool, jackpot pool, bootstrap pool, and reserve.

The prize pool (aka Powerball Set Prize Pool) is filled weekly by each state lottery to pay the small prizes. Ignoring Power Play, it should receive at least \$4 / 38.32 + ... + \$1M / 11.7M = 32 cents per ticket to be able to pay out the prizes. In-between two drawings, its balance is close to zero.

The jackpot pool (aka Grand Prize Pool) holds the jackpot money. When the other pools (usually the bootstrap pool) need to be topped-up, up to 5% of sales is transferred from it to them. By the time the jackpot reaches \$110M annuity/\$70M cash, ticket sales have filled all other pools, and the jackpot pool receives the full 68 cents per ticket.

The bootstrap pool (aka Set-Aside Account) backs up the jackpot pool when the jackpot is won at the beginning of a streak. For example, every streak starts with a jackpot of \$40M annuity/\$25M cash. These drawings usually sell 10 million tickets, ie \$20M in sales. The state takes \$10M, small prize winners \$3.2M (32 cents per ticket), and so there is only \$6.8M left to pay the \$25M jackpot. The extra \$18.2M comes from this pool. Fortunately, 10M tickets have only 4% chance to win the jackpot, so the bootstrap pool is rarely emptied. It is filled by "taxing" the jackpot pool 5% of sales, ie 10 cents per ticket, until it has reached its \$20M cap.

The reserve (aka PRA and SPRA) exists so that MUSL does not get bad press for not paying winners their full prize. This could happen because of a system error, miscalculation, or because all other pools are depleted. When the reserve itself is depleted, prizes stop being fixed (eg \$1M or \$7) and become parimutuel to prevent breaking the bank. Until the reserve reaches its \$40M cap, filling it takes precedence over the other pools.

## January 2016 vs February 2015

To illustrate how these pools work, we can use the streak of 20 drawings leading to the jackpot of \$1.5B annuity / \$930M cash as an example. The streak starts on November 7, when 374k 2-dollar tickets and 101k 3-dollar tickets won small prizes. Ticket sales (estimated) are 24.87 * (374k * \$2 + 101k * \$3) = \$26M. The state takes \$13M, and small-prize winners \$4M. Let's imagine that the reserve is full. The jackpot had reached \$90M cash on November 4, so the bootstrap pool should be full, but to illustrate its workings, let's assume it is empty. Since the jackpot is not won, the bootstrap pool receives 5% of sales = \$1.3M. The jackpot pool receives the remaining \$7.7M. This process goes on until December 19, when the bootstrap pool reaches its \$20M cap. All these numbers are listed in the first table below.

On closure day, January 13, when the \$930M cash jackpot is won, the ten-week streak has raised a total of \$3.4B. Around \$623M has been paid to small-prize winners, \$930M shared between the jackpot's three winners, and \$1.7B kept by the states. As for the February 2015 jackpot, the states only received \$679M in roughly the same amount of time (ten weeks and a half). Judging from these two jackpots only, the 2015 tweaks seem to have tripled Powerball's profits.

Pool amounts (in \$M) leading to the \$1.5B annuity jackpot
date jackpot
(cash)
ticket
sales
prize
pool
jackpot
pool
bootstrap
"tax"
bootstrap
pool
11/725264.27.61.31.3
11/1132223.0151.12.4
11/1438284.1231.43.8
11/1844247.7261.25.0
11/2150276.4321.36.3
11/2557283.1411.47.7
11/2863284.8491.49.1
12/269323.7591.610.7
12/580388.2681.912.6
12/991335.5781.714.3
12/12103387.4881.916.2
12/16113396.2992.018.2
12/19127519.61131.820
12/23143589.9132full20
12/26161546.3153full20
12/301898414181full20
1/221011821219full20
1/633337566341full20
1/9597963159663full20
1/139301,3742741,077full20
closure9303,4406230NA20
Pool amounts (in \$M) leading to the \$564M annuity jackpot
date jackpot
(cash)
ticket
sales
prize
pool
jackpot
pool
bootstrap
"tax"
bootstrap
pool
12/326222.27.71.11.1
12/633264.4151.32.4
12/1039254.1221.23.6
12/1346274.8291.35.0
12/1752254.4361.26.2
12/20593210.2401.67.8
12/2465359.2471.89.6
12/27723210.3511.611.1
12/3178388.4591.913.1
1/385354.6701.714.8
1/795355.0811.816.6
1/101054110.2902.118.6
1/14114387.01001.420
1/171264816108full20
1/211355212122full20
1/241506218135full20
1/281706011154full20
1/311887415176full20
2/420610018209full20
2/725715130255full20
2/1138140174381full20
closure3811,3582780NA20

The Powerball tweaks have only been implemented for three months now. With little data to rely on, it is not guaranteed that profits will stay triple what they were before. Profits may have soared this time because of the buzz surrounding the record-breaking jackpot. The next billion-dollar jackpot may see mediocre sales because people got tired of Powerball or found other games to play. Will the next billion-dollar jackpot generate a billion dollars in profits? Will players adapt to the new odds? We will probably find out within a year.

#### 1 comment:

1. Hi, there. Very interesting lottery info. Special thanks for the January series of PB posts. I've never played it before the record-breaking draw. Currently I do not miss a draw, checking USA lottery results weekly to analyze the frequency of numbers. Carry on!