Tuesday, November 22, 2011

Expected Powerball 2012 jackpot levels and growth - Part 2: Analysis of the new 2012 Powerball game changes

Powerball recently announced that it will modify the format of the Powerball game in January of 2012. You should expect to see:
  • Average jackpots of $115 to $145 million;
  • A high jackpot of $700 to $800 million;
  • Average jackpot growth of $15 to $20 million.

To help players understand the implications of these changes and whether they should continue to play the new Powerball game, we are writing a 3 part series of posts:
This post is Part 2 of our series. It addresses the potential impact of the new changes on the Jackpot offerings and projects the the anticipated jackpot offerings.

To begin, we summarize the two most significant changes that affect the annuity jackpot offerings. These are:
  1. Minimum jackpot is set at $40 million
  2. Cost of each ticket is $2 each.
Powerball's goal of offering larger jackpots will be achieved by doubling the ticket price to $2. Having twice the amount of money, they will be able to double the minimum jackpot from $20 million to $40 million.

Since jackpot levels will be higher, they believe that the players "buy" level will be reached more rapidly and that players will eagerly purchase tickets at the inflated costs. So, the questions arise:

How quickly will Powerball jackpots grow?
What will be the average size of Powerball jackpots?

Historical Jackpot Distributions
To begin, we review the range of winning Powerball and Mega Millions jackpots since 2001. In the graph below, we observe 4 historical jackpot ranges. The first two on the left illustrate Powerball, and the two on the right represent Mega Millions. Each range graph identifies 5 pieces of information:
  1. The complete range from minimum to maximum.
  2. The 84% range (shown by the thick white portion)
  3. The average (horizontal black line)
  4. The median (both the orange horizontal line and the purple square
  5. The 97% marker (orange square)
Current Powerball / Mega Millions Jackpot Ranges

This data is a graphic visualization of the table immediately below.

Jan 09
Jun 05
Average 66.6 74.2 56.3 65.0
Median 49.0 59.0 37.0 44.0
Mode 20.0 20.0 12.0 12.0
Maximum 365.0 260.0 370.0 370.0
Minimum 10.0 20.0 5.0 12.0

Since the format of both games changed, we wanted to see the impact of the most recent. Thus, we break apart the Powerball jackpots after January 2009 and the Mega Millions after its June 2005 changes.

Since the minimum jackpot offerings grew for both these games, we see that the average jackpot won increased as well. For Powerball, it increased from $66.6M to $74.2M; and Mega Millions increased from $56.3M to $65M. Interestingly, the median value (the 50% level) increased by the amount equal to the increase in jackpots. So, as the Powerball minimum moved from $10M to $20M, its median moved by $10M as well, from $49M to $59M. And, the Mega Millions median increased $7M (from $37.0M to $44.0M) after the minimum jackpot increased from $5M to $12M.

Additionally, the mode (the most frequent jackpot level) for both games is calculated to be the same as the minimum jackpot after the changes (i.e. $20M for Powerball, and $12M for Mega Millions).

Thus, we can conclude that the mode of Powerball after 2012 will later become $40 million.

Historical Jackpot Changes
To help estimate how the new 2012 Powerball jackpots will grow, we first examine the historical changes in jackpot growth as shown in the table below. Here we see the complete growth of all drawings, compared to growth when jackpots are below $40M (LT 40M), between $40M-$100M (40-100M), and above $100M (GT 100M).

Avg JP Avg Chg GT 100M 40-100M LT 40M
PB All 66.6 12.4 25.4 12.1 7.1
PB After 2009 74.2 15.0 25.7 15.0 8.7
MM All 56.3 11.5 30.4 11.9 6.4
MM After Jun 05 65.0 13.4 29.5 12.5 7.9

Since the minimum Mega Millions jackpot is $12M and Powerball is $20M, we find that Powerball jackpots increase at a faster rate than Mega Millions when the jackpot is $100 million or less. However, the differences are not as great as we would expect.

Once the jackpot (in either game) reaches $100M, we find that Mega Millions jackpots increase faster. We attribute this to the fact that the chances of winning Mega Millions (1 in 175 million) is less than Powerball (1 in 195 million).

However since the overall odds of the new 2012 Powerball game will be the same as the current Mega Millions game, we expect Powerball accretion to equal that of Mega Millions once the jackpot reaches and exceeds $100 million.

Expected Distribution
Looking at the distribution of the actual jackpots won, we see that the Mega Millions and Powerball jackpots are rather similar. Certainly, Mega Millions peaks around $50 million, whereas Powerball peaks at $80 million. Beyond that, we find that Mega Millions players have won more jackpots over $200M than those of Powerball.

Cumulative Winning Jackpot Distribution (Pct)

Estimating Future Powerball Jackpots after 2012
Utilizing all of the above information, we have prepared the table below indicating our estimates of future Powerball Jackpots. These are shown in Yellow. Next to our estimates are Mega Millions and the existing Powerball game.

Each game begins a sequence set to the the minimum Jackpot. Since the Powerball begins at $40 million, we expect each jackpot from $40M to $100M to increase by $15M. Once the $100 million level is reached, new Powerball will increase by $30M until the 10th drawing. At that point, it will double to $60M. When the jackpot reaches $400 million, subsequent jackpots will increase by $100 million each.

 Chg  PB 2012+ Projected Jackpots Dwg
     Chg  Current MM
     Chg  Current

15 40 1
8 12 1
9 20 1

55 2

20 2

29 2

70 3

28 3

38 3

85 4

36 4

47 4

100 5
13 44 5
15 56 5
30 115 6

57 6

71 6

145 7

70 7

86 7

175 8

83 8

101 8

205 9

96 9

116 9
60 235 10
30 109 10
25 131 10

295 11

139 11

156 11

355 12

169 12

181 12
100 415 13

199 13

206 13

515 14
60 229 14
60 231 14

615 15

289 15

291 15

715 16

319 16

316 16

Regarding the potentially largest jackpots, it is reasonable to expect to see a jackpot of $700 to $800 million. This would be reached after the 16th or 17 consecutive drawing without a winner. This amount would be in line with those previously reached by Mega Millions and Powerball (approximately $370 million).

Conclusion: Summary of Powerball 2012 Jackpots
Based on the above information, we can answer our initial questions and summarize our findings as follows:

  • Expect average jackpots to grow by $15 to $20 million.
  • Expect average jackpots of $115 to $145 million;
  • Look for jackpots to reach $700 to $800 million.

Word of Caution
Initially, we believed these estimates to be too low. But then we realized the conflict that the new Powerball 2012 game posed.

Although the new game offers jackpots twice the size of the existing game, players are expected to purchase tickets that cost twice as much. We believe the lure of the new jackpot level of $40 million will attract players to purchase the same dollar amount as they would currently spend. This means that jackpots will increase at the same rate of $15 million when levels are at or above $40M. This level of increase will be sustainable because Powerball will be paying out the same amount of money in the new game as they would in the old game.

But, the difference is only half the amount of tickets will be sold. Thus, on the average, it will still take 6 to 7 drawings before a jackpot is won. By then, the jackpot will be $115M to $145M.

Powerball 2012 will have the same winning frequency as the Mega Millions game which will continue to have jackpots of half the size (because tickets cost half as well).

Two factors pose risks for Powerball. If the expected jackpot levels are not reached and maintained, then players will become frustrated and reluctant to spend twice the money for a ticket. Further, if mega jackpot levels of $250 or more are not reached quickly, players will become more convinced that Mega Millions and other State lotteries offer better opportunities. If this happens, then the new 2012 Powerball will fail to succeed.

On the other hand, if these levels are reached quickly, players will eagerly flock to the new game regardless of cost. Thus, we have to wait and see.
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