Tuesday, October 18, 2011

Analysis of the new 2012 Powerball game changes. Part 1: Game summary & prize evaluation

In late June, the MUSL announced that it was going to change the format of Powerball. Since most available literature simply reiterates the notice of changes, we believe that players are wondering whether: these new changes are good for them, and if they should be eager to purchase tickets at the increased costs.

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 that:
Originally, we intended to include all of these topics in one post. But, we quickly realized that the length of the post was too long, thus we are breaking the analysis into these 3 parts.

This is Part 1. Its purpose is to explain what the new changes are, and what they will mean to lottery players with regard to prizes that the new Powerball game offers.

The 2012 Powerball Changes
The table below summarizes the array of the Powerball changes. Most notably, players will find that the cost of tickets will increase from $1 to $2 each and that the minimum jackpot will increase to $40 million.

Summary of 2012 Powerball Changes Power Play Prizes Fixed
Starting jackpot at $40 million (up from $20 million)
Match 5 prize fixed at $1 million (up from $200,000)
Matching Powerball Only prize at $4 (up from $3)
White Ball Remains at 1 to 59 (no change)
Powerballs 1 to 35 (down from 39)
Regular Ticket Costs $2 (up from $1)
Powerplay Ticket Costs $3 (up from $2)
Power Play Prize Amounts  Now Fixed (no multiples)
$1M Prize to $2M (2x)
$10,000 Prize to $40,000 (4x)
$100 Prizes to $200 (2x)
$7 Prize to $14 (2x)
$4 Prize to $12 (3x)

Because the number of white balls remains the same, the chances of winning the 2nd tier prize of 5+0 remains the same at 1 in 5,153,632.65. However, since the number of Powerballs decreases by 4 to 35, the overall chance of winning the Powerball jackpot will decrease by approximately 20 million to 1 in 175,223,510.

Implementation Date
Implementation of the new game format will coincide with the Powerball's 20th anniversary. The expected sales date for the new Powerball format is January 15, 2012 and the first drawing will be January 18, 2012.

Why the Changes? Powerball's Reasoning.
On its FAQ page, Powerball identified 9 reasons for modifying the game. The first eight provide their rationale why players will continue to purchase tickets at the increased ticket cost. Each of these addresses the players' psychology and takes advantage of their vulnerability. The last reason, "Game variety" is something that must be questioned.
  1. Scratch tickets costing $2, $3, $5, $10, $20 and $50 all sell
  2. Powerball price was fixed for 20 years
  3. Ticket sales increase more rapidly when jackpot is higher
  4. Jackpots should increase by $10M each drawing, reaching players "buy" level more quickly
  5. Average jackpot of new format will be $255 million (was $141 million)
  6. There will be more millionaires since all match 5+0 winners will receive $1M.
  7. A fixed Power Play takes uncertainty out of winning. Those matching 5+0 will get $2M, enough to pay taxes and still keep $1M
  8. There will be more winners.
  9. Game variety.
Game Variety?
With the new Powerball odds reduced to 1 in 175+ million, it is easy to conclude that the overall game format is very similar to Mega Millions which also boasts a 1 in 175+ million chance of winning. The major difference between the games will be: the ticket price; and the prizes for the top two prizes.

The table below summarizes the differences between the two games in a side by side manner. Powerball is shown in the light blue columns, and Mega Millions is shown in the pink columns.

Match MM 5/56+1/46
PB 5/59+1/35
Prize $
Prize $
Prize $
Prize $
Power Play
5+1 175,711,536.00 175,223,510.00 1 1 $12,000,000 $40,000,000 $12,000,000 $40,000,000
5+0 3,904,700.80 5,153,632.65 45 34 $250,000 $1,000,000 $1,000,000 $2,000,000
4+1 689,064.85 648,975.96 255 270 $10,000 $10,000 $34,762 $40,000
4+0 15,312.55 19,087.53 11,475 9,180 $150 $100 $521 $200
3+1 13,781.30 12,244.83 12,750 14,310 $150 $100 $521 $200
3+0 306.25 360.14 573,750 486,540 $7 $7 $24 $14
2+1 843.75 706.43 208,250 248,040 $10 $7 $35 $14
2+0 18.75 20.78

1+1 140.63 110.81 1,249,500 1,581,255 $3 $4 $10 $12
1+0 3.13 3.26

0+1 74.8 55.41 2,349,060 3,162,510 $2 $4 $7 $12
0+0 1.66 1.63

Illustrated are the odds (or chances), number of winners, prize payout for normal tickets, and prize payout for the multiplier (Megaplier and Power Play) tickets of both games.

The six graphs below illustrate various portions of this table, showing the Powerball players percent gain or loss in each of these pairs of information. The percentages are calculated by: dividing the Powerball values by the associated Mega Millions values; subtracting 1; and then multiplying by 100.

1. Compare Overall Odds of both Games
Chart P1 shows the differences between the odds of both games. As shown, the chance of winning the Powerball jackpot is only 0.3% less than winning the Mega Million jackpot (so they are about the same). However, odds of matching anywhere from 5 to 1 of the white balls and not the Powerball are much more difficult in Powerball. It is 32% harder to win the 2nd tier prize of 5+0, 24.7% harder to match 4+0, and 17.6% harder to obtain a 3+0 winner in Powerball.

But when a Powerball is matched, it is easier to win a prize. That is because there are less Powerballs than Megaballs. As shown in red, it is 5.8% easier to match a Powerball 4+1, 11.1% to easier for 3+1, and so on. Matching the Powerball only is 25.9% easier in Powerball.

If you are one of the typical 96.9% of players, you will probably not win anything at all. In Powerball, you are 1.8% more likely not to match any balls in Powerball than in Mega Millions. But, on the overall, there will be 0.6% more winners in Powerball.

2. Compare Total Winners in both Games
Chart P2 illustrates the differences between the numbers of winners in each category. In effect, it is the mirror image of the above odds comparison. In both games, there is only 1 jackpot winner, and no winners for matching 0, 1, or 2 white balls and not the bonus ball. This means players are indifferent to those categories.

Excluding the jackpot, Powerball offers more opportunities to win a prize whenever the Powerball bonus is matched. In these cases, the Powerball advantage ranges from 5.9% to 34.6%.

When the player does not match the bonus Powerball, Mega Millions outperforms (in red). There will be 24.4% more 2nd tier Mega Millions winners than Powerball. Similarly, those matching 4+0 or 3+0 are 20% and 15.2% more likely to win a prize in Mega Millions than in Powerball.

These differences are all explained by the fact that there are less white balls in Mega Millions and less bonus balls in Powerball.

3. Compare PB to MM Prizes per Ticket
Chart P3 summarizes the difference in prize winnings per ticket between the two games.

This verifies Powerball's goal of offering higher jackpot and 2nd tier prizes when the jackpot is set to minimum. Those who win a Powerball jackpot will collect 233.3% more than the Mega Millions winner, and will get 300% more when matching 5 white only.

The Powerball winning ticket also has the advantage for those matching the Powerball and 1 or 0 white balls which will pay out more than its rival game.

Those in the middle are better off with Mega Millions as players matching 4+0, 3+1, or 2+1 balls will receive approximately 1/3 larger prizes.

There is no difference in winnings for players matching 4+1 or 3+0 in either game. And, of course, all losing tickets will collect an even $0.

4. Compare PB to MM Prizes by Dollar Spent
Since Powerball tickets will cost $2 each and Mega Millions only $1, it is necessary to normalize the prize winnings to dollar spent.

Chart P4 illustrates this difference. Here we see that Powerball only pays out more for the jackpot and 2nd tier winners.

All other lower tier Powerball prizes pay substantially less than or equal to their associated Mega Millions counterparts.

5. Compare PB Ticket to MM Megaplier Ticket
So what happens if a player buys a $2 Megaplier ticket in comparison to the $2 Powerball ticket?

In each case, the player pays $2 either way. But, except for the 1st prize, Powerball players receive lesser prize amounts. Depending on their winning, a player will receive 42.5% to 80.8% less than a Mega Millions winner.

If the player is lucky enough to claim the winning jackpot ticket, the Powerball winner will be paid 233.3% more. Whereas, it you match all 5 white balls and not the bonus ball, you will win the same amount of money in both games.

6. Compare PB Powerplay to MM Megaplier
Lastly, a player may wish to buy the multiplier options in both games, which means he will spend $3 for a Powerball Powerplay ticket, and $2 for a Mega Millions Megaplier ticket.

Here we see a pattern similar to that of buying a single Powerball and Mega Millions ticket.

In this case, Chart P6 summarizes the winning payouts. Here, the Powerball player will win more if they win any of the first 3 prizes or the bottom two.

Those whose tickets fall in the middle will receive smaller Powerball prizes compared to Mega Millions.

In summary, we can agree that the Powerball game will pay out higher jackpot prizes. However, we do not believe the extra cost enhances the desirability of the prize.

Players have to remember that approximately 97% of all tickets sold will be losers. This means that only 3% will win something.

Since the chances of winning the jackpot is about the same in both Mega Millions and Powerball, we believe that it is more beneficial for players to buy 2 individual Mega Millions tickets instead of 1 Powerball ticket. By doing this, the Mega Millions player will have twice as many chances of winning a prize compared to the Powerball player. On a per dollar basis, the prize structure for Mega Millions is more attractive as well.

However, if your goal is to win a prize of at least $1 million, then it is better to buy 1 Mega Millions ticket with the Megaplier option. Except for the jackpot, these players lucky enough to have a winning ticket will always win more than the Powerball ticket holder.

Powerball® Enhancements Start January 2012 (Nebraska Lottery)
Powerball FAQ/History/News (Official Site)
How 2009 Powerball Changes Effect You
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