This is a fun (quick and dirty) analysis of winning Powerball numbers to date. Wager at your own risk.

The basic question is whether the Powerball numbers drawn are entirely “Random”. The answer is, not surprisingly, no. The big caveat, of course is that as of 2016-01-10, there have only been 29 drawings under the new rules… Over the long run, these should get closer to “random”. Still, it’s a man-made machine drawing the balls, so it may never be random.

Figure 1: These numbers are over-represented in the winning numbers data. We would only expect a frequency close to 2 if the draws were random.

Figure 2: These numbers are under-represented in the winning numbers data.

Figure 3: These ‘PowerBall’ numbers are under-represented in the winning numbers data. We would expect around one draw per available number.

Interestingly, There are several PowerBall numbers that have yet to come up in any of the drawings…

Never Been Drawn

            3
            8
           12
           14
           16
           23
           24
           26

So, what does this mean? Well, probably not much. There’s not really enough information currently to tell whether the Powerball numbers are truly random. It doesn’t change my belief one way or the other. So here’s another way to think about it:

1- If I believe the game is random, it doesn’t change my behaviour in the slightest. The next draw will also be random.

2- If I believe the game is not random, I could take this information and change what numbers I choose accordingly. That is, I would choose numbers that have a higher likelihood of being drawn, and avoid those that are less likely.

3- The third position, is of course, that there is a negative net expected value (In the long run, I always expect to lose money; statistically speaking), and you should not bet on Powerball in any case. (Which is probably the smartest choice overall.)

So, if you decide to play, play well, and if you are in school of thought number two, and fortunate enough to win using this information, send me a note at: http://www.twitter.com/dataminerx