Preface: I don't commonly play the lottery. I am a software engineer and this post (my first on this forum) is a result of a work discussion which inadvertently resulted in something I find strange. I'm interested in responses from all you lottery gurus and this forum seemed like a pretty lively place for such a response.
The powerball machines are loaded in a sorted order. Starting with the number 1 ball, bottom to top, right to left. Mega Millions on the other hand seems to be loaded in random order using some unknown means. One might assume with the length of time and random spinning of the machine carousel, all bias is removed. That would be the most prominent and seemingly reasonable assumption. To test this we looked at the last 2 years of both MM and PB and compared the distribution of the two. What I found wasn't necessarily shocking, but still a little odd / maybe? We started with October 2015 in both samples using the last 205 draws to eliminate the data from when the PB format changed numbers. Here are just the first summaries:
Powerball summary nums 205 draws:
WB1 |
WB2 |
WB3 |
WB4 |
WB5 |
Min |
1 |
1 |
1 |
2 |
1 |
Max |
69 |
69 |
69 |
69 |
69 |
Avg |
34.69 |
33.83 |
36.11 |
39.05 |
34.93 |
med |
33 |
31 |
36 |
41 |
32 |
stdev |
19.75 |
20.48 |
19.79 |
20.12 |
20.45 |
MegaMillions summary nums 205 draws:
WB1 |
WB2 |
WB3 |
WB4 |
WB5 |
Min |
1 |
1 |
1 |
1 |
1 |
Max |
74 |
75 |
75 |
75 |
75 |
Avg |
36.84 |
37.30 |
36.15 |
37.81 |
38.76 |
med |
37 |
37 |
36 |
37 |
38 |
stdev |
20.31 |
20.61 |
22.55 |
20.64 |
20.94 |
Look at how much more boring / normalized the MM numbers are. Is there some sort of machine bias, maybe somehow caused by the way the powerball numbers or loaded? I also split the PB data into two samples of 102 and 103. Guess what, nothing changed. I then created my own random number generated in excel and ran it 205 times for 5 numbers between 1 and 69. Interesting... much more boring data as would be expected!
WB1 |
WB2 |
WB3 |
WB4 |
WB5 |
Min |
1 |
1 |
1 |
1 |
1 |
Max |
69 |
69 |
69 |
69 |
69 |
Avg |
34.92 |
34.63 |
34.57 |
34.38 |
33.69 |
med |
33 |
35 |
37 |
35 |
35 |
stdev |
20.52 |
19.82 |
19.03 |
20.17 |
19.97 |
I then ran this 100 times on the same sample size to see if I could generate anything with a bias like real PB history. A large deviation coupled with a higher average (39) seems to occur in about 5% of the runs.
My post is 100% curiosity. I'm a programmer not a statistician or avid gambler. Just curious assuming a lot of you guys dwell on this kind of stuff, what your thoughts are. Is this significant / worth a deeper dive or would you dismiss it as just an anomaly of nature which will eventually even out in a few more years?