# Statistical Analysis of MegaMillions

Good Morning Group,

So, I am an accountant, not a statistician.  I suspect there are some on here that are much more versed in the Statistical analysis of large random number drawing sets.

I was doing some analysis in Excel, and wanted to share some of what I observed.  Do with it what you will, but I thought the findings somewhat interesting.

Ok, so the background:

I downloaded the drawings of the Mega millions results; the data set dates back to approximately February 2010

I aligned the results in descending order; it is posted in a csv file as drawn (i.e.: 25,7,43,58,6)  This alignment is necessary to understanding the numbers drawn by position, their range, etc.

With the number position aligned, I then looked at the standard deviation of each number set (N1 = 1st number result in numeric order, N2=2nd number result, etc).  This tells me how far beyond the median the result appear in approximately 68% of the time.  This bell curve, and the width of the bell curve determining the range in which the number fall into 68% of the time.

As an example, N1 has a median of 8, and a standard deviation of 4.  That means that 68% of the time, the N1 drawing result should appear in a range of the numbers of 4 through 12.  With me so far?  Good, lets keep going.

I applied the analysis to all 5 of the MMs number draws, as well as the MB number.

 N1 N2 N3 N4 N5 MB Range 08 24 22 24 24 12

Now, I then took the range calculated from the above analysis, and divided it into 3rds, rounded of course.  This provided me with a 1/3rd range of the following:

 N1 N2 N3 N4 N5 MB 3 8 7 8 8 4

I then looked at the percentage of times in which there were 0 through 5 times numbers drawn, by position, fell within the Lower 3rd, Middle 3rd, and Upper 3rd of the range.  Still with me?

Ok, so the following are the results of my review of 160 draws, 80 draws, and 20 draws respectively (i.e.: 20 draws from the last, 80 draws back from the last, etc).  This should represent the Long, medium and short runs ( in my opinion/thought process anyway):

 L3rd Analysis -160 Draws M3rd Analysis - 160 Draws U3rd Analysis - 160 Draws 1 41 25.6% 1 44 27.5% 1 14 8.8% 2 20 12.5% 2 32 20.0% 2 27 16.9% 3 8 5.0% 3 13 8.1% 3 22 13.8% 4 7 4.4% 4 2 1.3% 4 42 26.3% 5 5 3.1% 5 0 0.0% 5 37 23.1% 0 79 49.4% 0 69 43.1% 0 18 11.3% L3rd Analysis -80 Draws M3rd Analysis - 80 Draws U3rd Analysis - 80 Draws 1 20 25.0% 1 21 26.3% 1 6 7.5% 2 12 15.0% 2 15 18.8% 2 15 18.8% 3 3 3.8% 3 8 10.0% 3 10 12.5% 4 2 2.5% 4 2 2.5% 4 20 25.0% 5 1 1.3% 5 0 0.0% 5 20 25.0% 0 41 51.3% 0 33 41.3% 0 8 10.0% L3rd Analysis -20 Draws M3rd Analysis - 20 Draws U3rd Analysis - 20 Draws 1 5 25.0% 1 7 35.0% 1 0 0.0% 2 2 10.0% 2 5 25.0% 2 5 25.0% 3 2 10.0% 3 3 15.0% 3 2 10.0% 4 1 5.0% 4 1 5.0% 4 5 25.0% 5 1 5.0% 5 0 0.0% 5 2 10.0% 0 9 45.0% 0 4 20.0% 0 6 30.0%

This data primarily speaks to the results at more of a 10,000 foot level.  It is interesting to see the similarities in the short run vs long runs stats on say the number of times one of the draw number will come from the lower 3rd of the numbers drawn range (approximately 25 - 25.6% of the time).

So what can you do with this data?  My thought would be that it could be incorporated in potentials for getting winning numbers that are gleamed from what I refer to as a "squeeze" process.  To me this means that someone may have anecdotal information that would tell them that based on recent activity, or a presentation of whatever and how they view a particular game draws, that they should expect to see a number drawn with an 8 in it.  This extrapolating this to a next level with something like this information telling me that there is an "X%" probability that the next drawing should have numbers from the L3rd, 1 from the M3rd, and 2 from the U3rd.

All this should allow for a closer assessment of the pools of numbers to focus on.

Best to all

CountingMan

Since the beginning of humanity people have looked at everything from clouds to stars to ham sandwiches in an attempt to discern patterns that prove some sort of meaning or order. The ham sandwich case (I suppose clouds and cups of coffee too) has included appearances by Jesus and the Virgin Mary. Astrology, with it's beginnings in ancient history, survives today in supermarket checkout tabloids. Does this mean a true pattern/bias/meaning exists? Not at all. In fact it would be surprising if these "revelatory" or "miraculous" events did not appear. In practical terms a virtually infinite number of statistical "events" happen every instant of time. Humans tend to pick up on ones that mean something to them.

Is there likely to be any actionable bias in the MegaMillions lottery? Extremely (to the power of extremely) unlikely. The lottery administrators go to extreme (sorry for the repetition) lengths to ensure that doesn't happen. I would sooner believe in the tooth fairy than believe in lottery systems, especially those based on frequency.

Orange71

In the greater scheme of things, I would have to agree.

I would not "back up the truck" nor "bet the farm" on anecdotal evidence.  That having been said, I tend to trust my own instincts or read on the current state of things than trust a quasi RNG that is any given convenience store's lottery terminal.

Is the data that I originally posted, on its face actionable?.  I would say no without hesitation.  However, could it be used as part of a larger process? I would have to say I think it would be helpful to the right person to be part of a larger process.

Best of luck!

CountingMan...

That's pretty good info... I wish you would do the same Analysis, but in the 3 categories of 100 games, 50 games & 10 games..!! then email those results to me... Info such as that can be very usefulwhen combined with Probability Math..!!