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I studied the distribution of delta numbers in a year's worth of winning numbers from the New York, California and Michigan lotteries. When I did this, I discovered something exciting but at first, truly puzzling. They are not randomly distributed, but instead have a clear bias toward smaller numbers!
Hard to believe? Check out some of the raw data yourself by clicking HERE.
This chart shows the distribution of delta numbers in several months' worth of Michigan lotto drawings:
| 01 +++++++++++++++++++++++++++++++++++++++
It turns out that nearly 60% of the time, a delta calculated from a winning number will be SIX or less! 30% of the time, the delta will be THREE or less!
In fact, ONE is the single most popular number, occurring almost 15% of the time. That translates to more than half the time in any given six-number pick. The predominance of the number ONE means that adjacent number pairing in winning lotto numbers must be quite common (and it is quite common, just look at any series of winning lotto numbers.)
Therefore, most of the Delta numbers you will be guessing can be picked from an even smaller set of numbers!
Why the low number bias exists in our calculated delta numbers is a challenge to explain. I expected to find a nice even distribution, perhaps clustered around 7 or 8, since that would be the average spacing when 50 is divided by six numbers. Instead, I see numbers below 8 coming up much more often. Why?
Well, there are valid statistical reasons this happens. When you consider that the sum of all the Deltas have to add up to the highest lotto digit, it's apparent that there isn't room for many large numbers. But the patterns I'm seeing still often seem out-of-the-ordinary. One possibility is that the balls in many lotto picking machines at times do not thoroughly mix. The excess of small delta numbers, and especially the predominance of ONE, mean that balls that went in the lotto machine next to each other are coming up together! It's not obvious in the lotto numbers themselves, but the delta calculation reveals the pattern.
To visualize this, imagine a lotto number machine where the balls all enter lined up in numerical order (like they do here in Michigan.) Now imagine that the numbers are picked without mixing the balls. What would happen? Well the picks would still be somewhat random, of course. But the balls nearest the exit ports of the machine would be the ones most likely to be picked. And All the balls near the exit port are consecutive numbers, since that's how they went into the machine. You might not know what numbers they are. But if you track Deltas, those number pairs would show up as ones. Now, this is an extreme example. But if the balls don't mix enough, you can see how some of these tendencies could remain.
Lending support to this theory are apparent trends (look at the raw data) in the frequency of number ONE in the deltas. The beginning of the chart shows lots of ones. Later on, they taper off, then start appearing more often again. This sort of behavior might occur with changes in the operation of the lotto machine. Perhaps some weeks the balls are allowed to mix longer than at other times, owing to TV schedules or other factors. An astute observer might pay attention to these trends and play lots of adjacent pairs when there are many delta ONEs coming up.
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