Now when all the fools know, what has been selfevident to thinking persons, the
futility and outright absudity of basing number predictions for powerball and other
lotto games on the announced past drawings, maybe it is time to inject a bit of
reality into the process and examine what can be predicted.
If all the possible combinations in a given lotto game were generated and the sum
of the integers, not the digits, were calculated one would obtain a frequency
distribution practically equal to a normal bellshaped curve. This shape and the
data can then be subjected tostandard statistical methods. Thus ther will be mean
and a standard deviation. Each of these can be calculated from two simple
formulas anybody can use.
The first part of Powerball ,5/53, is a typical lotto game and will serve as an
illustration. The sums will vary from 15 to 255 with a mean of 135 and a std.dev.
32.9. This implies that in the long run 2/3 of all sums will fall in the range 135+32
to 135-32, i.e. 167 to 103, while 90 be between 135+54 and 135-54, i.e. 189 to
81, and 95% will fall between 135+65 and 135-65, i.e. 199 and 71.
The above ranges are specific to PB while each other lotto game must have a
unique set of parameters, which must be calculated separately. Also, there will be
a spread within each set of five or six numbers in a game. It is 14.7 for PB.
It would require hundreds of thousands if not millions of drawings to establish
a near bell shaped curve for most games.
The 205 drawings of PB since it went 5/53 yielded a mean of 135.2 with a s.d. of
32.2 for the sums and a mean internal s.d for the set of five of 14.9 +/-3.9.
This discussion is intended as a contribution to the mathematics of lotto and not
system for predicting specific winning numbers. Each player may use it to weed out
the most unlikely combinations. The spread in a set of five consequtive numbers
is only 1.6 while the mean s.d.is 14.7. That might serve as a guide.
Bertil