Range Probability

[Frank]

Hi Peter, i think you are into the realms of overdueness when you note how long a ball has been absent and then try and use this to infer that it should appear because it is statistically overdue. I don't know if you've come across this before but I will cover it just in case. For a 6/49 lotto (including bonus ball drawn from the same pool) you draw 7 balls at a time and have 49 available, So you expect on average to see any ball every 49/7 = 7 draws. The probability of seeing any ball in any draw is 7/49= 14.286% and leads to an expected probability in 7 draws of 7 X 14.286% = 100% , which doesn't always happen. A ball has as much chance of appearing as a bonus ball as it does a main ball ( its anly an accident of position drawn), so only looking at main balls skews the reality of the statistic in my opinion.
So we work out the overdue factor by dividing (number of draws missing) by ( number of draws expected before appearance) . Actually ball 22 appeared as a bonus ball in draw 1596 , ironically 7 draws ago. So its overdue factor would have been 1 had it not appeared right on time.

A better example is ball 24 which hasn't appeared in any capacity since draw 1580 ( 22 draws ago) incidentally as a main ball. So it is 22/7= 3.143 (the value of PI) times overdue. The longest absence of any UK ball was number 17 for 73 draws =73/7 = 10.42 times overdue. A good excercise to do would be to work out over lotto history a table of frequencies absence periods and express as a % of all the draws. You will get something like:- ( 1 = no absence= direct repeat, 2= missed one draw etc.)
1 16.11%.. of the time
2 12.15%
3 10.77%
4 9.30%
5 7.27%
6 6.81%
7 6.45%
8 5.80%
9 4.88%
10 4.05%
11 3.96%
12 2.12%
13 2.12%
14 1.84%
15 1.93%
16 0.92%
17 1.10%
18 1.38%
19 1.01%

This isn't a full analysis, I took a sample of about 6 balls just to be quick. Its a statement of the obvious, that quick returns are more likely that long absences.

Which brings us nicely back to the law of averages. I quickly worked out that by the time you get to 49 draws absent ( 7 times overdue) then the law of averages suggests that its time this number appeared. It doesn't work to specific draw though, its just an indicator.

My site is Lotterygen