Range Probability

[Peter]

I Frank,
So I've had a crack and come out with this but I'm not sure what I can take from it or even how to interpret it. A little help needed I think lol.

It's based on 6 main balls and no bonus.
See attachment.

I've sort of lumped all 49 balls together. I think that's what you did with your 6.

I didn't do this in excel - don't know where to start. I wrote a quick basic program in qb64 though.

Pete

[Frank]

(05-02-2011 05:22 AM)Peter Wrote:  I Frank,
So I've had a crack and come out with this but I'm not sure what I can take from it or even how to interpret it. A little help needed I think lol.

It's based on 6 main balls and no bonus.
See attachment.

I've sort of lumped all 49 balls together. I think that's what you did with your 6.

I didn't do this in excel - don't know where to start. I wrote a quick basic program in qb64 though.

Pete

I'm sorry I got the impression from your charts that they were Excel charts, and mistakenly thought you were using it for your analysis.

Well it took me a while to get my head around what you are showing in your PDF file ( I dislike PDF as a format as you cannot import the data it displays on a web page into a spreadsheet, its read only). Despite the fact that you ignore the bonus ball and also use the convention that 0= direct repeat and hence your results do not mimic mine I do agree with the general trend of your results. They look OK. What I suggest you do is plot them on a chart, that is your percentages on the vertical axis and gap on the horizonta axis to reveal the exponential decay curve. I also took logs of the original 1-49 totals (e.g log to base e of 1224 for a gap of 0, log to base e of 960 for a gap of 1 etc. using your data) and plotted those to reveal a linear graph . For results including bonus ball this told me that the vast majority of gaps are less than 49 hence this sets the max overdue flag at 7 when using overdues to predict a return of a ball in any of the 7 positions. See what you come up with .

[Peter]

I have got all my data in excel spreadsheets but I don't know how to collect this bit from the main data set. That's why I wrote a quick program asking it to count the gaps for each ball.

Anyway, I printed the output to to a csv and then changed it to xls so you can see. It says to me that 70% have reappeared in 7 draws and nearly all by 28 draws.

What do you think?
   

ps, this time i've included the bonus

[Frank]

You could interpret it that way. but thats why I take logs to get the linear trend. Ths is your data plotted.







When you see the log plot, It says to me you can only be confident that its really overdue ( due for a gap of 0) when its approaching a gap of 50. Hence my original suggestion of an overdue of 7.
Of course the majority of the time you can say that by 10 draws is getting a little late, and make up a rule based on whatever you think. Its a matter of personal judgement but I hope you agree that by doing this you get a picture of the probabilites and can make a more considered judgement.

[Peter]

Going back to the result of just using 6 main numbers shown in the earlier attached pdf,
I've converted the cumulative column to a number by multiplying it by 49.



What's interesting about that is it returns a number for each gap.
So for gap 0 you'd expect to see 6 balls ie. 43 balls not appearing in last draw.
Gap 1, the graph shows 11 ie. 38 balls not appearing in last 2 draws.
Gap 2, the graph shows 16 ie. 33 balls not appearing in last 3 draws.
...
Gap 14, the graph shows 42 ie. 7 balls not appearing in last 15 draws.
Gap 20, the graph shows 45 ie. 4 balls not appearing in last 21 draws.

This tallies nicely with the actual gap record after draw 1602
gap 0, 6
gap 1, 10
gap 2, 13
...
gap 14, 8
gap 20, 4

I think I'll persue this a little further when I've got time.
Cheers,
Pete

[Frank]

Good luck !

[sonja]

(05-01-2011 10:30 PM)Frank Wrote:  Hi Peter, I have been reading your posts with interest. You sound a bit like I was 17 years ago when I first started using lottery Analysis using Excel. I have stayed out of this discussion till now as I'm in semi retirement from major lottery analysis and don't want to get drawn into time consuming analysis any more. Suffice it to say, you name the statistic, I've probably been there, done it and bought the T shirt. Some of the stuff I've done is on my website, but most of it is on the hundreds of spreadsheets I've devised over the years to analyse various aspects, questions, queries cropping up in 14 years of being a member of various lottery forums. Your charts make perfect sense to me, the million dollar question is how dow we use them to predict future draws. Well , I've been doing it since 1994 and I'm not a millionaire so maybe that answers your question.
The particular topic of this thread is range low to high and as you have found from your research, all the probabilities are very low for any range, your best chance being about 5% for a range of about 40 ( going by your curve). So at best you've a 1 in 20 chance of correctly guessing the range of a future draw. If you do decide to have a go, you'll need a database of all the results that satisfy that range. You have noticed in your study of the last 158 draws that there are statistical 'pockets' of ranges that temporarily appear more than 5% of the time , I see you've spotted a span of 38 has been doing better than theoretical over the period, whereas range 35 has only done half the appearances it should.
All this is interesting. great fun to do if you're into Excel but what can you read into this for the future ?
Well I've come to the conclusion that because the lottery is random you cannot use these methods to pinpoint a named draw in the future and infer its possible range of results. However, I think just as the weather can be approximately forecast, but not exactly, these trends can illustrate short anomalies in lottery behaviour which might persist for a few draws, before correcting themselves. The trick is spotting this and deciding if it will persist or correct, and over a band of how many draws. Its far from an exact science, but thats statistics for you. Everything is as predicted in the long run on average, but in the middle you have some rough variations.
Don't let me discourage you, If you like maths and you like Excel there are far worse things you can use it for than getting your head around statistics and combinatorics, its a fascinating adventure that has given me years of pleasure.

Hi Frank!

What is your website? I'm sure I can get some inspiration from all your hard work since 1994!!