Range Probability

[Peter]

I had a thought that if I could guess the Range of the next draw, I could use that info when choosing the first and last number.

I created this chart this morning.
What do you think? Any merit in it?

Looking at the table or chart, what range would you predict is more likely to occur?

[ido]

Hi Peter ,
sorry for my poor english , wath is the subject same of your "range"?
It's the 49 balls?
Range 30-46 means the numbers 30 to 46 and it's appearance on
the first and last position,the range number should mean a frequence
in a given column than?

Because without knowing the responce ,from the quic glance on
your table what I see and wath second me you have proof is that
in mater of the "range 30-46"(wathever it is) the UK Lotto in
it's History kept a quite normal(see the shortcut attached ), even
too close to the theoretical expectations behaviour...

....but In such a normality,pitty, usualy is difficult to find a patterns
for good predict if use a statistic methods....

Or maybe I didn't understand your initial idea?

[Peter]

The statistical range of a set of numbers that is a draw containing 6. a,b,c,d,e,f
the range being "f minus a"
eg a range of 40 could be column 1 = 8, column 6 = 48

30 to 46 account for over 3 quarters of all draw combinations, 76.01% to be exact, and that is why I'm focusing on those 17 out of a possible 44 statistical ranges.

To explain one row
eg the row for a range of 32

The theoretical probability of a the last number of a lottery draw (after being sorted in ascending order) minus the first equalling 32 is 3.83%. After 1601 draws, you could expect that 61 draws would have a range of 32. As it turns out, that is exactly what we've had.

I've also included a recent sample of the last 2 and a half years. ie 158 draws. This shows that a range of 32 hasn't performed as expected of late.

Compare the 'overall' with the 'sample' as you will to help you come to a decision.

Maybe I've got this all wrong as maths isn't a strong subject of mine. I'm just curious if I can increase my chances of selecting the correct 6 numbers.

If I was to guess the correct range, let's say, 35 - there would still be 14 different sets of 2 to choose from. What I'd do then is narrow those down by looking at other frequency tables.

Let me know if I'm talking nonsense won't you.

[Peter]

Well the range for 1602 was 43.

This was my second choice after 35.
I'd never have picked 1 and 44 though given that 44 had already been out the last 4 draws in a row. 5 in a row is ridiculous.

[Len]

Hi Peter
To pick a range, look at the past data, attached.
What I do is divide the draws into ten draw sections
as this draw was the start of a new ten draw section
look back at the first draw in the previous sections
some time's you can get repeats this time it was 21 & 44
the draw before had repeat numbers 06,32,44
the draw before that got repeat number 10


I hope I put that OK?

[Peter]

Hi Len, I don't think you understand what I meant. The probability of getting at least one ball repeated in a draw from the previous draw (or from nDraws ago) is 56.404%. I have a whole table for ball repeats which I'm confident I have right. I'm not so confident about the Range stats page. It's clear I'll have to add better labels to it. Maybe Statistical Range - percentages.

This is what I meant by Range
http://www.mathsisfun.com/definitions/ra...tics-.html

Take last night for example. If I could have guessed from my table that the Statistical Range had a decent chance of being 43, then I would then have a 1 in 6 chance of getting the first and last number correct. 1,44 - 2,45 - 3,46 - 4,47 - 5,48 - 6,49.

I've added another attachment - this time the distribution curve.
I hope I've made this a little clearer.

Best,
Pete

[Frank]

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.

[Peter]

Cheers Frank and thanks for that response and I totally agree with what you've said regarding prediction. I've been playing with these numbers since I downloaded the csv file from the merseyworld site 4 weeks ago. I came to the same conclusion that over a large amount of time, everything will seem to average out and in the short to middle term there will be those variations you talk about.

My main question to the seasoned analysts here is about the law of averages. Is it worth the paper it's written on? I've been thinking about another way today and you've probably been there and wore that t-shirt too. Take ball number 22 - according to my spreadsheet, it hasn't appeared for 36 draws. Now, I've been tempted to say, "the law of averages says...blah, blah, blah", but I should be saying, what is the probability of a number not being drawn 36, 37 or n times in a row and doing the maths to see if I can get any hints. But it all hurts my head. As it's random, each ball still has the 12.245% probability of appearing in the next draw and 87.755% of not appearing at all.

If all balls adhered to the theoretical, ball 22 should have come out 4 times over since it's last appearance, which is like flicking a fair coin 8 times and getting tails each time. I don't know what it that's telling me to pick heads next!

---

Forgot to ask, is your website still current? Do you mind giving out the url?

Cheers
Pete

[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

[Peter]

Cheers Frank for this information.

I've been working off the 6 main draw balls and wisely or not, casting bonus ball aside - so what constitutes an overdue ball to me might not be overdue to you. Although for grouping purposes, I have 7 groups of 7 with 7 colours representing each group instead of the familiar 5.

I like your idea of the 'overdue factor'.
If I use your example of ball 24, I see this as being absent for the same 22 draws but I would divide that by 49/6 giving me an overdue rating of 2.693 instead of your custard pi.

You've certainly given me something to think about. And I'll have a go at working out the actual average return time too although I don't know quite where to start in excel for that yet.

Cheers
Pete