Poisson Distribution - This Can Help You

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Re: Poisson Distribution - This Can Help You

Postby davidg3907 » Tue Dec 19, 2017 2:00 pm

Any tabular formation would have taken too much space, so I shall endeavour to convey as much information as possible in prose form.
Taking each category separately, some are performing better than others, but even the weaker aspects have been improving due to the ongoing tweaks.

Average Goals. Split into 3 bands of 60, but 6 bands of 30 produced similar results.
Apart from the anomaly with exactly 4 goals occurring in too many matches in the lowest range (which is offset by a shortage of games with 5 or more goals), the figures are fairly consistent through the bands. I feel there are two primary reasons for this; the number of goals scored is still below the statistical average on which the spreadsheet is based (2.70) and the possibility that Poisson itself tends to flatten the graph. This is something I aim to check over Christmas using actual results from the past 10 seasons.

Over/Under 2.5 Goals.
The figures are distorted by the slight shortage of goals, but this is getting closer to expectations.

1-30 60%+ 16 over 14 under. 31-60 53.50-60.00% 16 over 14 under. 61-90 48.37-53.49% 15 over 15 under.
91-120 43.13-48.36% 16 over 14 under. 121-150 36.98-43.12% 17 over 13 under. 151-180 23.28-36.97% 9 over 21 under.

Under 2.5 Goals.
Obviously, the shortage of goals helps these figures to the same extent, so results are the reverse of those above (i.e. the new 1-30 becomes 21 under and 9 over).

Home win to nil. 6 batches of 30, with 4 figures showing Won to nil, Won BTTS, Draw, and Lost.
1-30 16-7-4-3 31-60 14-5-9-2 61-90 9-6-4-11 91-120 9-3-10-8 121-150 4-3-11-12 151-180 2-4-14-20

That is highly encouraging. It is a similar story if using bands of %s.

Over 32% 28-12-10-4 23-32% 20-8-15-17 Under 23% 6-8-17-35

Away win to nil. 6 batches of 30, with 4 figures showing Won to nil, Won BTTS, Draw, and Lost.
1-30 11-7-5-7 31-60 6-5-10-9 61-90 5-3-12-10 91-120 7-5-6-12 121-150 4-1-5-20 151-180 0-1-5-24

Apart from what is probably a very slight statistical blob in 91-120, that looks very promising. Again using %s shows the following.
Over 21% 16-11-15-14 12.5-21% 15-9-18-26 Under 12.5% 2-2-10-42

These figures will mean more once W-0 odds (in the case of rounds 1-11 approx odds) can be added.

BTTS YES. Displayed as overs-unders. Another set hampered by the shortage of goals but recovering.
1-30 12-18 31-60 13-17 61-90 12-18 91-120 17-13 121-150 14-16 151-180 10-20

As %s should give a better indication, they are shown too.

Over 55% 9-12 50-55% 15-19 47-50% 9-13 43-47% 23-24 Under 43% 22-34

BTTS NO. The bands will give the reverse of the YES figures. They are displayed as unders-overs.
1-30 20-10 31-60 16-14 61-90 13-17 91-120 18-12 121-150 17-13 151-180 18-12

Split into % bands possibly gives a more accurate picture again.

Over 60% 24-15 55-60% 19-16 50-55% 28-23 47-50% 13-12 Under 47% 18-12
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Re: Poisson Distribution - This Can Help You

Postby davidg3907 » Tue Dec 19, 2017 4:05 pm

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Fortunately for you, I am not a mathematician, so I can't explain this in mathematical terminology.
Unfortunately for you, that means I shall have to do my best in "layspeak".


Column 1 is the finite number of goals per match.
Columns 2 & 3 show Poisson estimating the frequency of those given 473 goals in 180 matches this season, and 10302 over 3800 matches in the previous 10 seasons.
Column 4 is the actual total of each event over 10 years.
Columns 5, 6, and 7 show the respective figures for Under & Over 2.5 goals.
Column 8 shows the figures for this season to date, converted to a full season in column 9 and a 10 year total in column 10.
The 10 year and 1 year totals at bottom left are just a check on Poisson to ensure the total goals figures are correct.

Explanation out of the way, what does it indicate?

Ignoring for now the 6 goals and above from this season as the sample size is too small, Poisson is within reasonable tolerance over 10 seasons.

However, comparing the actual totals in column 4 with the Poisson calculations in columns 2 & 3 would suggest that Poisson is about right with the frequency of 3 or 5 goals, overestimates the likelihood of 1 or 2 goals, and underestimates that of 0 or 4 goals.

Column 6 is within an acceptable variance from column 7 suggesting the overall split between Overs and Unders is not too far out.

This season's projection in column 10 seems to confirm the bias, with 0, 1, 4, and 5 goals higher than the Poisson expectations in column 2, with 2 & 3 goals being well below those expectations.
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Re: Poisson Distribution - This Can Help You

Postby davidg3907 » Wed Dec 20, 2017 8:30 pm

I have made a few adjustments that will reduce goal averages from the 2.70 start point to 2.65 (current average this season is 2.63 but it has been rising slowly). They are mainly tweaks to the expected goals Poisson calculation but also widening the spread of ratings slightly (the effect of the latter being minimal). As all teams play one game at home and one away in the next two matches, there is no urgency to enter the score data after the first set so I shall post them simultaneously. The home/away goals ratio will favour the away team in the first set and the home team in the second due to there being an imbalance of the big 6 at home or away each week.

Happy Christmas to all following this. I will return in time to post for the New Year program.

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Re: Poisson Distribution - This Can Help You

Postby davidg3907 » Wed Dec 20, 2017 8:33 pm

Both sets have an above average goal ratio in favour of the away team but I'll have to see how it goes.


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Re: Poisson Distribution - This Can Help You

Postby wonderwall » Wed Dec 27, 2017 5:31 pm

Very good, I still think its a bit of a misnomer to try to get the precision on Over/Under Goals on all matches - If it were possible to get hold of the spreadsheet, it would be possible to comment more productively. At this point, I would suggest to put the Odds in there, which you can match with your spreadsheet prediction probabilities and then the ones that have the Top Value (Probability expressed in Odds terms >Actual Odds) are the ones that you could do some more work on, just because I don't believe its possible to predict everything, but you do want to focus on the ones you have an Edge.

Also, the Win to Nil, I would ignore as you've got goal posts, dodgy penalty, whatevers, which mess up the probability. I suppose you could trade this to a degree.

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Re: Poisson Distribution - This Can Help You

Postby davidg3907 » Wed Dec 27, 2017 8:35 pm

Wonderwall,

I've sent you 2 copies by email already. Please feel free to reply at any time as any input would be helpful. This is most certainly NOT a finished product and I am trying to evolve in real time without resorting to any form of back-fitting other than using some standard historical data to set the pattern.

The same applies to anyone else who feels they could add anything.

One other piece of info that I have been able to glean recently (up to round 18 included) is the 1X2 odds, something I had not really looked at previously.

For 18 rounds that is 540 pts if 1 pt was placed on each outcome in each match. The Poisson figures have shown a return of just 528.59 while par is obviously 540 and actual SP is 552.89 so this is another avenue I shall continue to explore.

The slightly lower than average number of goals scored has meant that Overs have suffered to some extent, with Unders reaping the benefit. I have possibly rectified to some degree Poisson's desire to steer goals to a central figure, something that is not reflected in the past 10 seasons' records, and that matches between two strong teams are assumed to be goal-fests but aren't. I am trying to get the new figures to settle in.

Win-to-nils have been relatively successful in cases where home teams are rated to have a better than 32% chance, a range that may be extended with away teams as odds tend to be better. I am still working on backdating W-0 odds for the season, so this will be a long process if nobody has a record of them.
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Re: Poisson Distribution - This Can Help You

Postby davidg3907 » Fri Dec 29, 2017 5:58 pm

The results from 22nd/23rd saw 31 goals with 6 over 2.5 goals, 6 BTTS Yes, and 3 Win to nils ( 2 home 1 away).

Average Goals top.
4 6 0 1 2
Average Goals bottom.
3 4 5 4 2
Over 2.5 Goals.
4 6 0 1 2
Under 2.5 Goals. (The quoted figures are for OVER so deduct from 100)
4 3 4 5 2
Home teams winning to nil.
Yes Drew Drew Won Lost Drew Lost Yes Drew Drew
Away teams winning to nil.
Yes Drew Drew Drew Lost Lost Won Drew Drew Lost
BTTS Yes.
Won Lost Lost Lost Won
BTTS No. (The quoted figures are for YES so deduct from 100)
Won Lost Lost Lost Lost




The results from 26th/28th saw 35 goals with 5 over 2.5 goals, 6 BTTS Yes, and 3 Win to nils ( 2 home 1 away).

That brings the average goals per match up to the 2.70 on which the program was based.


Average Goals top.
6 7 5 3 1
Average Goals bottom.
0 2 2 5 4
Over 2.5 Goals.
6 5 7 3 1
Under 2.5 Goals. (The quoted figures are for OVER so deduct from 100)
0 2 2 4 5
Home teams winning to nil.
Yes Draw Won Yes Draw Draw Draw Won Lost Lost
Away teams winning to nil.
Yes Won Lost Draw Draw Draw Lost Lost Drew Lost
BTTS Yes.
Won Won Won Lost Won
BTTS No. (The quoted figures are for YES so deduct from 100)
Won Lost Won Lost Won

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Re: Poisson Distribution - This Can Help You

Postby davidg3907 » Fri Dec 29, 2017 10:07 pm

These two rounds of matches continue to show a ratio of home to away goals that favours the away side too much.
This will be looked at again over the F A Cup weekend.

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Re: Poisson Distribution - This Can Help You

Postby davidg3907 » Fri Jan 05, 2018 11:01 am

The results from week 21 saw 18 goals with 4 over 2.5 goals, 5 BTTS Yes, and 1 Win to nil (1 home 0 away).

Average Goals top.
2 2 5 3 0
Average Goals bottom.
0 0 3 3 0
Over 2.5 Goals.
2 5 2 3 0
Under 2.5 Goals. (The quoted figures are for OVER so deduct from 100)
0 0 3 3 0
Home teams winning to nil.
Drew Yes Drew Won Drew Lost Won Drew Drew Drew
Away teams winning to nil.
Drew Drew Drew Drew Won Lost Lost Drew Drew Lost
BTTS Yes.
Won Won Won Won Lost
BTTS No. (The quoted figures are for YES so deduct from 100)
Won Won Won Won Lost




The results from week 22 saw 35 goals with 7 over 2.5 goals, 6 BTTS Yes, and 4 Win to nils (1 home 3 away).


Average Goals top.
4 4 3 2 3
Average Goals bottom.
3 4 3 2 1
Over 2.5 Goals.
4 4 3 2 3
Under 2.5 Goals. (The quoted figures are for OVER so deduct from 100)
3 4 3 1 2
Home teams winning to nil.
Won Yes Lost Draw Won Draw Lost Lost Lost Lost
Away teams winning to nil.
Yes Yes Won Lost Draw Yes Draw Won Lost Lost
BTTS Yes.
Won Lost Lost Lost Won
BTTS No. (The quoted figures are for YES so deduct from 100)
Won Lost Lost Lost Lost

The Home/Away goal ratio has been adjusted slightly for week 23. This has also led to a small increase in the expected goals total.
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Re: Poisson Distribution - This Can Help You

Postby davidg3907 » Sun Jan 07, 2018 4:43 pm

For Round 23, I have (over?)adjusted the Home/Away goals ratio in favour of the home teams, and made alterations to the ratings in keeping with the changing performances of teams.

This season there have been 586 goals in 220 matches, an average of 2.64 which has again dropped below the 10 year average of 2.71.

323/263 goals have been scored by the home/away sides making a 55.12/44.88% split. The previous 10 years shows a 57.25/42.75% split.

Points have been split 344/257 with home/away sides taking 57.24/42.76% respectively. The previous 10 years shows a 58.82/41.18% split.

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Re: Poisson Distribution - This Can Help You

Postby pandabear123 » Fri Jan 12, 2018 8:42 pm

Gareth P has written a blog on Poisson Distribution and a great read it is. https://www.olbg.com/blogs/post.php?id=412201

This kind of study should help all of us make better bets and focus our minds on chance/percentages/variation.

Can members advise how the distribution could help them

Do you have any questions about it?

Do you use this already for narrowing down bets

Can you run a test yourself?

See if you can predict a score using it

Can you predict the highest scoring game of the weekend

What other factors do we need to consider after the calculation

Which team this weekend do you think is the most out of kilter compared to their actual chance?
Great, I just finished reading it, and it's very useful info. thank you for sharing it with us. Cheers

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Re: Poisson Distribution - This Can Help You

Postby davidg3907 » Mon Jan 15, 2018 11:42 pm

The results from week 23 saw 31 goals with 6 over 2.5 goals, 5 BTTS Yes, and 4 Wins to nil (all home).

Average Goals top.
0 3 7 4 3
Average Goals bottom.
2 1 2 4 5
Over 2.5 Goals.
0 3 4 7 3
Under 2.5 Goals. (The quoted figures are for OVER so deduct from 100)
2 1 2 4 5
Home teams winning to nil.
Yes Yes Draw Yes Draw Yes Draw Won Lost Won
Away teams winning to nil.
Lost Won Lost Lost Draw Draw Lost Draw Lost Lost
BTTS Yes.
Won Lost Won Won Won
BTTS No. (The quoted figures are for YES so deduct from 100)
Won Won Won Won Lost

The Home/Away goal ratio was adjusted slightly for week 23. This also led to a small increase in the expected goals total. The average goals per match is now 2.682, still a shade below overall expectations.

This is the best set of results to date. All teams that played at home in this set of fixtures are away in the next set, so that should give a much better picture over the two sets of results.
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