Poisson Distribution - This Can Help You

nors
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Poisson Distribution - This Can Help You

Postby nors » Fri Jan 20, 2017 2:01 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?

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Re: Poisson Distribution - This Can Help You

Postby zorrobet1 » Sun Jan 22, 2017 2:21 pm

useful post, thank you!

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Re: Poisson Distribution - This Can Help You

Postby Inquisitorem » Mon Jan 23, 2017 2:03 pm

Excellent article!

It's difficult to discover mistakes that layers have made in their calculations if we adopt the same strategy for working them out. However, this kind of calculation is effective and should be used. Better still, if you can identify the games where both teams are odds against, and focus more of your time on the finer details of those matches, it could be advantageous. Only because layers may not be able to do likewise in every game in every league.

Taking this idea further, knowing that teams on average score 1 goal for every 8 shots ( or 1 for every 4 on target ), you can get insight as to whether a favourable result has been achieved on merit ( creative superiority ) or whether a team has just converted brutally well. Not forgetting to factor in that the top sides will usually better these averages, and that's why they finish higher up.

However, just out of curiosity, if we take Manchester City as an example, and their 2-2 draw against Tottenham. City had 17 attempts on goal, suggesting they were worth 2 goals on balance ( although they just fell short of the average 8 on target ). Tottenham on the other hand, got more reward than their build up / creativity / cutting edge might have ordinarily returned. Their shot tally, and those recorded on target, suggest they possibly over achieved.

Not only can City regard themselves as slightly unfortunate against Tottenham, but they can feel even more aggrieved at their 4-0 defeat at Goodison Park.
Both teams at the business end of their match play would normally have hit the net once ( on average ) based on their level of attacking investment ( shots / on target ) on the day.

We can't re-distribute the goals according to what we think is fair ( based on hindsight ), but this information should fire off a warning at least. City in theory, on another day, might have come out of those two games 3 points better off ( beating Tottenham and drawing with Everton ). Who would have written them off, had they been 7 points adrift with 51 to play for? Pep? The media?

My point is this, Everton are not suddenly great, Tottenham ( albeit on a good run of form ) are beatable, and City are not lacking in ability or know-how. These considerations might provide value when assessing the next set of fixtures. And perhaps, going to greater lengths with regard to a unique aspect, might just expose a layer or two.
Last edited by Inquisitorem on Mon Jan 23, 2017 2:28 pm, edited 4 times in total.
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Re: Poisson Distribution - This Can Help You

Postby Inquisitorem » Mon Jan 23, 2017 2:13 pm

To highlight the article's main point, Crystal Palace v Everton on Saturday is a good working example ( based on recent form ) perhaps?

Palace's previous 6 matches 0-3, 0-0, 1-2, 0-2, 1-1, 1-1
Everton's previous 6 matches 4--0, 1-2, 3-0, 2-2, 2-0, 0-1

Palace were unlikely to score a whole goal ( 3 scored in 6 games ), and were likely to concede a whole goal ( 9 conceded in 6 games )
Everton were likely to score a whole goal ( 12 scored in 6 games ), and were not likely to concede a whole goal ( 5 conceded in 6 games )

Both team's recent form suggest the same probability - Palace would not score / Everton would

What price Everton to win to nil?
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Re: Poisson Distribution - This Can Help You

Postby nors » Tue Jan 24, 2017 8:57 am

This is another useful string to our betting bow. I do agree though that
Everton are not suddenly great, Tottenham ( albeit on a good run of form ) are beatable, and City are not lacking in ability or know-how.
You tend to get an overreaction to results from punters and bookmakers, the poisson distribution can bring this back into line.

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Re: Poisson Distribution - This Can Help You

Postby Inquisitorem » Tue Jan 24, 2017 9:44 am

Absolutely, Nors! Great analytical tool!
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Re: Poisson Distribution - This Can Help You

Postby spacetime » Wed Feb 08, 2017 6:17 pm

Hi Nors,

I was interested in this some years back and wrote a spreadsheet in excel using the goals for and against as the basis for poisson distribution and predicting scores. I have included some screenshots. You enter the scores and the predictions are calculated based on the average goals home and away, home goals for and away goals for. I have to say that this demonstrated to me just how difficult correct score prediction is. The sheet includes a table that automatically sorts the league, stats on number of goals scored and percentage of scores so far this season for example 13% 1-1 draws.

If anyone would like a copy of the sheet for free I would happily upload it for you to distribute. It is up to date and only covers the premier league although could easily be adapted for other leagues.

Image

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Mick

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Re: Poisson Distribution - This Can Help You

Postby nors » Thu Feb 09, 2017 9:02 am

Thanks Spacetime, your work on this and i expect other betting issues could be a real help to forum members. Did you have any joy from a winning perspective using the sheets?

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Re: Poisson Distribution - This Can Help You

Postby davidg3907 » Thu Feb 09, 2017 9:18 am

Hi Spacetime,

In conjunction with Gareth, I have been working on a set of spreadsheets to this end from a slightly different angle.

Currently, we have two issues - with calculations of the 0-0 draw and gravitating towards the average goals for each team. This is something I expected to a point due to the nature of Poisson.

It would be a great help if you could provide a copy of your workings; similarly, I could let you have a copy of current musings and would appreciate any comments and possible ways to overcome this matter.
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Re: Poisson Distribution - This Can Help You

Postby davidg3907 » Fri Mar 03, 2017 3:11 pm

Things have progressed since the last post (albeit slowly for the most part), but some form of working model is now in place.

It is far from a finished article, and as such any figures are literally a guide from a Work In Progress and should be treated in that way.

My main concern at the moment is the narrow band into which odds for the draw fall. The problem is possibly due to Poisson's desire to concentrate on the 'most likely', which in turn means close to the average. In turn that may distort the odds, resulting in them being higher or lower than should be the case.

Results are however encouraging. The following was produced prior to the last round of matches and for ease is displayed in the following format.

Match
Most likely score - that IS NOT the same as a Correct Score prediction. It is an attempt to replicate a market not too far removed from standard lists.
Estimated goals.
Estimated odds for Home Draw Away - again looking for value rather than trying to pick a winner.

These are set to 100% book with several variables included so are NOT a true Poisson, which was giving very odd results earlier.

Any constructive input welcome. :D

February 25th/27th

Chelsea Draw Swansea 2-0 3.34 1.23 8.01 16.72
Crystal Palace Draw Middlesbrough 0-0 3.15 3.68 2.43 2.39
Everton Draw Sunderland 2-0 2.80 1.48 5.12 7.75
Hull Draw Burnley 0-0 2.27 3.16 3.56 2.49
West Brom Draw Bournemouth 1-0 2.45 1.96 3.89 4.28
Watford Draw West Ham 1-1 2.88 2.80 4.05 2.52
Tottenham Draw Stoke 1-0 2.79 1.61 4.63 6.10
Leicester Draw Liverpool 0-1 2.98 4.61 4.61 1.77

March 4th/6th

Man Utd Draw Bournemouth 2-0 2.76 1.50 4.96 7.69
Leicester Draw Hull 1-0 2.57 1.91 4.85 3.68
Stoke Draw Middlesbrough 1-0 2.33 2.02 3.85 4.10
Swansea Draw Burnley 0-0 2.32 3.29 3.60 2.39
Watford Draw Southampton 1-1 2.62 2.61 3.89 2.78
West Brom Draw Crystal Pal 2-0 2.80 1.65 4.63 5.64
Liverpool Draw Arsenal 0-1 3.23 2.39 4.88 2.66
Tottenham Draw Everton 1-0 2.81 1.81 4.40 4.57
Sunderland Draw Man City 0-1 3.01 7.35 5.18 1.45
West Ham Draw Chelsea 0-1 2.45 4.71 3.86 2.12

Check the original blog on this subject. Your Bookmaker Uses Poisson Distribution and So Should You
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Re: Poisson Distribution - This Can Help You

Postby davidg3907 » Mon Apr 03, 2017 4:18 pm

Time had been a bit short to pursue this matter, but having made a few (not all minor) adjustments, I put it to the test again over the weekend.

The checks were done 3 ways (no it isn't Masterchef! :D ) with two reasonable looking sets of figures and one that looked and proved unattractive.

Eventually, I found out the error of my ways. To make presentation easier, I had amended the layout of one spreadsheet and by leaving it for a while, forgot that I had done so, letting it to do calculations vertically instead of horizontally. Need I say any more? :oops:

This had a negative effect on most away teams, particularly the stronger ones, thereby accounting for the lack of away favourites in the new layout.

Fortunately, correcting the fault involved little more than swapping two numbers and re-labelling two tables.

Having corrected the relevant parts, I have settled on one set of variables and will post the midweek games and those for the forthcoming weekend, along with last wekend's amended copy. The fact that the data used includes one match already played will make virtually no difference.
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Re: Poisson Distribution - This Can Help You

Postby davidg3907 » Tue Apr 04, 2017 6:34 pm

After yesterday's false start, it is time for another go. Things are looking better now as the away teams are getting closer to their true odds - but I'm still a little way off anything that I would trust completely. I have been using 50%, 70%, and 90% weightings as for/against variables, but am (for now at least) discarding the 90% figures, but may use 75% or 80% as a trial at some point.

The overall number of goals is in the right ball park, but only 39% to the away side and this needs to be over 42%. It is actually very close to a 4;3 ratio and if using 2.80 goals per match as the target, the arithmetic becomes easy to follow.

Predictions for tonight and tomorrow are as follows.

Matches to be played April 4th/5th
Analysis using FOR 50 AGST 50 in first table and FOR 70 AGST 30 in the second.
Season weighting 2 4 9 10 Odds set to 100%


Greatest % score
Odds guide
Est Average goals

Burnley Draw Stoke 1-0 1.89 3.86 4.70 2.39
Hull Draw Middlesbrough 1-0 2.20 3.48 3.89 2.11
Leicester Draw Sunderland 2-0 1.70 4.42 5.41 2.75
Swansea Draw Tottenham 1-1 2.90 3.86 2.53 2.69
Watford Draw West Brom 1-0 2.12 3.63 3.98 2.27
Manch Utd Draw Everton 1-0 1.86 3.95 4.77 2.39
Arsenal Draw West Ham 1-0 1.81 4.37 4.56 2.78
Chelsea Draw Manch City 1-1 2.13 4.31 3.36 2.96
Liverpool Draw Bournemouth 2-0 1.58 4.77 6.42 3.02
Southampton Draw Crystal Palace 1-1 1.94 4.10 4.14 2.71

That gives average goals of 2.61, split 60.9%/39.1%

Burnley Draw Stoke 1-0 1.92 3.84 4.56 2.40
Hull Draw Middlesbrough 1-0 1.92 3.60 4.96 2.06
Leicester Draw Sunderland 2-0 1.68 4.46 5.52 2.78
Swansea Draw Tottenham 1-1 2.80 3.97 2.56 2.85
Watford Draw West Brom 1-0 1.98 3.70 4.45 2.27
Manch Utd Draw Everton 1-0 1.90 4.08 4.38 2.60
Arsenal Draw West Ham 2-1 1.84 4.52 4.26 3.06
Chelsea Draw Manch City 2-1 2.06 4.63 3.36 3.39
Liverpool Draw Bournemouth 2-1 1.57 5.05 6.12 3.15
Southampton Draw Crystal Palace 2-1 1.94 4.19 4.06 2.85

Now the average goals are 2.74, split 58.5%/41.5% which is a lot more satisfactory.

I have edited the format (but NOT the figures) to save space and make reading easier. I should point out that Greatest % Chance may only be a couple of decimal places ahead so is never really a firm prediction at this stage, even though signs are hopeful over the two weeks so far.

I shall then post last weekend's and next weekend's figures in the same format for consistency.
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