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Poisson. Dixon Coles approach


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Hello to all. I am new to the community, and it is actually my very first post on this forum. I am a mathematician myself, and recently had started to get into football modeling. I was playing around with Betfair for years now, but just recently had concentrated on it full time. I am fascinated by the scope on how deep math could be applied at Betfair markets. When researching football modeling I had stumbled upon a highly regarded Dixon, Coles (1997) paper "Modelling Association Football Scores and Inefficiencies in the Football Betting Market" which applies time factor and very important correlation factor for low scoring games to Poisson regression. It took me some time in figuring out how to translate those formulas to real numbers that will tell me what is the chance of a score x-y happening in a game N. I did it at the end, and now have a system that can generate a probability of all possible scores (from which a lot of other probabilities such as 1X2, Over\Under and so on, can be generated) for all major leagues. Those Poisson values are now play a critical role in my overall strategy, that forecasts a return of 5-7% (only time will tell a real value). When working on it, I was looking for resources that will provide me concrete help in getting those values, with little luck. And that is when I had an idea of building a subscription based website that will provide detailed and scientifically backed probabilities (for 3 Correct Score markets, Match Odds and Over\Under markets) for every match of every major football league. It can be used either as part of your strategy, or as an extra confirmation check. There are numerous uses for such data. I realize that not all punters have an in-depth math knowledge that is required for getting those values, and that is why I think such a website would be very helpful for many. Why I am writing this? Well, since most of my research and development I did on my own, with no contact to "outside" world (i.e the community), I am not sure if such a service would be useful and needed. Not sure if such a service already exists (which will mean that my Google skills aren't as great as I thought). Not sure, on maybe everybody and thier uncle had already figured it out and successfully using Dixon Coles Poisson, and I am here playing an old record. What are your thoughts?

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Re: Poisson. Dixon Coles approach Explain Dixon Coles Poisson. Have no idea what it says. I come across the word Poisson frequently as a massage for Soccer stats but have no idea of its effectiveness. Perhaps you could give us some of your picks.? I noted the words " subscription based " .

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Re: Poisson. Dixon Coles approach Hi, Porcupine, :welcome to the forum! It's nice to have another mathematician on board! (no, I'm not the one, but there are some here!) As for your idea, I also noted the same words as Methuselah; though, it's a bit too fast, methinks - people will pay subscription only if they know they got some value for their money. So, you have first to prove your system is profitable, and only then to switch it to paid one. So, I think he gave you a good advice: start posting your picks, and results combined with readers' feedback will be the best evaluation of your system. If you want to do so, you're in the right subforum, and you can continue posting picks in this thread, but please take a minute and read Betting Systems Rules! :ok This thread may give you an idea how the guy promoted his site by running the system here. You also have to note that you need approval by Forum ownr, Paul Ross, before posting link to your site; otherwise, it may be considered as spam, since the site will be commercial. As for Methuselah's question on Dixon - Coles approach, googling out "Dixon Coles paper" replies the question, but he is right, you might want to give some short introduction how it works, for us non-mathematicians with mathematic aspirtions... :) Hope you'll enjoy the forum, and we'll see your picks soon! :OK

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Re: Poisson. Dixon Coles approach Methuselah, froment, thanks for your reply. In short. Poisson distribution provides a probability that a give score will happen. Poisson function requires an input of goal expectancy for every team involved in a game. Goal expectancy is calculated using attack and defense rate of each team and home field advantage factor. There are different approaches in calculating those values, Dixon Coles approach being the one that is praised the most for its efficiency. Simple Poisson distribution is known for incorrectly calculating probabilities for low scores (0-0, 1-0, 0-1, 1-1) and that's were Dixon-Coles proposed incorporating a correlation factor that fixes that problem... I've realized that I just started to mumble math stuff. It is not an easy stuff even for mathematician, for a non-mathematician it is very complex. This Wikipedia article explains a little about statistical football prediction in general http://en.wikipedia.org/wiki/Statistical_association_football_predictions As to the "subscription based" and "give us your picks". Yes, the idea is to do it on a subscription basis, since it involves quite a bit of work to gather information and calculate results, and since, in my opinion it provides a lot of value to any strategy. The main point, that I think i didn't get out clearly is that it is not a strategy. I would call it a valuable information that could be used for a great profit in capable hands. It is up to the individual on how to use it. I will provide an example on what data am I talking about. Inter - Parma. Serie A. December 8. [TABLE=width: 512]

[TR] [TD]Score[/TD] [TD=colspan: 2]Probability[/TD] [TD]Score[/TD] [TD=colspan: 2]Probability[/TD] [TD]Score[/TD] [TD]Probability[/TD] [/TR] [TR] [TD]0-0[/TD] [TD=align: right]6.830%[/TD] [TD][/TD] [TD]4-2[/TD] [TD=align: right]1.424%[/TD] [TD][/TD] [TD]2-6[/TD] [TD=align: right]0.025%[/TD] [/TR] [TR] [TD]0-1[/TD] [TD=align: right]4.973%[/TD] [TD][/TD] [TD]5-0[/TD] [TD=align: right]0.788%[/TD] [TD][/TD] [TD]0-7[/TD] [TD=align: right]0.003%[/TD] [/TR] [TR] [TD]0-2[/TD] [TD=align: right]3.532%[/TD] [TD][/TD] [TD]5-1[/TD] [TD=align: right]0.890%[/TD] [TD][/TD] [TD]1-7[/TD] [TD=align: right]0.005%[/TD] [/TR] [TR] [TD]0-3[/TD] [TD=align: right]1.329%[/TD] [TD][/TD] [TD]5-2[/TD] [TD=align: right]0.502%[/TD] [TD][/TD] [TD]2-7[/TD] [TD=align: right]0.004%[/TD] [/TR] [TR] [TD]1-0[/TD] [TD=align: right]8.494%[/TD] [TD][/TD] [TD]6-0[/TD] [TD=align: right]0.232%[/TD] [TD][/TD] [TD]4-3[/TD] [TD=align: right]0.536%[/TD] [/TR] [TR] [TD]1-1[/TD] [TD=align: right]12.322%[/TD] [TD][/TD] [TD]6-1[/TD] [TD=align: right]0.262%[/TD] [TD][/TD] [TD]3-4[/TD] [TD=align: right]0.343%[/TD] [/TR] [TR] [TD]1-2[/TD] [TD=align: right]6.229%[/TD] [TD][/TD] [TD]6-2[/TD] [TD=align: right]0.148%[/TD] [TD][/TD] [TD]4-4[/TD] [TD=align: right]0.151%[/TD] [/TR] [TR] [TD]1-3[/TD] [TD=align: right]2.343%[/TD] [TD][/TD] [TD]7-0[/TD] [TD=align: right]0.058%[/TD] [TD][/TD] [TD]5-3[/TD] [TD=align: right]0.189%[/TD] [/TR] [TR] [TD]2-0[/TD] [TD=align: right]8.623%[/TD] [TD][/TD] [TD]7-1[/TD] [TD=align: right]0.066%[/TD] [TD][/TD] [TD]6-3[/TD] [TD=align: right]0.056%[/TD] [/TR] [TR] [TD]2-1[/TD] [TD=align: right]9.733%[/TD] [TD][/TD] [TD]7-2[/TD] [TD=align: right]0.037%[/TD] [TD][/TD] [TD]7-3[/TD] [TD=align: right]0.014%[/TD] [/TR] [TR] [TD]2-2[/TD] [TD=align: right]5.493%[/TD] [TD][/TD] [TD]0-4[/TD] [TD=align: right]0.375%[/TD] [TD][/TD] [TD]6-5[/TD] [TD=align: right]0.053%[/TD] [/TR] [TR] [TD]2-3[/TD] [TD=align: right]2.066%[/TD] [TD][/TD] [TD]1-4[/TD] [TD=align: right]0.661%[/TD] [TD][/TD] [TD]6-4[/TD] [TD=align: right]0.016%[/TD] [/TR] [TR] [TD]3-0[/TD] [TD=align: right]5.069%[/TD] [TD][/TD] [TD]2-4[/TD] [TD=align: right]0.583%[/TD] [TD][/TD] [TD]3-5[/TD] [TD=align: right]0.077%[/TD] [/TR] [TR] [TD]3-1[/TD] [TD=align: right]5.722%[/TD] [TD][/TD] [TD]0-5[/TD] [TD=align: right]0.085%[/TD] [TD][/TD] [TD]3-6[/TD] [TD=align: right]0.015%[/TD] [/TR] [TR] [TD]3-2[/TD] [TD=align: right]3.229%[/TD] [TD][/TD] [TD]1-5[/TD] [TD=align: right]0.149%[/TD] [TD][/TD] [TD]3-7[/TD] [TD=align: right]0.002%[/TD] [/TR] [TR] [TD]3-3[/TD] [TD=align: right]1.215%[/TD] [TD][/TD] [TD]2-5[/TD] [TD=align: right]0.132%[/TD] [TD][/TD] [TD]4-5[/TD] [TD=align: right]0.034%[/TD] [/TR] [TR] [TD]4-0[/TD] [TD=align: right]2.235%[/TD] [TD][/TD] [TD]0-6[/TD] [TD=align: right]0.016%[/TD] [TD][/TD] [TD]4-6[/TD] [TD=align: right]0.006%[/TD] [/TR] [TR] [TD]4-1[/TD] [TD=align: right]2.523%[/TD] [TD][/TD] [TD]1-6[/TD] [TD=align: right]0.028%[/TD] [TD][/TD] [TD]5-5[/TD] [TD=align: right]0.012%[/TD] [/TR] [/TABLE] [TABLE=width: 192] [TR] [TD=width: 64]Over/Under[/TD] [TD=width: 64] Over[/TD] [TD=width: 64] Under[/TD] [/TR] [TR] [TD]0.5[/TD] [TD=class: xl156, align: right]93.170%[/TD] [TD=class: xl156, align: right]6.830%[/TD] [/TR] [TR] [TD]1.5[/TD] [TD=class: xl156, align: right]79.703%[/TD] [TD=class: xl156, align: right]20.297%[/TD] [/TR] [TR] [TD]2.5[/TD] [TD=class: xl156, align: right]55.226%[/TD] [TD=class: xl156, align: right]44.774%[/TD] [/TR] [TR] [TD]3.5[/TD] [TD=class: xl156, align: right] 32.866%[/TD] [TD=class: xl156, align: right] 67.134%[/TD] [/TR] [/TABLE] [TABLE=width: 143] [TR] [TD]Inter Win[/TD] [TD=align: right]50.898%[/TD] [/TR] [TR] [TD]Draw[/TD] [TD=align: right]26.087%[/TD] [/TR] [TR] [TD]Parma Win[/TD] [TD=align: right]23.015%[/TD] [/TR] [/TABLE] Formatting is a bit off, still figuring out the forum functionality. Probabilities could easily be converted to decimal odds by doing 1/probability. So Inter Win odds as per this calculations are 1/0.50898 = 1.96. Current Betfair odds for Inter win is 1.76 What is given is purely scientific Poisson distribution calculated by Dixon Coles approach. My calculations follow the mentioned paper word by word. Nothing less, nothing more. As I have stated before, how to use this information is up to the individual. You can start at simple Over/Under 2.5 goals and look for over\under priced markets on Betfair, and go to as far as complex multi market analysis and Correct Score betting. I hope this clarifies my original post a bit.
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Re: Poisson. Dixon Coles approach Just an observation. Converted my O/U 2.5 probabilities for Inter - Parma match into odds and got the following Over 2.5 goals = 55.226% = 1/0.55226 = 1.81 Under 2.5 golas = 44.774% = 1/0.44774 = 2.23 Current Betfair odds: Over 2.5 goals = 1.81 Under 2.5 golas = 2.22 A good indication on how accurate the properly calculated Poisson can be.

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Re: Poisson. Dixon Coles approach I experimented with this for a while before moving onto various other methods of doing this. The main problem of the method is that it uses two poison distributions (for number of goals each team scores) and multiplies them together as though they are independent when they clearly are not. Gives you a good starting point to a strategy but you will need more factors to arrive at the probabilities to be able to begin to form a profitable system. For under/overs and 1x2 its much more powerful to model directly than trying to model goals scores. A further issue is that the same model won't work across leagues. I found this with all my models which i why i have produced league specific models

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Re: Poisson. Dixon Coles approach

The main problem of the method is that it uses two poison distributions (for number of goals each team scores) and multiplies them together as though they are independent when they clearly are not.
It does seem like that on a surface, but in the core is not true. Yes, you do multiplication of two Poisson distributions, but a key input of every Poisson is goal expectancy. And goal expectancy of a home team = attack rate of home team * defense rate of away team * home field advantage And goal expectancy of away team = attack rate of away team * defense rate of home team. From that, we clearly see that Poisson distributions are not independent since we use data of both teams in every Poisson. That is, goal expectancy of Wigan against Stoke will be higher than the same against Arsenal.
A further issue is that the same model won't work across leagues. I found this with all my models which i why i have produced league specific models
Yes, separate model should be build for every league, since home advantage and correlation factors are different for every league. From a summary of Dixon Coles paper: Maximum likelihood estimates are shown to be computationally obtainable, and the model is shown to have a positive return when used as the basis of a betting strategy.
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Re: Poisson. Dixon Coles approach

Sounds similar to www.football-bet-data.com. They give predicted odds on over under' date= 1X2, both teams to score and also predict the final score and then show the average and max odds available. Did you come across that via google?
Yes, I use their Data Archive service for raw historical data. And I've seen their prediction services, and I bet that they use Poisson in some shape or form. The main difference is that they don't provide Correct Score odds (at least not in easily accessible form). Key element in my own strategy, and the only data you actually need (if looking for Poisson probabilities), since with that you can easily calculate all O\U, 1x2 and other markets. And I am not sure which variation of Poisson(if any at all) they use.
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Re: Poisson. Dixon Coles approach Thanks for your reply Porcupine., and the replies of others. I am not a mathematician but a failing Punter. My losses are steady but modest and I feel that perhaps a study of Chaos Theory would be appropriate for us Punters. I believe that the Bookies who set the prices have the best statisticians available and they then set prices much to their advantage. Still, it's good fun to try and beat them.

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Re: Poisson. Dixon Coles approach

Thanks for your reply Porcupine., and the replies of others. I am not a mathematician but a failing Punter. My losses are steady but modest and I feel that perhaps a study of Chaos Theory would be appropriate for us Punters. I believe that the Bookies who set the prices have the best statisticians available and they then set prices much to their advantage. Still, it's good fun to try and beat them.
The bookies rely on us making steady losses. I feel modelling better than them will give us an edge somewhere so porcupine should keep going as i am doing with my many models. Finding a good model though is not too difficult but finding a winning strategy is harder. I am not so sure the bookies do get the best statisticians. They don't pay that well from what i have seen as i have been considering this myself.
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Re: Poisson. Dixon Coles approach Why would you want to beat bookies when you have such a great invention as Betfair? All bookies cripple your abilities on what can you do, and how can you bet to the point that it is almost impossible to make long-term profit with them. Betfair on the other hand is a level field for everyone involved, and the game is simple - the smartest takes the money of the dumbest (and pays 5% commission on it :)), that is why information gives you advantage, and Poisson is a great piece of information that can be used against those that are less smart in order for you to take their money. And don't forget that bookies goal is not to predict correct odds, but to balance their books in order to guarantee their profit. So often they intentionally over value or under value some results to achieve the balance. Also, bookies are known to do the so called Favourite-longshot bias (http://en.wikipedia.org/wiki/Favourite-longshot_bias). I will follow advice that was given to me and will start to post some Poisson probabilities for certain matches over here, with possibly even some picks, just for the fun of it.

Finding a good model though is not too difficult but finding a winning strategy is harder.
Those are the golden words. Cannot agree more.
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Re: Poisson. Dixon Coles approach You keep popping up on old threads about poisson. Why dont you just use the search facility and read whats been written about it, there are also free spreadsheets available to download in some of those threads if you take the time to look. Poisson is only an estimation and a poor one at that in my opinion, its is not and never has been profitable overall in its purest state regardless of what you read.

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Re: Poisson. Dixon Coles approach Regardless how you work out the parameters to input into poisson it will not make money,if that were the case do you not think everyone would be rich by applying a simple formula. I am just trying to save you some time and effort (and money). Heres an example tonights game 19.45 ko Luton v shrewsbury [TABLE=width: 512]

[TR] [TD=class: xl65, width: 64]Goals[/TD] [TD=class: xl68, width: 64]0[/TD] [TD=class: xl68, width: 64]1[/TD] [TD=class: xl68, width: 64]2[/TD] [TD=class: xl68, width: 64]3[/TD] [TD=class: xl68, width: 64]4[/TD] [TD=class: xl68, width: 64]5[/TD] [TD=class: xl68, width: 64]6[/TD] [/TR] [TR] [TD=class: xl67]Luton[/TD] [TD=class: xl66, align: right]0.26[/TD] [TD=class: xl66, align: right]0.35[/TD] [TD=class: xl66, align: right]0.23[/TD] [TD=class: xl66, align: right]0.10[/TD] [TD=class: xl66, align: right]0.04[/TD] [TD=class: xl66, align: right]0.01[/TD] [TD=class: xl66, align: right]0.00[/TD] [/TR] [TR] [TD=class: xl67]Shrews[/TD] [TD=class: xl66, align: right]0.38[/TD] [TD=class: xl66, align: right]0.37[/TD] [TD=class: xl66, align: right]0.18[/TD] [TD=class: xl66, align: right]0.06[/TD] [TD=class: xl66, align: right]0.01[/TD] [TD=class: xl66, align: right]0.00[/TD] [TD=class: xl66, align: right]0.00[/TD] [/TR] [/TABLE] According to poisson Lutons expected goals are 1 @ 35% Shrews expected goals are 0 @ 38% or 1 @ 37% (a close call) Luton win 1-0 = 0.35 * 0.38 = 0.133 or odds of 7.5 bookmakers odds are 7 @ PP Luton draw 1-1 = 0.35 * 0.37 = 0.13 or odds of 7.69 bookmaker odds are 6 @ PP So even if poisson was a perfect fit (which its not) the books are way ahead and under price the actual chance you have of winning therefore there is no way you can overcome the overound and become profitable.
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Re: Poisson. Dixon Coles approach Poisson is a good probability system. It is accurate and robust, but like 'artificial intelligence' it cannot display the nuances of human perception. There are too many variables at play that affect a match that cannot be weighted to a probability system, so Poisson can only suggest probability based on historical data...in other words, Poisson is a guide only, even when it is correct with its probabilities. I use it myself, but I also look at other factors that are both resonant and complimentary to Poisson probability. One thing I don't use within my Poisson tables is last season's results, they do not affect the current season in any way (how could they?). In fact, even within the current season, past a certain amount of recent games, no past result affects the mindset of the players, and mindset has everything to do with form, and it is playing good form wherein goals are scored to win matches. The more a team plays as a team with equal distribution of good form amongst them, the more likely they are to achieve a positive result, so look for teams that are displaying 'team' effort, where the whole team is singing equally from the same song sheet. Regards

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