A football rating system, discussions, ideas

[mr onemore]

Re: A football rating system, discussions, ideas Appreciate the comments Paul - :ok I hope you'll stick around with this for a bit - really. We'll need some normal people on this to stop us all talking in maths nonsense at some point and put it all back into words!! At the end of this - I can see a few spreadsheets given out that anyone could use whether or not they really followed the thread in detail. Of course I'd encourage all to participate, but there's room for everyone's way here. :)

[Dino]

Re: A football rating system, discussions, ideas Hi MO,just found this,a thread on LS,great. Hope you don't mind a few observations. Firstly it's as you say a really elegant method to analyse large numbers of matches where strength of schedules are incomplete.Each new result just sends a faint ripple through the overall ratings instead of the saw toothing that occurs if you only use a small number of previous games. Having said that the biggest problem I've found with this method is still knowing when you've got sufficient numbers of results for a team's scoring percentages to hit their true values. Take the trivial case of one game in isolation to illustrate the point. Team A beats team B 3-0. You then have to rate team A as 3 goals superior to team B and very few teams from the same division is 3 goals superior in the long run to another. You've got the old problem of relating short term happenings to longterm probability. More games help. Half a season is obviously better,but imo the ratings "gaps" are still too big,particularly at the extremes & you need to add a bit of extra maths to "normalise" them. A whole season's worth of results probably hits the mark but then you defenitely have to weight the most recent results. So either way a straight LS approach usually falls short...not telling you anything you don't already know. Works well for Champs league stuff.I know a guy who's LS'd all the European leagues using the uefa/champs league to connect them,which is a bit ambitious. Using different metrics is an interesting idea,like you I don't think anything will correlate as well as MOV,but using past results and a bit of regression would do the trick as regards converting the different metrics to odds. Digressing to an earlier point,imo the midweek w/l/d anomalies is a bit overstated.I doubt it's statistically significant & I think its mostly down to sample size. Much fewer midweek games,especially if you further subdivide by days of the week,therefore you're less likely to get a representative range of odds & the win/lose/draw percentages are also less likely to have tended towards their true values. It's like tossing a coin 13 times and expecting heads to be as close to 50% as it would if you'd done it 200 times. Neat thread,I'll keep an eye out. DINO

[mr onemore]

Re: A football rating system, discussions, ideas Hi Dino, Welcome aboard!!:) Hope you'll keep posting your observations as we move along. Very shortly I will post up my list of 'for' and 'against' for using the LS method as it stands here - though I agree with most of what you say above. The idea of connecting all the euro leagues via the champs league/uefa results is one I've also dabbled with in the past - suffice to say I also think it is a bit ambitious and difficult to rely on with so few connecting matches. There is a similar problem with trying to link divisions in the same national league by using cup results between inter-divisional encounters. After my own experiences I now just concentrate on one league and division in isolation from the rest - though that's not to rule out the idea entirely if someone wants to try that. This also raises the problem of what to do with promoted teams that arrive in the top division, with no previous games to rate - I have a few things to say about that later on in the thread...but it is a factor that should be addressed IMO.

[muppet77]

Re: A football rating system, discussions, ideas concerning new entrants to a division (up or down) how about simply exchanging their ratings. eg 3rd bottom in prem switches ratings with top of championship. 2nd bottom swithes with 2nd top and bottom with 3rd?

[bcrazy]

Re: A football rating system, discussions, ideas Thanks Mr. O- was forgetting A wasn't a square matrix so that wasn't helping me ;) Nice to see some uses of matrices seeing as they've been boring me for the last few weeks (doing my maths A2 at the moment). Muppet, I'd personally be wary of that approach, unless you are going to allow yourself to change it in special cases, due to teams like Fulham when they got promoted who were clearly going to be stronger than the team they were replacing. I think my simplified method of dealing with the problem would be to just look at how the bookies rate their chances and who they are similar to and base it on the similar teams ratings. Obviously using outside help though so definitely not very systematic if you are using judgement.

[mr onemore]

[muppet77]

Re: A football rating system, discussions, ideas nice bit of research there boss. found that out myself when i accidentally deleted arsenal beating palace 5-1 from the sheet and replacing it with 1-5. this massively affected the ratings. i suppose doing two halves of the season would also get around the problem of a maximum of 256 games rather than 380 for the premiership. but you say that you prefer a different method? ideally i would like to have a solution that allows overlap of divisions (like the RFO index).

[muppet77]

Re: A football rating system, discussions, ideas

Ladbrokes rating for % chance of winning a game

(overroundnot taken into account)

 

1	Chelsea	56.53%
2	Arsenal	56.51%
3	Man United	50.47%
4	Liverpool	32.91%
5	Newcastle	20.85%
6	Aston Villa	15.79%
7	Middlesboro	12.05%
8	Tottenham	11.79%
9	Everton	11.72%
10	Bolton	5.04%
11	Man City	4.39%
12	Birmingham	2.45%
13	Charlton	0.84%
14	West Brom	0.00%
15	Fulham	-1.26%
16	Portsmouth	-4.44%
17	Blackburn	-5.29%
18	Southampton	-7.61%
19	Norwich	-14.50%
20	Crystal Palace	-15.08%

 

 

I have also removed the 0.4 value you included to counter home advantage.

[muppet77]

Re: A football rating system, discussions, ideas also forgot to mention the average home advantage is 17%, so for example, chelsea at home to palace gives 56.53 - -15.08 + 17 = 88.61% difference between the odds. NB. bookies odds include overround of about 113%, so this means 88.61% difference out of 113%.

[oddsfellow]

Re: A football rating system, discussions, ideas Mr Onemore, Congratulations what a great thread already :clap Personally i have experimented with both Elo and Glicko ratings (variation of Elo) on football with limited success, so have some experience of rating systems. Having come into this later than some i have just read the entire thread. The point was made early on and a few times later about having obtained the ratings the need to then calculate probability. You use the historical approach (i would use the true mathematical term for this but dont want to give the impression of being a nerd ;) ) which i would imagine works well. However in the same way that recent form can be of more importance than historical form would last seasons results and trends as a guide to odds be more reliable than say that of 5 years ago? I haven't looked into this as of yet but does anybody know how spread firms calculate goal supremacy? The reason being i know that all spread quotes are interlinked and all come off the original match quote as a base. Therefore working the supremacy quote backwards should be able to derive match odds. It is obviously early days so will hang fire with anymore questions until i have read more and brushed up on matrices. Looking forward to the next installment..........

[marku]

Re: A football rating system, discussions, ideas Are you going to carry on with this? Excellent thread.

[lapin]

Re: A football rating system, discussions, ideas Hello all, I'm new and my English is very poor. Sorry :( @ Mr Onemore I followed this excellent thread and "math and me" : this is not the real pleasure. And in English, very very diffucult for me :( But i'm very interesting and i want understand matrix, rating systems. I downlowded the spreadcheet and i would love have an concrete example. Champions'league (or others champs) * Juventus-Real What i must write (or enter) in your excels tables please ??? And wich table give the score predictions please? Thanks for your helps :)

[CJ Mars]

Re: A football rating system, discussions, ideas

I haven't looked into this as of yet but does anybody know how spread firms calculate goal supremacy? The reason being i know that all spread quotes are interlinked and all come off the original match quote as a base.

Its actually the other way around I think. I don't have the book ("Racing Post Guide to Sports Bettiong" ) to hand but in a piece by Kevin Pueillin he rates how the firms set the BASE odds by the goal supremacy of one team over another. He has a handy reay reckoner chart in the book for caluclating the odds when you have the match supremacies.

[oddsfellow]

Re: A football rating system, discussions, ideas Cjmars, you are of course quite correct. I do have the book you mentioned but have not read that particualr chapter yet. Just referred to it and there in all its glory is the aforementioned chart. It look very useful actually comparing not only goal supremacy with the windex, but also with fixed odds and asian handicaps. However I did also remember reading in Dan Townsend spread betting book about sometimes spread firms will have different quotes for the windex as oppposed to supremacy. So i have just re read that particualr piece as well. His example of this is Arsenal having played a tough game midweek are up against a mid table team and are strong favourites. The market maker is happy to lay them but the exposure from going low in a supremacy quote is too much whilst the windex gives an opportunity to take on a favourite with lower liability.

[CJ Mars]

Re: A football rating system, discussions, ideas I've read axtracts of the Townsend book. Looks interesting. Is it worth getting? Interesting on the difference between supremacy and the windex

[oddsfellow]

Re: A football rating system, discussions, ideas I wouldn't say its the sort of book that will change your way of betting but it does offer some points which make you sit up and take notice. He does highlight the pitfalls of some bets and how to interpert the different quotes. At about £9 from Amazon i wouldn't put you off it.

[mr onemore]

Re: A football rating system, discussions, ideas Chapter 2 Generating rating lists - A simplified LS solution + another solution that approximates a LS solution method I hold in my hand 1379 pages of tax simplification! - Delbert Latta Going to push this along now - time to simplify the method... At the moment then we are using a very basic metric, and the purest form of Least-Squares solution. I, and others, happen to think that this form of LS solution is too oversensitive to use as a predictive model. There are no end of modifications that have been tried here though. Hammerings - like the Arsenal 5-1 of Palace quoted by Muppet above - tend to cause quite a large ripple as they filter through the system. As a consequence, some have tried changing the metric, truncating large score differences. There are also quite complicated ways of weighting the importance of games so that consistent teams and results have more importance to the system. This way 'freak' results have less impact. I think that all these changes, though perhaps mathematically sound, are all forms of fine tuning - and that it's more pragmatic to just look for a better metric in the first place. I will add though, that for sports where fixture scheduling is not uniform, and where players/teams may play varying amounts of games, (Champions League, Tennis, Boxing etc) then this pure form of LS solution is probably a good way to stick with - or modify as outlined above. In cases such as league football though, the following simplifications are highly suitable - they in fact make the computations much simpler - and also tend to desensitize the system from being greatly affected by freak results... You don't get all these benefits for nothing though - so I will have to post up a little bit of maths theory again! However, in practice we will end up with just two very simple formulae that can be placed in a spreadsheet and used by anyone...(in fact, in my early days I used a calculator to update my ratings, so it's not hard to use...)

[brookes]

Re: A football rating system, discussions, ideas nice to see this thread continuing Mr O , I hope it is a bit more simple mathematically. Cheers

[mr onemore]

Re: A football rating system, discussions, ideas So here's the maths part... By definition, we are using a ratings system where, Each teams rating = Average of all previous opponents ratings + Average performance against each opponent (as given by the metric) Now, let us consider two teams, Team A, and Team B, that have just played a game against each other. We will assume that it is some time after the season (rating period) has already started. We know the result of the game, and now want to update their ratings. There are several variables here, but only two unknowns, (the new ratings for A and B). So we are going to set up the ('mother of all') system of simultaneous equations to solve... Let's use: RatA for the new updated rating for Team A NumA for the number of games that Team A has already played in the rating period OldA for the rating of Team A prior to the update. (similarly for Team B) Lastly, p is the performance result of the game using the metric between A and B. (It will be +p for team A, and -p for team B) So, to obtain the new rating for A, we use; RatA = ( 1 / NumA ) * ( ( NumA - 1 ) * OldA + RatB + p ) and RatB = ( 1 / NumB ) * ( ( NumB - 1 ) * OldB + RatA - p ) If you solve these simultaneously to find RatA and RatB, you will get (after some considerable amount of tidying up!) RatA = OldA + ( numB - 1 ) / (( numA * numB) - 1 ) * ( p - ( OldA -OldB )) and similarly for team B RatB = Old B + ( numA - 1 ) / (( numA * numB) - 1 ) * (- p - ( OldB - OldA )) These equations are a simplified version (!) of the LS solution. Each teams rating is only updated after each game that they play. This is a big difference from the previous LS solution, where all teams ratings are affected when a new result is fed into the system. One consequence of this, is that the system is desensitized - and (personal) practice shows this simplified system is better as a prediction tool when used in this way. Now we can make a further simplification here when dealing with league based systems - or where it is usual that teams have played roughly the same amounts of games as others (if doesn't really matter if there are a few teams out of synch with the rest - trends...- though if you are studying 'form' it might be best to stay with above formulae...) The assumption is that teams have played about the same number of games, so NumA = NumB. That simplifies the above equations to, RatA = OldA + ( 1 / ( NumA + 1 )) * ( p - ( OldA - OldB )) with a similar result for team B RatB = OldB + ( 1 / ( NumB + 1 )) * ( -p - ( OldB - OldA )) This is a formula that approximates a LS solution This last equation really is very easy to use. If you have a record of the previous ratings of the teams, the number of games played, and the new result - you just plug into the formula, and the new rating pops out. I'll put up a new spreadsheet with these formulae in sometime - but it really is a simple exercise to do yourself (I think...) In practice, I use the second formula for my ratings projects - and only use the first formula when the number of games is small (ie start of season). There is one big problem though before rushing off and using these... These formulas were derived assuming that you know the previous, old rating, of each team. Of course, when you start your system, what ratings do you give... There are two ways of tackling this. If you have a large databank of results, you can just start each rating at a nominal value (anything, say 10?, as it's only the differences in ratings that are important, not the absolute values), and roll through the data. There is an interesting mathematical result that proves that for all rating systems of these types, the ratings will tend towards the true values, given enough time...so how much is enough time? You can do a lot of complex maths here - but I've found that a couple of seasons, or even about 50 games for each team, are more than enough for the system to settle dowm. To speed up the settling down, you can even start the ratings off 'where you think they should be...' This is perhaps necessary when you have very little back data. A more mathematically based process for this is to iterate over a small number of games - but I won't go into this unless someone asks... Better, IMO, is to have plenty of data, and let the system settle down itself... Lots more to say, but that is enough for me today. As I said, I'll put a speadsheet up sometime, but hopefully I have explained enough so that anyone can experiment a bit with the formulae above...

[mr onemore]

Re: A football rating system, discussions, ideas Sorry - let me put in an example so you can see how easy it is to use these... Say, Team A, with a rating of 10, beats Team B, with a rating of 8. Let's say the score was 3 - 0, a little more than we might have predicted. Let's also say that this was the tenth game of the season for ech team... so, using the last formula above, an approximated LS solution, gives New Rating for Team A = 10 + (1 / 11) * ( 3 - (10 - 8)) New Rating for Team A = 10.09 and for Team B, New Rating for Team B = 8 + (1 / 11) * ( -3 - (8-10)) New Rating for Team B = 7.91

[brookes]

Re: A football rating system, discussions, ideas thanks for post 110 because post 109 had me confused . I intended reading it again later on , but the example clears it up. Am I correct in assuming that the more games played the lower the change in rating will be ? I have a few questions ,but am sure you will cover most of them .I will await the end of the chapter, Cheers

[mr onemore]

Re: A football rating system, discussions, ideas

Am I correct in assuming that the more games played the lower the change in rating will be ?

Yes - absolutely. All we have done here is find an easier way of using a LS solution, that incorporates all games played since the start, each game of equal value. The answers from repeated use of the formulae from start to finish, will give pretty much the same as a pure LS solution used on all the games. There are some differences though, and when using as a predictive tool (later) the fact that the system is desensitized somewhat is a singnificant factor IMO. Now, I actually use a yet further modification of the above formula - a very simple change - so that the formula can be used soundly over a specific number of games for each team - rather than use all the games in the database right from the start for working out each rating, but I'll leave that until later. Any other questions though - please fire away...:) I'm happy to have a go answering, and there will be others too who will want to post their opinions - I hope... Thanks

[dietcoke]

Re: A football rating system, discussions, ideas Just found this Mr Onemore. Super stuff

[merlin]

Re: A football rating system, discussions, ideas Hi there Mr.Onemore I have just waded through the whole six pages of this absorbing thread having arrived here tonight as a complete Newbie to PL but as an ardent supporter of rating systems.At the moment I feel as if my head is bursting with facts and figures,but at the same time my pulse is racing and tingling with excitement at the prospect of tinkering with yet another unheard of system.I have my own rating system similar to Paul Steele's with modifications based on another top football forum, but may add that it is not exactly setting the world alight!I really need to sit and digest some of the more important postings I have printed off to get the 'hang' of just what is going on, looks a bit cumbersome at first, but like the look of the more simpler presentation with your latest example, something that I think the ordinary layman will appreciate.I can well understand those who find the road a wee bit arduous with the maths terminology,as I understand your need to put your teaching methods into practice to get the message across to your captivated audience.But please is there any chance of keeping it nice and simple to allow the little grey cells to receive the information on the frequency it has become accustomed to.Nevertheless a first class thread and I look forward to many happy hours of digesting your further findings.;)

[dietcoke]

Re: A football rating system, discussions, ideas Mr Onemore, Looking at the final formula you have come up with, the use of 1/NumA means the rating value, while becoming more accurate as the season goes by it also becomes less sensitive to current form. Also, the resetting of the value means that current form is over weighted at the start of the season. Is it not preferable to use a constant of say 1/Num where Num = the number of games in a season thus ensuring consistency in what is being measured? With this you will, over the course of two seasons of data develop a rolling form measure which may have some validity at the start of the season.

[dietcoke]

Re: A football rating system, discussions, ideas Dohhh!! I've just read post 111 and 112 and I think that my question has already been raised and partially answered

[mr onemore]

Re: A football rating system, discussions, ideas Hi dietcoke, Yep - I agree with what you say - we've come to the same conclusion here;) I'll come to this bit soon in the thread, but the small modification I alluded to is in fact what you suggest...:ok

[merlin]

Re: A football rating system, discussions, ideas Can I ask a question Mr.Onemore, may sound silly, but a lot of us old hands last performed at Maths too many years ago to remember! Going back to basics at the very start, you gave examples on how to write the three equations for the three matches in question as:- l 1 - 1 0 lRa l l2 l l 0 1 -1 lRb l = l 3 l l-1 0 1 lRc l l1 l How does one then go about writing the equations for say ten equations or more when getting around to match predictions? ;) l

[mr onemore]

Re: A football rating system, discussions, ideas Hi Merlin - no problems! Yes, you can write out a whole system of equations for each match - but the computer does these things very easily... There is a sample spreadsheet I put up, on about page 4 I think, that if you download I think you can see how I've set the computer up to do all the hard work in forming the equations in a matrix form. If you want to put in your own data, then you can just replace the match data in the spreadsheet - but if you change the number of matches analysed or teams analysed, then you're going to have to re-size the matrices accordingly. Matrices are quite difficult to work with though, hence the simplified techniques in this chapter...I'll put a spreadsheet up for these too sometime if it helps... Any more questions - no problems here...hope you're enjoying seeing an application for all that old maths!!

[dietcoke]

Re: A football rating system, discussions, ideas I've just pumped a few values into a spreadsheet and I'm finding that the formula sometimes gives a negative rating. When a negatively rated team then loses to a positively rated team, the formula seems to break down by reversing the points awards. The negative teams rating increases even though they lost while the winning team suffers a fall in rating. Heres an example:

EXAMPLE	RESULT			HomeTeamBefore	HomeTeamAfter	AwayTeamBefore	AwayTeamAfter
1	0	4	A	1.05	-0.68	-0.14	1.59
2	2	1	H	3.75	2.78	-0.17	0.8
3	4	0	H	-0.13	1.89	1.94	-0.08

As you can see in example 2, the home teams rating fell even though it was the winner:wall Any ideas, on how this can be avoided.