Question

[MattR]

This is probably one for Mathare to get his teeth into.


Supposing I have an average goals scored/conceded figure for both teams, how would you go about getting the probability for a particular score?

[mathare]

There are probably umpteen different ways to do this but I'm only going to discuss those that spring instantly to mind.

One way would be to use Poisson distributions (http://en.wikipedia.org/wiki/Poisson_distribution)to work out the probability of each team scoring a given number of goals.

But the problem you have here is you've got two different values for each element of the score line (home goals for/ away goals against - away goals for/home goals against) so which of those values you use or how you combine them is the first hurdle to get over.

You could just average the two values and go from there. Let's work with real figures here to make things easier. I'll use the Fulham v Man Utd game that is due to kick off in under an hour. Fulham have scored 12 and conceded 10 in 13 home games whereas Man Utd have scored 28 and conceded 10 in 13 away games. So divide goals by games and we get:
HGF = 12/13 = 0.92
HGA = 10/13 = 0.77
AGF = 28/13 = 2.15
AGA = 10/13 = 0.77

We can now average these out to get an expected average scoreline of:
Home goals = (HGF + AGA) / 2 = 0.84
Away goals = (HGA + AGF) / 2 = 1.46
=> Fulham 0.84 - 1.46 Man Utd

Chances of getting that score line? 0% guaranteed :D

But we can see that the advantage lies with Man Utd and we'd expect them to win based on these averages. But we are after correct score bets here, and through working out the probability we can keep Ginge happy and look for value.

In fact as a quick aside football betting is one of my main areas for value betting as the number of variables is far less than horse racing and you can estimate the probability for a given event more accurately. For example, you can use head to head stats, home/away form or whatever to look for value. Suppose Team B are visiting Team A for the 10th time. In the previous 9 games between these two it's 3 wins each and 3 draws. If you can get better than 2/1 on any of the results (draw is the most likely to be 11/5 or so) you have identified a value bet, based on the stats you have used. Is it true value? You don't know because you don't, and can never, know the true odds of an outcome. But these sorts of value bets can be back tested as you can use rules to make the selections and apply the rules to historical data.

Anyway, back on topic. Correct score betting for Fulham 0.84 - 1.46 Man Utd. Using the Poisson functions in Excel we can get the probability of each team scoring a set number of goals.
=POISSON(0,0.84,FALSE) gives us the probability of Fulham scoring 0 goals (42.9%). Generically you need
=POISSON([goals],[average],FALSE), the FALSE telling Excel to give you the probability for only the specified number of goals, e.g exactly 2 goals not 0, 1 and 2 goals.
Apply this for 0 to 4 goals for both teams and you'll see:
Ful 0 = 42.91%
Ful 1 = 36.31%
Ful 2 = 15.36%
Ful 3 = 4.33%
Ful 4 = 0.92%
Man 0 = 23.19%
Man 1 = 33.89%
Man 2 = 24.77%
Man 3 = 12.07%
Man 4 = 4.41%

You can then multiply these percentages together to get the probability of a given scoreline. For example, Man Utd to win 3-0 would be 12.07 * 42.91 = 5.18% so you'd be looking for around 20/1 for a value bet there (it's 10/1 best price with the bookmakers).

This all of course assumes that goals follow the Poisson distro. They may do, they may not - we can't be sure either way really. They may follow another mathematical distribution that we can calculate probabilities from but Poisson is handy as Excel does all the hard work for us.

Other options would be to forget averages and use past score data, e.g. how many times over the past X games have Fulham scored 0, 1, 2 etc. and similarly for Man Utd and then work out percentages again dividing frequency by total number of games. Then multiply as above. So if in the last 10 games Fulham have scored 0 5 times, 1 goal 3 times, 2 goals once and 3 goals once then
Ful 0 = 50%
Ful 1 = 30%
Ful 2 = 10%
Ful 3 = 10%
Ful 4 = 0%

This means any scoreline that has Fulham scoring 4 goals or more will have a probability of 0. So immediately you have a fault with the model as Fulham could score 4 goals in an afternoon, it's not impossible, just improbable. But as I said above you'll never get true odds for this (or anything with so many variables), just an estimation of the odds.

Hope that helps.

[MattR]

Excellent stuff Mat, plenty of food for thought there. Be interesting to see how the Fulham v Man U game comes out. There it's suggesting most likely outcomes will be Fulham scoring 0 or 1 and Man Utd 1 or 2 which is about what you'd expect I would say.

For the sake of a bit of fun then let's say a dutch on the following

0-1 8.00
1-1 9.60
0-2 7.40
1-2 8.80

Dutched odds of 1.1/1 2.10
Man Utd win is 1.49 so could probably even throw in 0-3 and 1-3 at 12.00 and 12.50 (now makes it 1.56) so providing they don't hit 4+ or Fulham score 2 you have better odds and the 1-1 draw is covered.

Will play around with that poisson in excel then Mat and see what I can come up with. Might do a little 1000 challenge thread based on it.


Thanks once again for help/ideas etc.

[mathare]

If you do a challenge based on this it might be worth trying it 3 ways:
1) Poisson based on the goal averages as shown above
2) Poisson based on home team goal averages only
3) Poisson based on away team goal averages only

[MattR]

Good idea, may get some time tomorrow to get something going on that then . :)

[MattR]

Right, been playing around with this and will try something on some of tonights games.


I've used the first option of HF+AA , AF+HA to get the values required. However I've used two sets. One for the season and one based on the last ten games (so between 4 to 6 home or away games) to give a 'recent form' slant to it. Then I've taken the average of the two results to get the probability based odds for each score on Betfair. Alongside this I've put the actual available odds alongside and am using a combination of the rank of each score happening alongside the perceived (key word Ginge :D ) value on offer on betfair. From that I've got a score that will give me in theory a hybrid most likely/best value list of likely scores. Or not as the case may be! :laugh

Will add some more of tonights games later but have done Birmingham v Leeds for now. No ideas yet on what sort of bets to do (dutch 5 scores, 3 scores, whatever) but at the moment will just list what is coming up as the five most likely using the system and see what pans out



Ave Prob Odds first then betfair (in blue) available odds

Birmingham v Leeds

1-0...8.65.....7.60
1-1... 8.80....8.80
ANY..9.40.....8.80
2-0...10.24...7.60
1-2...17.88...26.00


I'm curious to see if Any will keep coming up. For what it's worth next two on list are 0-1 and 2-1


more to follow in a while

[MattR]

Ave Prob Odds first then betfair (in blue) available odds

Birmingham v Leeds

1-0...8.65.....7.60
1-1... 8.80....8.80
ANY..9.40.....8.80
2-0...10.24...7.60
1-2...17.88...26.00

Norwich v Luton

ANY....7.15......13.00
1-1.....9.33.......7.60
2-1.....10.42....11.00
1-0.....11.40.....8.20
2-0.....12.76....15.00

Crew v Scunthorpe

1-1....8.56.......7.60
ANY...9.16......10.50
0-1....10.04....12.00
1-2....10.64.....9.40
0-2....12.48....17.00

Doncaster v Yeovil

1-1.....8.45.......7.60
ANY....9.99.......18.00
0-1.....11.32.....9.20
1-2.....11.69.....13.00
1-0.....12.34.....8.80

Oldham v Blackpool

1-1.....7.99.......7.60
1-0.....9.47.......8.00
0-1.....10.95.....10.50
2-1.....11.68.....10.00
ANY....12.24.....15.00

Rotherham v Swansea

ANY.....6.11........13.00
1-1......10.16......7.60
2-1......11.92......13.00
1-2......9.80........9.80
2-2......14.75......15.50


As correct scores are very hard to find in general I'm going to try a lay of all scores that are 80% or less of the perceived odds using this formula.

LAYS: £2 lay stake
Betfair lay price

Birmingham v Leeds
2-0 7.80
3-0 14.00

Luton v Norwich
0-0 12.50
0-1 11.50
0-2 21.00
1-0 8.20

Crewe v Scunthorpe
2-1 11.00
2-2 14.50
3-0 46.00
3-1 29.00
3-2 34.00
3-3 50.00

Doncaster v Yeovil
0-0 10.50
1-0 8.80
2-0 12.50
3-0 30.00

Oldham v Blackpool
None

Rotherham v Swansea
0-0 14.50
0-1 9.60
0-2 15.00
1-0 12.50
1-1 7.80
1-2 10.00

[MattR]

Birmingham v Leeds 1-0

1-0...8.65.....7.60
1-1... 8.80....8.80
ANY..9.40.....8.80
2-0...10.24...7.60
1-2...17.88...26.00

Norwich v Luton 2-3

ANY....7.15......13.00
1-1.....9.33.......7.60
2-1.....10.42....11.00
1-0.....11.40.....8.20
2-0.....12.76....15.00

Crew v Scunthorpe 2-3

1-1....8.56.......7.60
ANY...9.16......10.50
0-1....10.04....12.00
1-2....10.64.....9.40
0-2....12.48....17.00

Doncaster v Yeovil 0-0

1-1.....8.45.......7.60
ANY....9.99.......18.00
0-1.....11.32.....9.20
1-2.....11.69.....13.00
1-0.....12.34.....8.80

Oldham v Blackpool 0-1

1-1.....7.99.......7.60
1-0.....9.47.......8.00
0-1.....10.95.....10.50
2-1.....11.68.....10.00
ANY....12.24.....15.00

Rotherham v Swansea 1-2

ANY.....6.11........13.00
1-1......10.16......7.60
2-1......11.92......13.00
1-2......9.80........9.80
2-2......14.75......15.50

Interesting results. 3 from 6 were in top four predicted scores. I don't really think you can dutch more than about 3, otherwise you're getting down to anywhere from 6/4 to odds on which means you'd have to hit just about every game.
.

LAYS: £2 lay stake
Betfair lay price

Birmingham v Leeds 1-0
2-0 7.80 Won
3-0 14.00 Won

Luton v Norwich 2-3
0-0 12.50 Won
0-1 11.50 Won
0-2 21.00 Won
1-0 8.20 Won

Crewe v Scunthorpe 2-3
2-1 11.00 Won
2-2 14.50 Won
3-0 46.00 Won
3-1 29.00 Won
3-2 34.00 Won
3-3 50.00 Won

Doncaster v Yeovil 0-0
0-0 10.50 LOST
1-0 8.80 Won
2-0 12.50 Won
3-0 30.00 Won

Oldham v Blackpool
None

Rotherham v Swansea
0-0 14.50 Won
0-1 9.60 Won
0-2 15.00 Won
1-0 12.50 Won
1-1 7.80 Won
1-2 10.00 Lost


Lays 20/22 21*2 £42 minus comm would be £39.90 2 losses at 10.50 and 10.00 would be -£37.50 So these would have produced a net profit of £2.40. Not sure I'd want to
be laying 40 and 50/1 but perhaps a cut off of around 15-20 could be interesting.


Would probably be worth laying the game to a fixed liability as well instead of a fixed stake