Calculating expected goals per team

[Borga]

Hi all, a quick question that will hopefully yield a quick answer...

If Team A is playing Team B, and I have a bookie's Over/Under prices at hand, how can I calculate the expected goals scored by both Team A and Team B?

Simple example: Team A and Team B are both paying exactly the same price ($2.75) and the Over 2.5 goals is priced at even money ($1.95). I would assume that the expected number of goals for both teams is 1.25 (2.5 divided by 2). So a formula to work out expected goals for Team A would be (1-(A/X))*G where A = Team A's price ($2.75), X = Team A's price + Team B's price ($5.50) and G = expected goals (2.5).

I'm pretty sure this works out, but just a bit unsure whether this formula holds for any circumstance. If Barcelona are a $1.05 favourite against a $30 underdog, with total expected goals of 4.5 (Over 4.5 = $1.95) then the formula would yield Barcelona = 4.35 expected goals and Underdog = 0.15 expected goals. It does seem right but it's nagging me that I can't confirm, partly because I'm not sure how the Draw price factors into things...

So I only have one question, does all this have the ring of truth? Cheers in advance.

Edited February 22, 2020 by Borga

[harry_rag]

I don’t know and I’d just use the spreads as it’s much easier! You could do that to check if your method gives reasonable looking results. 

Taking Barca v Eibar today, one firm quotes supremacy at 1.9-2.1 and the other 2-2.2. The total goals quotes are 3.35-3.55 and 3.45-3.65. 

Taking the midpoint of those quotes suggests Barca are 2.05 goal favourites in a game where 3.5 goals are expected which gives (rounded up) 2.78 goals for Barca and 0.78 for Eibar. You also get the same results by simply using the quotes for team total goals, e.g. best priced spreads are 2.7-2.85 for Barca and 0.65-0.8 for Eibar.

Take a sample of games and see if your results are in the same ballpark.

[Borga]

Thanks harry_rag, and you're right; using the quoted prices for Team Goals is ideal. The problem I'm having, which I probably should have specified, is that I'm having trouble finding these prices for historical data. I've been using OddsPortal for backtesting for some time now, which I've found valuable, but there are no prices given for Team Goals events. If you know of a resource that offers these prices historically, let me know. 

As an aside, the formula I gave doesn't tally very well with the prices you quoted for Barca-Eibar, suggesting that it's probably a bit flawed...

 

 

[ray2520]

If the price for over 2.5 is, say 2.0, then that would imply that the probability of over 2.5 is 1/2. So the probability of under 2.5 is also 1/2.  The number of goals can be modelled by a Poisson distribution, and if you use that, since we know that P(X <= 2) is 0.5, we can find the expected number of goals that is implied by the price of over 2.5 being 2.0.

 

Here's a few values I've worked out in the past... Not sure if this will format well

Price of under 2.5      Expected number of goals in match

1.5                                       2.04

2.0                                       2.67

2.5                                       3.11

3.0                                       3.43 

 

This doesn't separate the teams out however. I will say though that when I used this method to work out the prob of say under 1.5 or under 3.5 it was extremely accurate. I think this is how people do it on the exchanges.

[paparainbow]

you have to create a correct score model. keep in mind that expected goals are not the only variables needed. you should need also something like correlation or draw factor.

then you reverse enginer your model based on the true probabilities that come out of bookies' prices