Reverse Poisson, how to work backwards?

[Shinigami]

Hi, just wondering if someone mathematically inclined could help me with this... i understand how you can use average goals scored for the home & away team to derive the probabilities of Home win, Draw, and Away win.. and i have the excel spreadsheet to compute this.. My question now is, if i have a set of probabilities, say 43%/27%/30% and i want to reverse the process to compute the average goals scored.. how do i go about this using the excel spreadsheet?

[Shinigami]

Re: Reverse Poisson, how to work backwards? i believe there should be a certain formula to decompose the Poisson result back & find the two X,Y variables (average goals scored)... so does anyone know how? thanks...

[clay747]

Re: Reverse Poisson, how to work backwards?

i believe there should be a certain formula to decompose the Poisson result back & find the two X,Y variables (average goals scored)... so does anyone know how? thanks...

I bookmarked this thread awhile ago on inverse Poission http://www.actuarialoutpost.com/actuarial_discussion_forum/archive/index.php/t-7730.html Check out Brad Giles function. I have not used it myself, but it should be easy to check that it works. But, 1 X 2 odds are a product of Average Goals and Supremacy and without knowing one value you can not calculate the other. that is, there wont be a single answer as many different combinations of Average Goals and Supremacy will produce the same odds. You can reverse the Over/Under 2.5 goal odds to get the Average Goals.

[pacey]

Re: Reverse Poisson, how to work backwards? Hello. go to this address there is a free Excel spreadsheet that calculates the poisson http://www.pro-soccer.info/poisson-distribution-on-soccer-game/

[Shinigami]

Re: Reverse Poisson, how to work backwards?

Hello. go to this address there is a free Excel spreadsheet that calculates the poisson http://www.pro-soccer.info/poisson-distribution-on-soccer-game/

thanks bro, but this isn't what i was looking for. i'm looking for the spreadsheet that allows me to reverse the process..

[Lardonio]

Re: Reverse Poisson, how to work backwards? I don't think that spreadsheet exists, as you would now some data to base the reverse process on.

[salford_student]

Re: Reverse Poisson, how to work backwards?

I bookmarked this thread awhile ago on inverse Poission http://www.actuarialoutpost.com/actuarial_discussion_forum/archive/index.php/t-7730.html Check out Brad Giles function. I have not used it myself, but it should be easy to check that it works. But, 1 X 2 odds are a product of Average Goals and Supremacy and without knowing one value you can not calculate the other. that is, there wont be a single answer as many different combinations of Average Goals and Supremacy will produce the same odds. You can reverse the Over/Under 2.5 goal odds to get the Average Goals.

Thats not strictly true, your assuming that for any given win odds that the draw odds will always be the same. You can have same the win probability but different draw probs and these different draw odds will be as a result of different total goals. e.g. try the following values in a double poisson A=1.3 B=0.73 these give H=0.5 D=0.29 A=0.21 A=1.0 B=0.395 these give H=0.5 D=0.356 A=0.144 both sets of poisson parameters give the same win probs for team A, but different draw probs, hence knowledge of the draw probs should allow the total goals to be calculated. theres several ways to reverse engineer this calculation, the easiest would be to use the solver function in excel. However this is all assuming that the double poisson is a very accurate model for a football match, which I dont beleive it is and wont be sensitive enough to allow one to determine the total goals using the draw price in conjuction with the win price.