i believe number of goals scored in a soccer match is poisson.

suppose some1 is offering odds of over 2.5 goals is 2.12 and under at 1.802. i want to know what they think the mean score is.

the no commission implied probability is

1/2.12=0.47

1/1.802=0.55

=0.47/0.47+0.55=0.46

then use the poisson formula here

i guess P < 3 = 0.54

x = 0, 1, 2

e = 2.71828

μ is ur answer

P(x; μ) = (e^-μ) (μ^x) / x!

so u need 0.54=[(2.71828^-μ) (μ^0) / 0!]+[(2.71828-μ) (μ^1!) / 1]+[(2.71828^-μ) (μ^2) / 2!]

can any1 help me solve this or even better where can i find a formula for the mean.

would be amazing if there was something i could use in excel to solve this also.

many thanks