[Blax0r]

Originally posted on 04/19/2011:

Is there a formula to convert an odds value to a probability value for example:

home tie visitor
If in a soccer match we have odds of 2.1 3.2 2.9

What is the probability for the home team win based in 2.1 odds, for the visitor win based in 2.9 odds and the tie based in 3.2 odds

I'll do the process for this example; then you guys can probably make your own spreadsheet.

H - 2.1
D - 3.2
A - 2.9

First let's figure out the implied probability of each of these positions with the EV equation:

(amount won)*p - (amount lost)*q = 0
(amount won)*p - (1 - p)*(amount lost) = 0
(amount won + amount lost)*p - (amount lost) = 0
p = (amount lost)/(amount won + amount lost)

where p is P(win) and q is P(loss).

H - 2.1 --> 1/2.1 = 47.62%
D - 3.2 --> 1/3.2 = 31.25%
A - 2.9 --> 1/2.9 = 34.48%

These are the necessary probabilities in order for you to have 0 EV (if you bet on one of these positions). However, this doesn't exactly indicate the true probability of the event since the book should be offering lower odds than the actual probability (ie, give themselves +EV).

This is now just reduced to a regular ratio problem that you guys probably saw on the SATs or middle school math.

H - 47.62
D - 31.25
A - 34.48
total: 113.35

The total should actually be 100, since P(A) + P(H) + P(D) = 1. I'll assume the book's juicing each position evenly, but you can easily modify this.

47.62 : 113.35 should be the same ratio as X : 100:
47.62/113.35 = X/100; solve for X.

H - 42%
D - 27.57%
A - 34.42%

These are the event's true probabilities implied by the book's odds; making an excel sheet to automate this is probably fairly simple.