Derive Asian Handicap odds

[paparainbow]

Hi, i have a question that initially I thought it was simple, but that’s not the case i guess.

Let’s say i have a model, and i can calculate the probability of all correct scores for a given match ( it really doesn’t matter the model as long as i have a probability density function f(x,y) that returns correct score x-y).

 

How can I calculate asian handicaps 0, 0.25, 0.5, 0.75 etc?

0.5 is easy, i take all matches that x>=y (0-0,1-0,2-0....., 1-1,2-1,3-1,..... )

similarly 1.5: x>=y+1 etc

 

what about the asian handicaps? Any idea?

[paparainbow]

On 11/17/2018 at 5:03 PM, laprikon said:

Variables 
P(Aw) = Probability of team A winning 
P(d) = Probability of draw 
P(Bw) = Probability of team B winning 
P(A|1) = Probability of Team A winning by exactly 1 goal = 0.191856-0.30565416*x+1.42165*x^2-1.21885522*x^3, where x=P(Aw)
P(A|2) = Probability of Team A winning by exactly 2 goals = 0.13482-0.553848*x+1.71645*x^2-1.08417508*x^3, where x=P(Aw)
TO(A|X) = True decimal odds of team A with handicap X 

Notes and Sources 
[1] To find true odds of Team B, use the following equation: 1-TO(A|X).

https://dropmefiles.com/qXmY2

You can use this spreadsheet

can you re-upload the spreadsheet, please? thanks for replying

 

with respect to your formulas, what are those numbers? and what is the formula for TO(A|X)?

Edited January 3, 2019 by paparainbow