question about calculating 1.5 points

[rsigley]

hi,

if i have a MLB total that is 9 and lets say +100 on each side for simplicity and push of 9 is 10%

o8.5 = push % of 9 + percentage of over 9 = 55%
o9.5 = percentage of over 9 = 45%

now i have the push percentage for 8 when the total is 9 and lets call that 5%

how would I calculate over 8? the half point calculator gives 57.89% for this case, but I don't know how to arrive at that.

i've been using the half point calculator for a while now, but i'd wanted to incorporate it into my database so it calculates automatically, but i can't seem to figure out how to calculate the over 8.

thanks!!

[Ganchrow]

i have a MLB total that is 9 and lets say +100 on each side for simplicity and push of 9 is 10%

o8.5 = push % of 9 + percentage of over 9 = 55%
o9.5 = percentage of over 9 = 45%

now i have the push percentage for 8 when the total is 9 and lets call that 5%

how would I calculate over 8?

(Note that in the following Prob(over X) and Prob(under X) refer to the respective probabilities of winning an over or under X bet, "conditioned" on the bet not pushing.)

For all integer spreads, S:

Prob(over S) = Prob(over S+½)/(1-Prob(exactly S))
Prob(over S+½) = Prob(over S)*(1-Prob(exactly S))

and similarly,

Prob(under S) = Prob(under S-½)/(1-Prob(exactly S))
Prob(under S-½) = Prob(under S)*(1-Prob(exactly S))

So, given:

P(over 9) = P(under 9) = 50%
P(exactly 9) = 10%
p(exactly 8) = 5%

We have:

Prob(over 9½)
= Prob(over 9)*(1-Prob(exactly 9))
= 50% * 90%
P(over 9½) = 45%

Prob(over 8½)
= 1 - Prob(under 8½)
= 1 - Prob(under 9)*(1-Prob(exactly 9))
= 1 - 50% * 90%
P(over 8½) = 55%

Prob(over 8)
= Prob(over 8½)/(1-Prob(exactly 8))
= 55% / 95%
Prob(over 8) ≈ 57.895%

[rsigley]

wow thanks so much!!