20 points to whoever can answer this question.

[Rich Boy]

If the Pinny team total for a MLB game is:

OVER 3.5 -108
UNDER 3.5 -108

What is the fair price for this line

OVER 4.5 RBI
UNDER 4.5 RBI

Additional Info:
-Value of 0.5 runs on a team total = 6.8%
-Percentage of total runs that are RBI's = 94.7%

[OmgUrMom]

Over +4.5 RBI +141
Under +4.5 RBi - 157

[Rich Boy]

No sir.

[Sunde91]

Over +168
Under -180

[ZetaPsi808]

i have no fukkin idea

[nes84]

OVer +140
uNDER -185

[OmgUrMom]

im assuming we are sticking with the 16 cent line used in the example?

[forsberg21]

Over +237
Under -253

[beanbag]

over +148

under -148

[LT Profits]

No Vig = Under -151

If sticking with 16-cent line:

OVER 4.5 RBI +145
UNDER 4,5 RBI -161

[jeccross]

+/- 270 if talking about fair line.

[davidchong]

under -154

[Flyers21]

Based on your additional info:

Over 4.5 RBI +113

Under 4.5 RBI -130

[Rich Boy]

Good work Jeccross, this problem took me a few days to figure out. If you dont mind, please share your work for another 20 points.

[blackbox]

OVER 4 1/2 rbi + 1.38

[FreeFall]

Good work Jeccross, this problem took me a few days to figure out. If you dont mind, please share your work for another 20 points.

I'd appreciate this and throw in another 40.

[Rich Boy]

Ill tell you how I got the answer.

1. Convert 3.5 Runs to 4.5 Runs

.0682 * 2 = 13.5%

So the fair line for 4.5 Runs is

OVER 4.5 Runs = 36.37%
UNDER 4.5 Runs = 63.63%

2. Convert 4.5 Runs to 4.5 RBI's

This is where it gets tricky.

If it goes OVER 4.5 runs is where you need to calculate the odds of a run (or more) not counting as an RBI.

So using a binomial distribution, the odds of at least 1 run not counting if exactly 5 runs are scored is 21.39% (assuming 4.8% of total runs are NOT RBI's)

the odds of at least 2 runs not counting if exactly 6 runs are scored is 2.92%

And the odds are negligible after that.

So 21.39 + 2.92 = 24.31%

So there is a 24.31% chance that if this bet goes OVER 4.5 Runs, it stays UNDER 4.5 RBI's

So now I just calculate the odds of the bet going OVER 4.5 Runs and all runs counting as RBI's

Thats .3637 * (1-.2431) = 27.4%

27.4% is the probability of going OVER 4.5 RBI

OVER 4.5 RBI = 27.4%
UNDER 4.5 RBI = 72.6%

For a fair price of about +266/-266