Fair price on RBI prop

[Rich Boy]

Say a book is offering a prop on team RBI's... Im trying to find a way to compare the team total and put a fair price on team RBI's.

Ive looked at the stats and about 95% of total runs scored in MLB are RBI's and 5% are not RBI's (wild pitches, errors, walks, etc)

Say the team total for a game is

Over 3.5 -110
Under 3.5 -110

What would be the fair price for this bet?

team RBI's Over 3.5
team RBI's Under 3.5

My math gave me a 52.5% chance it goes Under 3.5 RBI's...

My formula is to multiply the "over" win probability by 0.95, but I have a feeling its wrong. Someone give me a hand with this one, thanks.

[Justin7]

If your assumptions are valid, and the old "fair"price was 3.5 total runs, you would expect the fair expected runs to be 3.5 * 0.95, or 3.325. Then you would need to figure out what the value of a half-run is on a team total.

[mathdotcom]

Justin

Of course there are easy ways to check for definite +EV, but pinpointing the exact number is difficult. Probably not worth it unless you see a big enough discrepancy.

[Justin7]

Justin

Of course there are easy ways to check for definite +EV, but pinpointing the exact number is difficult. Probably not worth it unless you see a big enough discrepancy.

Once you solve the problem generally though, you can price all these props. It would be a good thing to know if you can get a decent bet on it.

[Rich Boy]

Ive been working on the numbers and this is what I came up with...

Look at tonights game (SD @ LAD)

Pinny has SD team total at:

OVER 3 -113 (.511)
UNDER 3 -103 (.488)

Now I want to figure out what the win % is for UNDER 3.5 RBI's

I know that only 95.3% of the total runs SD scores will be counted towards my bet.

lets say SD scores 4 runs in this game.
That would give me a 16.27% chance of exactly 1 run not counting (exactly 1 run will NOT be an RBI)

lets say SD scores 5 runs in this game.
That would give me a 1.91% chance of exactly 2 runs not counting (exactly 2 runs will NOT be an RBI)

lets say SD scores 6 runs in this game.
That would give me a .18% chance of exactly 3 runs not counting (exactly 2 runs will NOT be an RBI)

If you add the probability of all 3 scenarios you will get roughly a 18.36% chance of me winning this wager but losing (or pushing) the Pinny team total...

Someone let me know if these numbers make sense to you.

[Rich Boy]

I know that a half run on a team total is worth around 5.5%. Im going to go with 5% just to be safe.

UNDER 3 runs is .488 according to Pinny

So UNDER 3.5 runs should be (.488 + .05) = .538

Then according to my math UNDER 3.5 RBI's should be (.538 + .1836) = .7216

The win % seems a little high to me.

[byronbb]

^^^ maybe multiply not add them together??

Just wanted to bump this for selfish reasons. Was wondering if RBI's and HITS can be assessed by Poisson distribution? Also lets say I have a HITS prop. Can I derive the expected # of hits by Pinny's Team Total just using the teams RUN per HIT ratio?

[TomG]

OP, I would just look at the Team Total and use that since you said 95% of total runs are runs that were batted in. It's a bit rough, but you can easily build yourself a margin of safety by not betting thin stuff. This is much easier and ultimately will be more accurate than trying to make sense of the product between 0.95 and a Team Total handicap. Also note that Team Totals are themselves a derivative market and thus less efficient. You're trying to value a derivative of a derivative. So be careful and leave yourself a lot of room for error.