Extracting team totals from the total and moneyline

**Data** · 08-13-10, 01:45 PM

Yes, it is possible to calculate prices of any derivative given ml and total. I made myself a spreadsheet that does that instantly. Took me a while to make it though. Good luck.

**MarketMaker** · 08-13-10, 03:43 PM

Originally posted by mathdotcom

Suppose you are interested in the probability of a baseball game ending with a team winning by exactly 1 run (not just the favorite - either team). Let me call this a 'tie'.

This really depends on the team totals. If both teams are expected to score 3 runs, then you have a good candidate for a tie. If both teams are expected to score 4 runs, you also have a decent candidate for a tie, but not as good as the first example.

Suppose you don't have the team totals. Shouldn't the information embedded in the total and moneyline be sufficient to answer the same question of what is the probability of a tie?

The first example of both teams expected to score 3 runs each should imply a total of about 6.5 and a fair moneyline close to +100. The second example should yield a total of 8 or 8.5 and again a fair moneyline close to +100.

Or in a more extreme example, suppose Team A is expected to score 7 runs and Team B is expected to score 0. Then we should have a total of about 7 and Team A would be a huge moneyline favorite.

Shouldn't this work backwards then? Given the moneyline and total you should be able to come up with decent estimates of the team totals.

What are the cases where using the moneyline and total in lieu of the team totals will lead to biased estimates?

Anytime you do a ML conversion based on team totals it is also very important to accurately estimate each teams standard deviation of scoring. This would also be necessary doing the reverse and estimating team total based on ML and total. I know this is of utmost importance in the NBA but I assume team specific scoring tendencies exist in baseball too.

For example if you have two NBA teams that are both totaled at 95. Team A shots from the field average 26.19% from 3 point range and 74.81% from inside the arc. Team B shots from the field average 15.84% from 3 point range and 84.16% from inside the arc. Team A will have more variance and will therefore have a higher SD from their expected score (team total). This means that everything else being equal Team A will have a lower moneyline as both a favorite and a dog at equal pointspreads compared to Team B.

**Arilou** · 08-13-10, 05:50 PM

A baseball game has two unknowns; you can express them as total and moneyline, or total and runline/spread, or two team totals. Any two different odds work. They are all different ways of saying how much both teams will score. This is in no way unique to baseball. The probability of a team winning by one can be extracted from any such pair if you have a good formula for it; which ones you use are up to you and what you find easiest to work with.

MarketMaker, I believe the magnitude of that effect is sufficiently small as to be ignorable.

**MonkeyF0cker** · 08-14-10, 04:12 AM

If you're only interested in the probability of one run games, why not simply derive a runline and alternate runline?

**mathdotcom** · 08-14-10, 09:17 AM

Monkey you're right, this was more of a hypothetical example to get at whether or not Team Totals matter. It goes back to an old thread on Salami spreads, where tomcowley suggested team totals would be required to come up with a good estimate of how many runs the home teams will win by.

I figured if I didn't motivate it with an example, simply posting "What are the cases where using the moneyline and total in lieu of the team totals will lead to biased estimates?" would not have gotten a lot of replies.