[mebaran]

Say I predict the total of an MLB game at 5.91 runs, and the price I'm getting from the book is:

Over 6.5 (-110)
Under 6.5 (-110)

How do I calculate theoretical edge on this bet if I want the under? I'm having a brain fart here...

[mebaran]

Anyone? What kind of simple distribution can I use without loss of too much accuracy? In the above example, if I predict 5.91 runs as the correct total, how to I find the distribution of those runs?

[Justin7]

In games where you project 5.7 to 6.1, how often do they land under 6.5?

[mebaran]

In games where you project 5.7 to 6.1, how often do they land under 6.5?

Say for the sake of discussion 60%.

[Dom177]

I'd play the under. Too many variables in baseball if your projections are that close...go with your gut.

[Justin7]

Say for the sake of discussion 60%.

IF you have a pretty big sample size (say 300+), you probably have a good edge, and I would bet it. The problem though... There are not many games totaled under 7. So if you look at your model as a whole, does it do reasonably well on unders when there is about a 10% disagreement on the total? For that matter, does it do well on the overs as well? A good model should see consistent results both ways, although a margin of 10% might not be enough to overcome model error.

[mebaran]

IF you have a pretty big sample size (say 300+), you probably have a good edge, and I would bet it. The problem though... There are not many games totaled under 7. So if you look at your model as a whole, does it do reasonably well on unders when there is about a 10% disagreement on the total? For that matter, does it do well on the overs as well? A good model should see consistent results both ways, although a margin of 10% might not be enough to overcome model error.

Yeah I understand with that low total, you're going to run into sample problems. My original post pertains to actually computing (the math behind it) your edge. I guess I'm looking for a simple solution, not a normal distribution, because I'm positive that can't be right for runs in baseball, but a distribution that will, generally, work.

[HuskerExpat]

Say I predict the total of an MLB game at 5.91 runs, and the price I'm getting from the book is:

Over 6.5 (-110)
Under 6.5 (-110)

How do I calculate theoretical edge on this bet if I want the under? I'm having a brain fart here...

You want to run a Poisson Distribution. A Poisson Distribution shows that with expected runs of 5.91, there is a 62% chance of being under. The money line equivalent of 62% is -164 (164/264). If you want a 5% edge, then you want to bet when the odds give you the equivalent of a 67% chance for under, which is -133 (133/233).

[Justin7]

You want to run a Poisson Distribution. A Poisson Distribution shows that with expected runs of 5.91, there is a 62% chance of being under. The money line equivalent of 62% is -164 (164/264). If you want a 5% edge, then you want to bet when the odds give you the equivalent of a 67% chance for under, which is -133 (133/233).

MLB distributions do not follow Poisson very well. If you expected 6 runs, a vast majority of your games would be within 2 runs of your total. MLB does not have that kind of distribution.

[mebaran]

You want to run a Poisson Distribution. A Poisson Distribution shows that with expected runs of 5.91, there is a 62% chance of being under. The money line equivalent of 62% is -164 (164/264). If you want a 5% edge, then you want to bet when the odds give you the equivalent of a 67% chance for under, which is -133 (133/233).

Correct, but runs scored in a baseball game do not follow a Poisson distribution right? More than one run can be scored at any given time, so Poisson is not the correct application here.

I know the general shape of the curve here, with the average runs in the league hovering around 4.80, but I read a paper on the fact that the most common number of runs scored in the league is 3, then 4, then 2. ALL of these are below the mean (4.8), so the curve is skewed. The reason for this is because a team can never score less than 0 runs, but can score as many runs as the other team will let them score.

Could I get away with using Poisson? Or is would I be better off just using something like a logarithmic?

[HuskerExpat]

The biggest problem with poisson, in my opinion, is that the game will not end if the score is tied. That makes it not a straight application of poisson. I have my own ideas about how to account for that, but they're not tested/proved. Other than that, I think poisson has a somewhat fair application to MLB totals.

[mebaran]

In my findings, Poisson, over time, isn't accurate in instances where teams score either a very small amount of runs, or a very large amount of runs.

I'll keep searching for a solution, but was just wondering if anyone had another angle I wasn't thinking of.

[TomG]

I wonder if bettors lose more money from Poisson than they make from it?

In any event, there is no easy solution to your question OP. It's not a "brain fart" situation, it's actually a complicated problem.

[mebaran]

I wonder if bettors lose more money from Poisson than they make from it?

In any event, there is no easy solution to your question OP. It's not a "brain fart" situation, it's actually a complicated problem.

I think Poisson is overused in general, so I often wonder the same.

Thanks for at least making me feel less...incompetent.

[Rufus]

A lot of things that most reasonably smart bettors assume actually fit a negative binomial distribution much better. With Poisson, the assumption is mean=variance, but negative binomial allows variance to vary (but only higher than mean).

For the run scoring distribution for MLB, I personally would model it using an ordered logistic regression. The model I have would convert a "true" total of 5.91 to a true line of under 6.5 -122

Edit: By true total I am NOT referring to mean expected total, but rather a (theoretical, as runs scored is not continuous) median.

[Dark Horse]

With a large enough sample size, just compare your winning expectation to the line. In my experience the very best models, no-juice lines, have a remarkable consistent 60% ceiling. So if your model is that good (a big IF), you would bet anything that beats -150.

My recommendation would be to stay away from extreme posted totals in baseball. Especially this early in the season. Given how many totals you can bet each season, an extreme total is just unnecessary trouble.

http://contests.covers.com/SportsCon...ortID=5&type=3

[mebaran]

With a large enough sample size, just compare your winning expectation to the line. In my experience the very best models, no-juice lines, have a remarkable consistent 60% ceiling. So if your model is that good (a big IF), you would bet anything that beats -150.

My recommendation would be to stay away from extreme posted totals in baseball. Especially this early in the season. Given how many totals you can bet each season, an extreme total is just unnecessary trouble.

http://contests.covers.com/SportsCon...ortID=5&type=3

What do you mean by that? (I understand that -150 is implying a 60% win rate, but I'm not sure what you're saying).

[mathdotcom]

Don't listen to DH, he doesn't even understand your question.

A very simple way to think about it is in basketball where there is not such a discrete difference in totals. So if your model predicts a total of 200.75 and you're trying to set a fair line then you would offer

O200.5 -102
U200.5 +102

where I'm assuming a half point is worth 4cents. You just convert the 1/4 of a point edge into cents since of course as a bookie you can't reflect the model's prediction by posting a line of 200.75 instead of 200.5.

With baseball you might want to be more careful using a rule of thumb for half point value, such as the commonly used 31 cent value for the 7, but this approach is a decent first start without getting into the underlying distributions of all the model's moving parts.

That said, it may also not be ideal to be modeling baseball totals in such a way that you get continuous estimates. I like Rufus's suggestion of using ordered probits, assuming you're in a regression framework which I assume you are.

[mebaran]

Thanks mathy. Definitely looking into other ways of getting around continuous distributions.

[Tkeni]

Anyone know where i can find the best MLB bullpen info?