A question about converting to run lines

[SteveAvery33]

Hey everyone,

I've been looking to take my moneyline numbers and make a runline number to see which has more value. If anyone can tell me if my methodology is correct, I would really appreciate it. I'll be using today's Reds/Dodgers game in my example.

First, I determine my probabilities that each team wins. I get 64.95% for the Dodgers and 35.05% for the Reds. Converting the Dodgers to ML, I get -185. Since that is better than Pinnacle's line of -165, I like the Dodgers. But I want to see if there if more value in taking the runline.

My next step is the run environment. I feel like using the fair market odds here are fine. I see an o/u at 8.5 with the over at -116 and the under at -106. I calculate that fair market percentages here are 51.06% for the over and 48.94% for the under.

Now ignoring if my probabilities for wins/losses by home and road teams at different run environments are correct, I'd like to know if this makes sense.

In order to figure out the Dodgers chances of covering the -1.5, I need to find two things. First I take their chance to win the game (.6495) times the chance the game is under 8.5 (.4894) times the chance that the home team wins by more than one run (.7098).

(.6495 x .4894 x .6236) = .1982

I then do the same thing for the over, using .7098 as the pct the home team wins by more than one run.

(.6495 x .5106 x .7098) = .2354

Adding them up gives me the probability that the Dodgers win by more than one with a total set at 8.5.

.1982 + .2354 = .4336

Converting that to a ML gives me +131.

Now, to determine the value, I think I must do this.

The runline at Pinnacle is +122. So to win $124, I would need to bet $100, which I believe would happen 43.36% of the time. The other times I would lose the $100.

(.4336 x 124) - (.5664 x 100) = -2.87

For the moneyline, Pinnacle is -165. Same betting pattern from above yields.

(.6495 x 100) - (.3505 x 165) = +7.12

Since the ML value is greater than the RL value, I should be the moneyline. I know this one is a pretty obvious example, but I want to make sure my method is correct. Any insight would be great.

[Ganchrow]

It certainly makes sense ... but there is at least one notable and readily identifiable problem with your methodology.

You're implicitly assuming that the probability of a home team winning by 1 run, conditioned on it winning the game at all, is invariant with respect to its raw game win probability.

Generally speaking, this is untrue. In reality the greater a team's expected game win probability the lower its conditional 1-run win probability.

This doesn't imply your analysis useless, however, but I would be hesitant to place much stock in its conclusions for games with odds deviating substantially from average.


On another note, the fastest way to determine the edge on a bet is to multiply the decimal odds by the expected win probability and then subtract 1.

So for a 43.36% win probability at a line of , the edge would be:

43.36% * 2.22 - 1 = -3.74%

And for a 64.95% win probability at a line of , the edge would be:

64.95% * 1.6061 - 1 = +4.31%

Now because only one of the two edges is positive, it's obviously easy to determine which would be the superior bet. If, however, both edges were positive with the longer odds bet at higher edge, you'd probably want to evaluate the two bets in terms of utility gained rather than simply in terms of EV.

[SteveAvery33]

Thanks for the prompt reply. Since you are the resident expert on all things mathematical around here, how difficult do you think it would be to set up some sort of conversion from my moneyline to a runline. Is this a task I probably shouldn't undertake? Sticking strictly to moneyline bets is fine, but adding more to my plate is definitely something I wouldn't have a problem with.

Also, do you know if anyone has done any work on this with success?

[Data]

I would be hesitant to place much stock in its conclusions for games with odds deviating substantially from even.

Why "even"? If the numbers provided are averages then the results are going to be closest for an average contest and the average line for a home team winner is somewhere around -125-130, I guess.

[Ganchrow]

Why "even"? If the numbers provided are averages then the results are going to be closest for an average contest and the average line for a home team winner is somewhere around -125-130, I guess.

I mistyped. I should have written "deviating substantially from average".

Geometric average fair fractional odds given a home team victory relate to US odds of about -124 on the favorite.

[Data]

US odds of about -124

I doubt it is correct to round that number (-124) to the nearest digit.

[Ganchrow]

I doubt it is correct to round that number (-124) to the nearest digit.

OK. So let's call it -123.7.

[Data]

I meant the other way. The observation errors do not call for such precision.

[Ganchrow]

I meant the other way. The observation errors do not call for such precision.

That was supposed to be a joke.

You had initially said -190 and I thought -124 a far superior estimate.

[Data]

You had initially said -190

I have no problem admitting my brain-farts. That was one those.

[xyz]

Generally speaking, this is untrue. In reality the greater a team's expected game win probability the lower its conditional 1-run win probability.

This certainly makes sense intuitively. The winning margin for a -200 favorite should be larger than a -120 favorite. Ganchrow, did you find this out through historical data or by other means? Thanks for your insight.

[Ganchrow]

This certainly makes sense intuitively. The winning margin for a -200 favorite should be larger than a -120 favorite. Ganchrow, did you find this out through historical data or by other means? Thanks for your insight.

I (and many others) have verified this with historical data.

But just to be clear, I should have said "the greater a team's expected game win probability the lower its conditional 1-run win probability" modulo the caveat "all else being equal".

[xyz]

I (and many others) have verified this with historical data.

But just to be clear, I should have said "the greater a team's expected game win probability the lower its conditional 1-run win probability" modulo the caveat "all else being equal".

Thanks for the clarification, Ganchrow. What does the run difference distribution curve look like? Just to clarify, the run difference graph I have in mind has the following on the x axis:

...Team A win by 2, Team A win by 1, 0, Team B win by 1, Team B win by 2, ...

0 is impossible, so we should have a minimum there. I suppose there is at least one maximum on each side of the origin. Can the maximum be calculated from the moneyline odds? If anyone has the historical data in a machine readable format, I would be interested in writing a program to produce the graphs for different moneyline and runline odds.

[Ganchrow]

Thanks for the clarification, Ganchrow. What does the run difference distribution curve look like? Just to clarify, the run difference graph I have in mind has the following on the x axis:

...Team A win by 2, Team A win by 1, 0, Team B win by 1, Team B win by 2, ...

0 is impossible, so we should have a minimum there. I suppose there is at least one maximum on each side of the origin. Can the maximum be calculated from the moneyline odds? If anyone has the historical data in a machine readable format, I would be interested in writing a program to produce the graphs for different moneyline and runline odds.

It's just going to look like a bell curve with the peak farther to the left the larger a favorite A is, and a peak farther to the right the larger a favorite B is.

[BadFinger]

throwing some small run line wagers on colorado and cubs tonight to see if it works.

[Data]

It's just going to look like a bell curve with the peak farther to the left the larger a favorite A is, and a peak farther to the right the larger a favorite B is.

The peak is always going to be at "home team by 1". That peak is isolated though.

[xyz]

It's just going to look like a bell curve with the peak farther to the left the larger a favorite A is, and a peak farther to the right the larger a favorite B is.

Thanks for the insight, Ganchrow. I assume you meant taking out the origin, then we have a bell curve. Otherwise, we have a discontinuity at the origin. Can the center of the bell curve be calculated from the moneyline and the run line odds. Thanks.

[Ganchrow]

The peak is always going to be at "home team by 1". That peak is isolated though.

Yes, I should have specified that there will be an outsize bump at H By 1. My bad.

It might not always be a peak, however, as in the case of large mismatches. For example, in the case of home dogs of +200 or more, we have

h by 4	2.0%
h by 3	3.7%
h by 2	6.1%
h by 1	10.5%
a by 1	12.9%
a by 2	10.5%
a by 3	13.6%
a by 4	6.5%
a by 5	6.1%

Unfortunately, for Home+200 or greater, the standard error of the differences in frequencies is too large to come to any real statistically meaningful conclusions about where the true population peak should lie.

I also should have specified that for the ranges of dogs/faves commonly seen in the MLB, the peak is always going to hover close to the origin, and it's going to be more of a general flattening.

[Ganchrow]

Thanks for the insight, Ganchrow. I assume you meant taking out the origin, then we have a bell curve. Otherwise, we have a discontinuity at the origin. Can the center of the bell curve be calculated from the moneyline and the run line odds. Thanks.

Yes. The x-axis would only contain valid margins of victory not including the case of the exceedingly rare tie. Also see my post to Data above.

You can't calculate the peak algebraically but rather would need to find the peak via cues from the historical record.

[xyz]

Yes, I should have specified that there will be an outsize bump at H By 1. My bad.

It might not always be a peak, however, as in the case of large mismatches. For example, in the case of home dogs of +200 or more, we have

h by 4	2.0%
h by 3	3.7%
h by 2	6.1%
h by 1	10.5%
a by 1	12.9%
a by 2	10.5%
a by 3	13.6%
a by 4	6.5%
a by 5	6.1%

Unfortunately, for Home+200 or greater, the standard error of the differences in frequencies is too large to come to any real statistically meaningful conclusions about where the true population peak should lie.

I also should have specified that for the ranges of dogs/faves commonly seen in the MLB, the peak is always going to hover close to the origin, and it's going to be more of a general flattening.

Thanks for sharing the data, Ganchrow. This data is very useful. I can already see several ways to use the chart above to know when a +Ev situation presents itself. What would the chart look like for a home favorite of -120? We should see odds of home favorite -120 more often than home dog +200.

[BadFinger]

is there any long term numbers on playing the run line on home favorites at -160 to -200? i started making small $25 wagers on some of them this week and it is positive. there is a lot of games that fit today but i am playing 2 on the white sox and indians.