Probability percentage from a rating

[Speed Figure]

Originally Posted by 098poi

You need to replace the ribbon in your typewriter.

Thanks! I have problems with this old commodore 64 sometimes.

[raybo]

Originally Posted by whodoyoulike

Good luck.

Sounds like you're getting into Bayes or maybe you can apply Monte Carlo simulation to improve the initial odds e.g., given the odds as presented insert the effect of variables such as slop, trainer ITM%, jockey ITM% etc.

Steveb once provided a flowchart as I recall which showed a method of using iterations to improve a factor's results at least that's the way I interpreted it.

What I hope to accomplish is to return a "logical" value for each horse in a race, not a perfect value, or even near perfect (because I personally believe that even near perfection is unattainable in horse racing. My philosophy is that what we need is something that is "good enough", to make a profit. What that means is that the average price we receive is high enough to offset our losses. If it were as simple as applying Bayes or Monte Carlo then lots of people would already have achieved profitability.

What I really think is that an oddsline will need to take into account field size, highest rating, lowest rating. median rating, groupings of similar ratings, gaps between ratings, etc.. What I have now is too flat, the top group of ratings is too close to the other groups of ratings, so the better ratings are being diminished and the lower groups are betting increased, in projected value. The better odds are too high and the lower odds are too low. The rankings themselves look fine, and the gaps look fine too, but the odds just don't jive.

[Capper Al]

Originally Posted by GameTheory

He has, many times. But that's not enough. ALL threads that mention odds lines need to be rescued by Capper Al lest we ever forget we shouldn't be talking about such useless instruments. It is for your own good, you see. Once you come around and think correctly, you'll thank him...

There's another uncanny point that you made- not only do I do the samething when odds lines come up, so does the rest of the forum. Don't blame repeating on me. If these guys wouldn't do it, I'd never be able to jump in. Like I said, odds lines are fun. But when wagering remember that it isn't based on solid math.

[cj]

Originally Posted by Capper Al

Like I said, odds lines are fun. But when wagering remember that it isn't based on solid math.

How do you know that?

[headhawg]

Originally Posted by PaceAdvantage

This is a perfect example of why people who don't know what they are talking about when it comes to a certain subject (value betting lines) really should not try to school people on said subject (value betting lines).

It's also how really good threads get derailed. Too many alleged "knowledgeable" handicappers butt in where they don't belong or are not needed. I'm tired of the "it won't work" or "you can't do it that way" posts. So before I really go off, thank you to the posters who made positive contributions to this thread.

[raybo]

Originally Posted by headhawg

It's also how really good threads get derailed. Too many alleged "knowledgeable" handicappers butt in where they don't belong or are not needed. I'm tired of the "it won't work" or "you can't do it that way" posts. So before I really go off, thank you to the posters who made positive contributions to this thread.

I agree! The topic is about creating a logical oddsline, not whether or not to create one. Al needs to apologize and stop posting in this thread unless he has something positive to contribute regarding the creation of a logical oddsline.

[Cratos]

Originally Posted by raybo

Ok you stats gurus, if I have a rating derived from multiple factors, each weighted according to significance, how do I get from that final rating to a projected win probability/percentage?

Let's start with the following final ratings for a race:

#1 -- 72.65
#2 -- 101.06
#3 -- 104.32
#4 -- 87.72
#5 -- 89.90
#6 -- 10.20
#7 -- 75.89
#8 -- 79.96
#9 - 105.25
#10 - 77.95
#11 - 73.84
#12 - 69.82

How do I get from those ratings to a calculated/projected win probability/percentage? I have always thought that you just divide each rating by the sum of all the ratings, but can't seem to find anything related to this type of calculation on the web, and I haven't tried to create a line in a long time, so I'm a bit rusty.

Ray,
Your problem is a straightforward conditional probability calculation, but some assumptions need to be made.

• All speed ratings are derived from the same factors
• p-value for this universal set is considered to be statistically significant because it is less than 5% and the likelihood that a change in the speed rating given for each horse is caused by something other than mere random chance.

Now we can move to the stage of “logical construct” or conditional probability and to do that we must determine each given speed rating in this set historical probability with respect to its win probability.

For instance, the historical probability for horse #1 speed rating of 72.65 wins x1-percent at this distance, in this class, on dirt; this is done for each horse.

The resulting probabilities are added and normalized for the universal set.

The total probabilities should add to a total of y-value and the probability for the speed rating of 72.65 becomes x1/y and the next speed rating becomes x2/y until we reach the total of 12 for the universal set; the probabilities are converted to odds by calculating the inverse of the probability for each horse.

These probabilities have absolutely nothing to do with the current tote board odds.

However if you want to associate these probabilities (odds) with the current tote board odds just calculate another set of conditional probabilities driven by the tote board odds.

An Excel spreadsheet can easily be constructed as a template for this calculation and by adding variables it can become very robust.

[raybo]

Originally Posted by Cratos

Ray,
Your problem is a straightforward conditional probability calculation, but some assumptions need to be made.

• All speed ratings are derived from the same factors
• p-value for this universal set is considered to be statistically significant because it is less than 5% and the likelihood that a change in the speed rating given for each horse is caused by something other than mere random chance.

Now we can move to the stage of “logical construct” or conditional probability and to do that we must determine each given speed rating in this set historical probability with respect to its win probability.

For instance, the historical probability for horse #1 speed rating of 72.65 wins x1-percent at this distance, in this class, on dirt; this is done for each horse.

The resulting probabilities are added and normalized for the universal set.

The total probabilities should add to a total of y-value and the probability for the speed rating of 72.65 becomes x1/y and the next speed rating becomes x2/y until we reach the total of 12 for the universal set; the probabilities are converted to odds by calculating the inverse of the probability for each horse.

These probabilities have absolutely nothing to do with the current tote board odds.

However if you want to associate these probabilities (odds) with the current tote board odds just calculate another set of conditional probabilities driven by the tote board odds.

An Excel spreadsheet can easily be constructed as a template for this calculation and by adding variables it can become very robust.

Thanks Cratos, I appreciate your input, but these aren't speed figures, they are weighted multi-factor ratings, an integrated rating that attempts to represent the relational value of each horse to all the other horses in the field.

Ray

[Cratos]

Originally Posted by raybo

Thanks Cratos, I appreciate your input, but these aren't speed figures, they are weighted multi-factor ratings, an integrated rating that attempts to represent the relational value of each horse to all the other horses in the field.

Ray

I apologize for calling your factors "speed ratings", but the analysis doesn't change because your factors are performance driven and single point entities.

You started a very good post.

[davew]

I was intrigued by Dave Swartz' recommendation to square the values before normalizing. Some sort of 'separation' needs to be applied to data to skew the data helping the higher scores and penalizing the lower scores. I decided to take the original values and then 1)square and normalize 2)cube and normalize and 3) quad (or whatever it is when you multiple it by itself 4 times). The values are then listed in percentage to the tenths for their respective columns (square, cube, quad).

original squared cubed quad
72.65 6.45% 5.26% 4.21%
101.06 12.47% 14.17% 15.75%
104.32 13.29% 15.59% 17.88%
87.72 9.40% 9.27% 8.94%
89.90 9.87% 9.97% 9.86%
10.20 0.13% 0.01% 0.00%
75.89 7.03% 6.00% 5.01%
79.96 7.81% 7.02% 6.17%
105.25 13.53% 16.01% 18.53%
77.95 7.42% 6.50% 5.57%
73.84 6.66% 5.53% 4.49%
69.82 5.95% 4.67% 3.59%

[Cratos]

Originally Posted by davew

I was intrigued by Dave Swartz' recommendation to square the values before normalizing. Some sort of 'separation' needs to be applied to data to skew the data helping the higher scores and penalizing the lower scores. I decided to take the original values and then 1)square and normalize 2)cube and normalize and 3) quad (or whatever it is when you multiple it by itself 4 times). The values are then listed in percentage to the tenths for their respective columns (square, cube, quad).

original squared cubed quad
72.65 6.45% 5.26% 4.21%
101.06 12.47% 14.17% 15.75%
104.32 13.29% 15.59% 17.88%
87.72 9.40% 9.27% 8.94%
89.90 9.87% 9.97% 9.86%
10.20 0.13% 0.01% 0.00%
75.89 7.03% 6.00% 5.01%
79.96 7.81% 7.02% 6.17%
105.25 13.53% 16.01% 18.53%
77.95 7.42% 6.50% 5.57%
73.84 6.66% 5.53% 4.49%
69.82 5.95% 4.67% 3.59%

Are you suggesting an exponential predictive curve?

[davew]

Originally Posted by Cratos

Are you suggesting an exponential predictive curve?

No, just looking for a 'separation factor'

[Cratos]

Originally Posted by davew

No, just looking for a 'separation factor'

There no need to look for a "separation factor" because the OP with his performance metric has included all relevant factors; this is just a simple Bayesian analysis.

[raybo]

Originally Posted by Cratos

I apologize for calling your factors "speed ratings", but the analysis doesn't change because your factors are performance driven and single point entities.

You started a very good post.

Yes, the rating is an all-inclusive factor, at least as all-inclusive as I can make it. The example I posted was a real race field, and the probabilities, converted to odds, for all but one horse were within a very narrow range, while the actual ratings themselves were in a a much more "normal" range, "normal", meaning they looked like a typical run of the mill field, 2 -3 top contenders, then a significant drop off with a few others in that range, and then one horse being obviously over-matched, by the rest of the field