Probability percentage from a rating

[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.

[Dave Schwartz]

Normalize it to 100%.

That is, add up the numbers and divide each score by the sum of the scores in the race.

[raybo]

Normalize it to 100%.

That is, add up the numbers and divide each score by the sum of the scores in the race.

So, I was correct that you divide each final rating by the sum of all the ratings in the race? If so, then these are the probabilities for each horse:

#1 -- 72.65 ---- 0.076589914
#2 -- 101.06 --- 0.106536888
#3 -- 104.32 --- 0.109981423
#4 -- 87.72 ---- 0.09247253
#5 -- 89.90 ---- 0.094780224
#6 -- 10.20 ---- 0.01074802
#7 -- 75.89 ---- 0.080008831
#8 -- 79.96 ---- 0.084296919
#9 - 105.25 --- 0.110960109
#10 - 77.95 --- 0.082172241
#11 - 73.84 --- 0.077847444
#12 - 69.82 --- 0.073605457

But, the odds those probabilities result in are not logical. They range from 8/1 to 13/1, except for the #6 horse who gets 92/1 odds.

[headhawg]

raybo,

Have you ever read the Four Quarters of Horse Investing by Steve Fierro? I think that trying to assign a "fair" oddsline to more than four or five horses is just folly. If you read his book you will understand what I mean. I'm not trying to diminish what you're attempting, but I think that fair odds becomes nearly impossible to do with any accuracy once the projected win probabilities fall below a certain percentage.

Good luck

[raybo]

raybo,

Have you ever read the Four Quarters of Horse Investing by Steve Fierro? I think that trying to assign a "fair" oddsline to more than four or five horses is just folly. If you read his book you will understand what I mean. I'm not trying to diminish what you're attempting, but I think that fair odds becomes nearly impossible to do with any accuracy once the projected win probabilities fall below a certain percentage.

Good luck

I have not read Fiero's book, but I've heard that one should only consider "actual" win contenders. While that's probably true, it doesn't address my problem, that being assigning win probabilities and their associated decimal odds to all horses in the race. There must be a way to scale the ratings in order to obtain more realistic probabilities and odds.

Sure, it would be easy to consider only those horses with at least a 10% probability, regarding assigning odds, however, there can be horses below that 10% that are decent bets, especially when you consider the price you're likely to get. Lots of people have automated methods of assigning realistic odds to every horse in a race. I guess that is my real question, how do they do it, without ending up with something unrealistic like this example?

I mean, really, in my example, there is a horse with a 105 rating, another with a 104, and another with a 101, with the next one way down at 89. And yet, all 4 of those top horses are only a couple of percentage points apart. The spread should be larger than that, IMO.

[whodoyoulike]

Isn't this similar to creating a M/L which means you'd need to consider the takeout % which differs by track if you're creating the odds e.g., some are 0.15 and others are 0.18 etc.?

How accurate are your ratings since they are very similar to each other which I would think the probabilities would then be close to each other?

[raybo]

Isn't this similar to creating a M/L which means you'd need to consider the takeout % if you're creating the odds?

How accurate are your ratings because they are very similar which I would think the probabilities would then be close to each other?

I have not considered takeout, yet, but I would suspect that the relationships between ratings would not change much, if any. The final ratings would still be too close to one another, for too many horses.

Perhaps the individual factor ratings are too "normalized", and that is causing the final ratings' probabilities to be too tight. I normalized all of the individual factor ratings to the same point range, 0 to 100. That might be the underlying problem. My thinking was that all of the factors should be relational, regarding scale, so that the weightings would not be skewed, higher or lower, simply due to the existence of different factor ranges. I've not much experience with weighted factors, so I'm learning as I go.

[Dave Schwartz]

But, the odds those probabilities result in are not logical. They range from 8/1 to 13/1, except for the #6 horse who gets 92/1 odds.

They are "logical."

The issue is that your numbers do not scale as the tote board does. They are "flat."

As an example, suppose you are building probabilities based upon speed ratings where every horse is in the range of 90-100. The difference from top to bottom is only 10 points. When you graph the horses you get a lightly sloping line or curve.

If you think about it, you don't actually want the speed ratings. You want something that represents how the speed ratings translate into win percentages or impact values.

In other words, you want to ask (and answer) such questions as "How does a horse 3 points below the top horse in the field perform?" (Or 5 points or 8 points, or 17 points.) There are more creative ways to express this but I was trying to keep it simple.

Tagging factors with weighted values is not an easy task.

You need to go back and question your original weighting system.


As a long-standing member on PA, I respect your many contributions. If you'd care to contact me, I'd be willing to spend some time with you in an online meeting and work through some of this stuff and help any way I can.

Just email me.
Dave

[raybo]

Tagging factors with weighted values is not an easy task.

You need to go back and question your original weighting system.



Dave

I appreciate the response Dave!

Are you saying that, by normalizing all of the individual factor ratings to the same scale, the factor weightings/multipliers will not have the desired effect?

The fact that some factor ratings have a very tight range, from highest to lowest, while others have a wider range, was the very reason I decided to normalize all the factor ratings to the same scale. Obviously, that doesn't work well, as the wider factor ranges get tightened up, while the tighter factor ranges get widened.

[whodoyoulike]

I agree with Dave's response which is the reason I asked "how accurate are your ratings". Maybe instead of calculating probabilities based on the ratings, approach it as Dave suggested.

... If you think about it, you don't actually want the speed ratings. You want something that represents how the speed ratings translate into win percentages or impact values.

In other words, you want to ask (and answer) such questions as "How does a horse 3 points below the top horse in the field perform?" (Or 5 points or 8 points, or 17 points.) There are more creative ways to express this but I was trying to keep it simple. ...

[Dave Schwartz]

Are you saying that, by normalizing all of the individual factor ratings to the same scale, the factor weightings/multipliers will not have the desired effect?

The fact that some factor ratings have a very tight range, from highest to lowest, while others have a wider range, was the very reason I decided to normalize all the factor ratings to the same scale. Obviously, that doesn't work well, as the wider factor ranges get tightened up, while the tighter factor ranges get widened.

Yes. All factors my scale similarly.

Example: In my system, all factors scale from 1 to 250.

Thus, Quirin Points go from 0 to 8, having 9 actual choices. Therefore, the value of a point is 27 points each and look like this:

0=1-27
1=28-54
2=55-81
3=82-108
4=109-135
5=136-162
6=163-189
7=190-216
8=217-243

The value of Speed Rating = 5 is returned as 149, the center point between high and low.


Speed ratings are scaled from the top of the field down to minus 25 below the top horse. This allows for 25 numbers. Specifically, if the top horse is a 97, he becomes 100 and the lowest horse is graded at 75. Any horse that comes in below 75 gets a 75.

Now that we know there will always be 25 numbers, we know that each number is worth 250/25 = 10 points.

[maddog42]

I have not read Fiero's book, but I've heard that one should only consider "actual" win contenders. While that's probably true, it doesn't address my problem, that being assigning win probabilities and their associated decimal odds to all horses in the race. There must be a way to scale the ratings in order to obtain more realistic probabilities and odds.

Sure, it would be easy to consider only those horses with at least a 10% probability, regarding assigning odds, however, there can be horses below that 10% that are decent bets, especially when you consider the price you're likely to get. Lots of people have automated methods of assigning realistic odds to every horse in a race. I guess that is my real question, how do they do it, without ending up with something unrealistic like this example?

I mean, really, in my example, there is a horse with a 105 rating, another with a 104, and another with a 101, with the next one way down at 89. And yet, all 4 of those top horses are only a couple of percentage points apart. The spread should be larger than that, IMO.

As a proponent of Fierro's book, I must admit that your dilemma is a common one for me. About 90 percent of the time I am able to get a field down to 4 or 5 contenders. That other 10 percent is as difficult as peeling an onion to find the differences. The onion gets sliced super thin and is almost transparent. This is something that you already know. There is value in the 6th and 7th contender sometimes. Hard to prove, but I know it is there.
Reality is the only thing that matters. Let your records show you how to manipulate and assign odds. This is complicated by the different distances/categories. At some distances/ tracks my line is a wreck and recognizing this is a way to make money at this game.

[davew]

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.

I have been trying to devise a method using standard deviations, but still have some snags. If you did probabilities by hand (from your numbers) what would you get? I guesstimated a probability line, but would have to see a few thousand races (with results) to see correlation with your numbers and results -> what percent of time would 2,3, or 9 win? Being able to go to the tenths would really help in lower odds horses...

#1 -- 72.65 -- 2
#2 -- 101.06 - 16
#3 -- 104.32 - 20
#4 -- 87.72 -- 9
#5 -- 89.90 -- 10
#6 -- 10.20 -- 1
#7 -- 75.89 -- 4
#8 -- 79.96 -- 6
#9 - 105.25 -- 22
#10 - 77.95 -- 5
#11 - 73.84 -- 3
#12 - 69.82 -- 2

[raybo]

I have been trying to devise a method using standard deviations, but still have some snags. If you did probabilities by hand (from your numbers) what would you get? I guesstimated a probability line, but would have to see a few thousand races (with results) to see correlation with your numbers and results -> what percent of time would 2,3, or 9 win? Being able to go to the tenths would really help in lower odds horses...

#1 -- 72.65 -- 2
#2 -- 101.06 - 16
#3 -- 104.32 - 20
#4 -- 87.72 -- 9
#5 -- 89.90 -- 10
#6 -- 10.20 -- 1
#7 -- 75.89 -- 4
#8 -- 79.96 -- 6
#9 - 105.25 -- 22
#10 - 77.95 -- 5
#11 - 73.84 -- 3
#12 - 69.82 -- 2

Obviously, at least to me, if the ratings are fairly accurate, then the top 3 horses should win about 60% of the time, over time. Your line has them at 58%, that's very close. Based on that, how did you differentiate between those 3 horses to get their portion of the 58% total probability? It appears that the relationships are not linear, but I haven't a clue as to how to come up with that non-linear scale/slope.

This set of numbers seems promising, regarding the separation/relationship between the 3 ratings. I found the average and then subtracted the 3 ratings from that average.

#2 _ -2.483333333
#3 _ 0.776666667
#9 _ 1.706666667

Based on those numbers this is what the probabilities percentage would be:

16.85
20.11
21.04

[lansdale]

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.

Hi Raybo,

I'm a little confused from what you've said in this thread whether this is a list of variable weights or a list of horses whose output is projected according to such weights. I'm guessing the latter.

If so, what the range of this data seem to resemble to me, since you've mentioned that your method is in the black, is the $net of a given field based on a few simple factors, which might explain the clustering. Also, since you've mentioned 'top 3' ranking as a part of your method, possibly you're penalizing horses who fall out of this grouping- would be consistent with this result. Since your description of your method implies that this is what you have sought to maximize, it would seem to make sense.

If it's not possible that this is what you've done, you already know this. But if it is, I would suggest just moving the decimal point two figures to the left and testing this against a database (you mentioned you're a client of J. Platt), and see how it stands up against a reasonably large sample. BTW, since the mean of even this small sample is 79, which would mean a return of .79 vs. all horses, which is quite close to what I believe is the mean return of all horses by the betting public, this may be quite accurate.

Cheers,

lansdale

[raybo]

Hi Raybo,

I'm a little confused from what you've said in this thread whether this is a list of variable weights or a list of horses whose output is projected according to such weights. I'm guessing the latter.

If so, what the range of this data seem to resemble to me, since you've mentioned that your method is in the black, is the $net of a given field based on a few simple factors, which might explain the clustering. Also, since you've mentioned 'top 3' ranking as a part of your method, possibly you're penalizing horses who fall out of this grouping- would be consistent with this result. Since your description of your method implies that this is what you have sought to maximize, it would seem to make sense.

If it's not possible that this is what you've done, you already know this. But if it is, I would suggest just moving the decimal point two figures to the left and testing this against a database (you mentioned you're a client of J. Platt), and see how it stands up against a reasonably large sample. BTW, since the mean of even this small sample is 79, which would mean a return of .79 vs. all horses, which is quite close to what I believe is the mean return of all horses by the betting public, this may be quite accurate.

Cheers,

lansdale

The example ratings are final ratings, after the weights have been applied. Many of the factors involved come directly from the raw data, jockey win and ITM percentages, trainer win and ITM percentages, horse win and ITM percentages, horse age and weight, horse power rating, horse pace and speed figures, etc.. There are a few other ratings that don't come directly from the raw data. There are 4 categories/sets of weightings, which is pretty standard to most weighted factor methods. But, there are some user preferences for several factors, and paceline selection preferences for the paceline related factors.

This method is not currently part of my Black Box, this is initially going to be a separate method, testable in batch processing mode, against any number of past races, which should help determine which factors are more important and which ones are not, also what the weightings for the final factor sets should be.

I'm looking ahead with this odds line thing, because we all know that, regardless of the accuracy of one's method, profit comes from win probability versus average price, otherwise known as "value". Sure, I could just produce the weightings method and let the user have at it, but the method will have more value to the user if there is a logical value metric included. So, I'm jumping the gun a bit via this thread, mostly because I know this portion is going to take the most time, and I want to get started now, rather than wait until the rest of the method is complete.

To answer your question, the horses, below the top 3, are not penalized at all in this method. All horses are going to receive equal treatment and live or die according to their data, and the factors and weightings each user decides to implement for each of the 4 race type categories of factor/preferences/weight settings.

[Dave Schwartz]

Raybo,

If you need to "un-flatten" the ratings, just raise them to a power.

This will exaggerate the differences between the horses.

[raybo]

Raybo,

If you need to "un-flatten" the ratings, just raise them to a power.

This will exaggerate the differences between the horses.

Thanks Dave, I'll try that. But, I kind of like the idea of looking at expected win rates based on the rating ranks, like the top 3, top 4, etc., of course I'll have to take into account virtual ties also, which will add a bit more complexity, or a bit of a different mindset.

[lansdale]

The example ratings are final ratings, after the weights have been applied. Many of the factors involved come directly from the raw data, jockey win and ITM percentages, trainer win and ITM percentages, horse win and ITM percentages, horse age and weight, horse power rating, horse pace and speed figures, etc.. There are a few other ratings that don't come directly from the raw data. There are 4 categories/sets of weightings, which is pretty standard to most weighted factor methods. But, there are some user preferences for several factors, and paceline selection preferences for the paceline related factors.

This method is not currently part of my Black Box, this is initially going to be a separate method, testable in batch processing mode, against any number of past races, which should help determine which factors are more important and which ones are not, also what the weightings for the final factor sets should be.

I'm looking ahead with this odds line thing, because we all know that, regardless of the accuracy of one's method, profit comes from win probability versus average price, otherwise known as "value". Sure, I could just produce the weightings method and let the user have at it, but the method will have more value to the user if there is a logical value metric included. So, I'm jumping the gun a bit via this thread, mostly because I know this portion is going to take the most time, and I want to get started now, rather than wait until the rest of the method is complete.

To answer your question, the horses, below the top 3, are not penalized at all in this method. All horses are going to receive equal treatment and live or die according to their data, and the factors and weightings each user decides to implement for each of the 4 race type categories of factor/preferences/weight settings.

Clearly you're not reverse-engineering the 'black box' model you've described here in the way I thought, so my suggestion wouldn't work. And after reading this post, I have to admit I am more confused than before about exactly what you are doing. If this is a product you're developing for clients involving 'user preferences' that would only seem to be muddying the waters. But whatever course you decide to take, hope it works out.

Cheers,

lansdale

[davew]

Obviously, at least to me, if the ratings are fairly accurate, then the top 3 horses should win about 60% of the time, over time. Your line has them at 58%, that's very close. Based on that, how did you differentiate between those 3 horses to get their portion of the 58% total probability? It appears that the relationships are not linear, but I haven't a clue as to how to come up with that non-linear scale/slope.

This set of numbers seems promising, regarding the separation/relationship between the 3 ratings. I found the average and then subtracted the 3 ratings from that average.

#2 _ -2.483333333
#3 _ 0.776666667
#9 _ 1.706666667

Based on those numbers this is what the probabilities percentage would be:

16.85
20.11
21.04


I wish I could say I had a formula you could put into a spreadsheet, but I do not. I did it by hand estimation. There is a chapter in an old classic -> The Odds on your Side by Mark Cramer that tells how to fine tune your own probability line (not to be confused with a morning line which is usually 115-120% to account for track take and estimate of closing odds) to bring it too 100%.

I have a problem with the numbers below the average - what do you do with the 10 in your example, almost a -3 standard deviation.

I have been thinking about this off and on for awhile, as I would like to be able to put the Bris Prime Power ratings into a probability line.

[raybo]

I wish I could say I had a formula you could put into a spreadsheet, but I do not. I did it by hand estimation. There is a chapter in an old classic -> The Odds on your Side by Mark Cramer that tells how to fine tune your own probability line (not to be confused with a morning line which is usually 115-120% to account for track take and estimate of closing odds) to bring it too 100%.

I have a problem with the numbers below the average - what do you do with the 10 in your example, almost a -3 standard deviation.

I have been thinking about this off and on for awhile, as I would like to be able to put the Bris Prime Power ratings into a probability line.

Well, we have, or can obtain, the long term probabilities (hit rates) for individual rankings (by field size probably), and also probabilities (hit rates) for groups of congruent rankings, like top ranked, top 2, top 3, top 4, etc., so I believe there must be a way to use those long term group probabilities to get a better handle on what type of separation, between assigned odds, there should be, in different categories of race types and fields.

Don't have any proof of the above, but I think it's worth exploring anyway.

If it doesn't pan out, there is always the ability to test different sets of factors and their scalings, as well as the odds produced by the probabilities. So, what I envision is not just a method that the user can use to select contenders, but more importantly, the ability to test and research the whole ball of wax, without having to pay large amounts of money for a traditional programming language app or traditional database app. It'll take longer in Excel, but it'll be so much simpler for the user, because of the extremely flat learning curve of an automated Excel application.

[classhandicapper]

I thought this was a very good article when I read it.

https://betting.betfair.com/horse-racing/bloggers/simon-rowlands/post-222-040810.html

[cj]

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.

Here is a simple method I posted many years ago that I still use often. It helps to have a cutoff, i.e. a spread that anything below is not considered a contender for the race. That is something only you would know what is best and pretty easy to test if you store your data as I imagine you do. For an example, I'll use 16 for your set. (Of course all this can be done with a program or spreadsheet, but I'm showing it manually here to show the details)

The top rating is 105.25, so to be included as a contender you need to be within 16 or 89.25.

That leaves four horses:

#2 -- 101.06
#3 -- 104.32
#5 -- 89.90
#9 -- 105.25

The minimum points I give a contender are 2. That number could vary for you and others just like the cutoff number. So I take the Min Contender rating, 89.90, deduct 2 = 87.90, and subtract that number from each rating.

#2 -- 13.16
#3 -- 16.42
#5 -- 2.00
#9 -- 17.35

I then add these up for a total of 48.93. Next, divide each rating into the total for a percentage:

#2 -- .27
#3 -- .34
#5 -- .04
#9 -- .35

Next, I account for the non-contenders. Some people like to assign a blanket number like 20%. I do it a little different but that is individual preference. I take the number of contenders, four in this case, and divide it by the field size, 33.333% in this case. I then average it with 100%. I find if I pick only four contenders in a 12 horse field I'm crazy if I think I'll have the winner 80% of the time. So in this case I use 66.6666% as my contender percentage. I then adjust the win percentages above by this estimate

#2 -- .27 / .66666 = .18
#3 -- .34 / .66666 = .23
#5 -- .04 / .66666 = .03
#9 -- .35 / .66666 = .23

I then convert to an odds line:

#2 -- .18 = 4.55
#3 -- .23 = 3.34
#5 -- .03 = 32.33
#9 -- .23 = 3.34

That is my fair odds line. I rounded here since I did it manually, will come out a little different if you program this, but that is the gist of it.

Oh, last thing, any horse with a "fair odds line" > than natural odds is tossed by me from the contender list, but again that is just from my experiences and numbers. Your mileage may vary.

[kingfin66]

I remember when you posted that method years ago and even printed it out. It is really well explained and very nice of you to share it again.

[Dave Schwartz]

CJ, that is just excellent.

Thank you!

[GameTheory]

Yeah, you can't just normalize any set of ratings directly and expect them to mean anything (beyond their rankings, which remain the same). You need something like CJ's ad-hoc method, tailor-made for horse racing, or for a more generalized method of turning a single rating on an unknown scale to a probability, use logistic regression. (Which should be easy enough in Excel -- aren't you a spreadsheet guru, Raybo?)

We had a long discussion about this once, probably in the thread that CJ originally posted his method. (I posted something similar which involved rescaling the range to something that would normalize better, and then normalizing.)

[formula_2002]

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.

Piece of cake.
You need to establish the dollar odds for each incremental rating.
using excel, make one column your rating, another the dollar odds it ran at, and another if it won. Simply use a "1" for a win.
(make it the true dollar odds by adjusting for the total booking percentage.)
you will also need a column for accumulated returns

now sort on your rating column. if you find profits within a specific range, test with new data.
At this time, don't be concerned by race type, surface, distance etc.. the public with take care of that for you.

I do this kind of stuff all the time, that's why I don't bet!!! :cool:


If your ratings are in a dbase format with a key field for track, race number and date, you can down load the results file from Bris and have fun with "what if".


Each data file race card was 25 cents some years ago.

ps, you may want to also normalize the results for each race and perhaps add a column for that. I would

[classhandicapper]

I wish I could say I had a formula you could put into a spreadsheet, but I do not. I did it by hand estimation.

In the link I posted, the author gives you the information you need to create a spreadsheet that I was able to duplicate and expand on. If you read the article and then the comments below it, you should be able to create a useful model. The key to it is selecting the correct power rating. That more or less defines how much a point on your scale is worth.

What I did was tinker with the power rating until it was producing odds lines that mimicked my thinking as a handicapper. Ultimately, I didn't use the spreadsheet much, but not because it wasn't a useful tool. I just found that I rarely go to the window unless I am fairly sure I actually have value. At that point, I really don't need an odds line. It kind of screams at you because the horse will generally be misranked by the public (in other words, the horse I am making the most likely winner, is the 3rd choice in the betting, the horse I am making 2nd most likely is the 5th choice etc..) So putting the rating into the spreadsheet was costing me time for very little gain.

[GameTheory]

Here's what I posted 12 years (!) ago for coming up with semi-reasonable probability numbers for a single race using any rating. (Assuming you don't know anything about the rating or haven't done a study of it anyway.)

See my post#7:

http://www.paceadvantage.com/forum/showthread.php?t=11081


Then there is the convoluted "tennis tournament" method from the old book "Beating the Races with a Computer" (1980). (Which is mainly a curiosity of how you might do such a study with the computer power of the late 70s) See this thread and my post#17:

http://www.paceadvantage.com/forum/showthread.php?t=60199


I'm not reposting it all here since the context of those other threads helps. (The bottom of the second thread has links to even more threads!)

[formula_2002]

Piece of cake.
You need to establish the dollar odds for each incremental rating.
using excel, make one column your rating, another the dollar odds it ran at, and another if it won. Simply use a "1" for a win.
(make it the true dollar odds by adjusting for the total booking percentage.)
you will also need a column for accumulated returns

now sort on your rating column. if you find profits within a specific range, test with new data.
At this time, don't be concerned by race type, surface, distance etc.. the public with take care of that for you.

I do this kind of stuff all the time, that's why I don't bet!!! :cool:


If your ratings are in a dbase format with a key field for track, race number and date, you can down load the results file from Bris and have fun with "what if".


Each data file race card was 25 cents some years ago.

ps, you may want to also normalize the results for each race and perhaps add a column for that. I would

one more thing, use another column for the odds at say 2 to 4 minutes to post, that's what you really need to determine a bet

[cj]

I looked over my code and there are a couple other tweaks I made over the years. If anyone is interested say the word and I'll post. None of the change the basic idea.

[Magister Ludi]

#~~~a~~~~~b~~~~~c~~~~~d~~~~~e~~~~~f~~~~~g~~~~~h
9~~105.5~~.111~~~.272~~~-.159~~~1~~~~.405~~~.135~~~.294
3~~104.3~~.110~~~.169~~~-.060~~~4.1~~~.159~~-.011~~~.049
2~~101.1~~.107~~~.129~~~-.023~~~6.9~~~.103~~-.027~~~.004
5~~~89.9~~.095~~~.110~~~-.015~~10.9~~~.068~~-.042~~~.027
4~~~87.72~~.092~~~.087~~~.005~~13.6~~~.055~~-.032~~~.037
8~~~79.96~~.084~~~.064~~~.020~~14~~~~.054~~-.010~~~.030
10~~77.95~~.082~~~.052~~~.030~~19.1~~~.040~~-.012~~~.042
7~~~75.89~~.080~~~.041~~~.039~~19.8~~~.039~~-.002~~~.041
11~~73.84~~.078~~~.031~~~~.047~~21.9~~~.035~~.004~ ~~.042
1~~~72.65~~.077~~~.025~~~.052~~~47.4~~~.017~~-.008~~.060
12~~69.82~~.074~~~.013~~~.061~~~51.3~~~.015~~~.002 ~~.058
6~~~10.2~~.011~~~.007~~~.004~~~89.6~~~.009~~~.002~ ~.002

a your ratings
b your ratings normalized to total 1
c track-dependant historical probabilities
d b - c information added by your ratings to historical probabilities
e tote odds
f tote probabilities normalized to total 1
g f - c information added by tote probabilities to historical probabilities
h absolute value of d - g. difference in information added by your ratings vs information added by tote odds

The probabilities in column c are historical probabilities which are developed for a specific track. What can be done with this data?

Examine the differences in column d. Do your ratings make sense in light of historical probabilities?

Compare d, g, and h. Example: can you really justify a .294 difference between your ratings and "the public" for #9?

Ala Benter, average b with c or f.

Where b > f, overlays. Conversely, where b < f, underlays.

I'm sure that if you try this method, you'll discover more useful work to do with this information.

[classhandicapper]

I love the idea of using a confidence interval.

Most of the line making models I come across assume that an "x" point advantage on your figures will always equal the same percentage advantage. But in real life sometimes I feel confident I know how good the horse is and how he's likely to run and at other times his record may be a mixture of races on different surfaces, off tracks, distances, layoffs, equipment changes etc.. that gives you a very muddy view of how good he is, let alone how he's going to run today. IMO those two extremes and everything in between should be built into your thinking about fair value. The greater the confidence, the less margin of safety you need above the actual odds to make the bet.

[whodoyoulike]

... I just found that I rarely go to the window unless I am fairly sure I actually have value. At that point, I really don't need an odds line. It kind of screams at you because the horse will generally be misranked by the public (in other words, the horse I am making the most likely winner, is the 3rd choice in the betting, the horse I am making 2nd most likely is the 5th choice etc..) So putting the rating into the spreadsheet was costing me time for very little gain.

This is also what I usually try to do.

And Raybo, we all have or will probably face your dilemma, for me I came up with an alternate solution which seems to work for me. But, I don't have a black box instead I make an evaluation of my program's data results.

[raybo]

Lots of things to read and mess with. Thanks guys! :ThmbUp:

[Dave Schwartz]

I looked over my code and there are a couple other tweaks I made over the years. If anyone is interested say the word and I'll post. None of the change the basic idea.


I am certainly all ears!

(Screen shots at the ready.)

[Capper Al]

It's all about having fun. Enjoy yourself with your odds line. Good luck!

[098poi]

Good thread. I remember years ago trying to convert some ratings I made straight across to an odds line and had the same result as Raybo. Evenly spread out and bearing little relation to an actual odds line where the first 3 or 4 favs dominate the lowest odds.

[cj]

I am certainly all ears!

(Screen shots at the ready.)

One is that the base minimum of 2 I up depending on the number of contenders.

Minimum

>5 contenders = 2
4 contenders = 3
3 contenders = 4
2 contenders = 5

The reason was if you keep the minimum too low with a small number of contenders it tends to overrate the highest rated horse. Anyone using this really needs to figure out how much of a spread between horses is meaningful with their own ratings. A minimum of 2 for a contender may work just fine for some ratings, maybe higher is good for others, and variable can work too.

The other thing wasn't really important here. It has to do with how I comprise the rating for each horse but it really doesn't matter to the method I outlined.

[Dave Schwartz]

CJ,

That entire concept is just excellent.

I am assuming several things:

1. This was designed to work with speed ratings (or numbers that approximate speed ratings).

2. Your experience has determined that 16-points-from-top is the threshold at which a hit rate graph would drop precipitously.

3. The 2-point (or 3,4,5) is derived from experience and designed as a margin of error.


Thanks for explaining this. Raises the bar nicely in this thread.


Regards,
Dave Schwartz

[cj]

CJ,

That entire concept is just excellent.

I am assuming several things:

1. This was designed to work with speed ratings (or numbers that approximate speed ratings).

2. Your experience has determined that 16-points-from-top is the threshold at which a hit rate graph would drop precipitously.

3. The 2-point (or 3,4,5) is derived from experience and designed as a margin of error.


Thanks for explaining this. Raises the bar nicely in this thread.


Regards,
Dave Schwartz

1) It was originally, but I don't always use speed figures. This is true for first time starters of course, but also trainer changes (especially to super trainers or from super trainers) and layoff types and a few other scenarios.

2) The 16 points was just used with raybo's data to include four horses and make a few extra points. I use about half of that, though it varies a little by class.

3) Exactly. You obviously can't use zero, so I worked up from there.

[Capper Al]

Building an odds line should only be understood as playing with numbers. What would be the predictive assertion be worth when our top choice is wrong at least two-thirds of the time? Odds line are more self serving as our own tribute to our systems and logic. In practice, they are useless. I too suffer from this ailment from loving my numbers. That's why we are handicappers.

[headhawg]

Building an odds line should only be understood as playing with numbers. What would be the predictive assertion be worth when our top choice is wrong at least two-thirds of the time? Odds line are more self serving as our own tribute to our systems and logic. In practice, they are useless. I too suffer from this ailment from loving my numbers. That's why we are handicappers.If you believe this then you must not believe in betting for value or you're still focused on predicting the winner. Betting the top choice (lowest odds) is only of value when you can do it at a rate and at a price that leads to a positive ROI. So if the chalk is even money, but the odds line is 3-5 that's a profitable situation. If it were possible to create a 100% accurate odds line then betting only overlays would lead to profits assuming the bettor understood how to make the bet(s).

[cj]

Building an odds line should only be understood as playing with numbers. What would be the predictive assertion be worth when our top choice is wrong at least two-thirds of the time? Odds line are more self serving as our own tribute to our systems and logic. In practice, they are useless. I too suffer from this ailment from loving my numbers. That's why we are handicappers.

Hogwash. It has nothing to do with if your percentages mirror the actual win percentages. Here is the simple test of an odds line. If your odds line leads you to bet on enough horses that you have as overlays to make you an overall winner, it is a fabulous tool. End of story.

[Capper Al]

I know that some believe that their odds lines reflect true value. And odds line are fun to make. Still, an odds line is only as good as the predictive powers of the odds maker. When it's time to wager, if our goal is profit, one must be honest and realize that they are in the dark about which horse will win and what these horses are really worth. There is only one absolute truth in handicapping: Good handicapping defeats random odds. Anything else is a guess. And that's no hogwash.

[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).

[Dave Schwartz]

I know that some believe that their odds lines reflect true value. And odds line are fun to make. Still, an odds line is only as good as the predictive powers of the odds maker. When it's time to wager, if our goal is profit, one must be honest and realize that they are in the dark about which horse will win and what these horses are really worth. There is only one absolute truth in handicapping: Good handicapping defeats random odds. Anything else is a guess. And that's no hogwash.

And better handicapping , with a learning component (i.e. gauging how well your methods work in order to make adjustments and actually making those adjustments) defeats "good handicapping."

Most people just will not make the effort.

I have found that the key to finding value is to track who you toss out in a race. Ask yourself this question: "When I toss out a horse (that ultimately goes off at) below 7/2, how much do those horses lose?"

If the answer to that question is, a $net of $1.30 or less, then you should be able to throw darts in those races and break even or better because there is enough pool money to recover the takeout.

In other words, if your low odds toss outs are losing 35% per wagered dollar, you should have no problem finding value in those races.

[Capper Al]

And better handicapping , with a learning component (i.e. gauging how well your methods work in order to make adjustments and actually making those adjustments) defeats "good handicapping."

Most people just will not make the effort.

I have found that the key to finding value is to track who you toss out in a race. Ask yourself this question: "When I toss out a horse (that ultimately goes off at) below 7/2, how much do those horses lose?"

If the answer to that question is, a $net of $1.30 or less, then you should be able to throw darts in those races and break even or better because there is enough pool money to recover the takeout.

In other words, if your low odds toss outs are losing 35% per wagered dollar, you should have no problem finding value in those races.

Funny, I believe the opposite. When my 7/2 horse goes up in odds is it because the barn or smart money know not to bet him? Wow! Odds as a red herring?

[Capper Al]

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).

The average race has 7 or 8 horses in a field. The public picks better than 1 out of 3 and the rookie handicapper should pick about 1 out of 4 or 5. All of which are less than the average size of a field which are an indisputable facts. Now with your righteous indignation, lets see your proof.

[PaceAdvantage]

The average race has 7 or 8 horses in a field. The public picks better than 1 out of 3 and the rookie handicapper should pick about 1 out of 4 or 5. All of which are less than the average size of a field which are an indisputable facts. Now with your righteous indignation, lets see your proof.Righteous indignation? I prefer to call it fact telling.

[raybo]

Building an odds line should only be understood as playing with numbers. What would be the predictive assertion be worth when our top choice is wrong at least two-thirds of the time? Odds line are more self serving as our own tribute to our systems and logic. In practice, they are useless. I too suffer from this ailment from loving my numbers. That's why we are handicappers.

Al, no disrespect meant, but if I wanted the opinions of others, regarding whether or not an oddsline is a worthy endeavor, I would have asked that in the first post. Since I didn't, then why do you even post this stuff? Start your own thread on that topic please. Most of us here are adults, who can think for ourselves.

[GameTheory]

Al, no disrespect meant, but if I wanted the opinions of others, regarding whether or not an oddsline is a worthy endeavor, I would have asked that in the first post. Since I didn't, then why do you even post this stuff? Start your own thread on that topic please. Most of us here are adults, who can think for ourselves.
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...

[Dave Schwartz]

Funny, I believe the opposite. When my 7/2 horse goes up in odds is it because the barn or smart money know not to bet him? Wow! Odds as a red herring?

I am thinking you did not understand what I said.

[Capper Al]

Al, no disrespect meant, but if I wanted the opinions of others, regarding whether or not an oddsline is a worthy endeavor, I would have asked that in the first post. Since I didn't, then why do you even post this stuff? Start your own thread on that topic please. Most of us here are adults, who can think for ourselves.

Fair enough.

[Capper Al]

Righteous indignation? I prefer to call it fact telling.

Then we are the facts?

[Capper Al]

I am thinking you did not understand what I said.

Maybe so. But what find more difficult is the reverse when my 7/2 goes off at 8/1. More times than not it's not a value play.

[Capper Al]

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...

You're actually right about some of that except I'm not expecting any thanks. I like to talk about what works.

[whodoyoulike]

Lots of things to read and mess with. Thanks guys! :ThmbUp:

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.

[Speed Figure]

Al, should get back to his rewrite!

[098poi]

Al, should get back to his rewrite!

You need to replace the ribbon in your typewriter.

[Speed Figure]

You need to replace the ribbon in your typewriter.Thanks! I have problems with this old commodore 64 sometimes.

[raybo]

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]

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]

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]

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]

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]

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]

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]

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]

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]

Are you suggesting an exponential predictive curve?

No, just looking for a 'separation factor'

[Cratos]

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]

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