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03 Nov 10
15:31
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Date Joined:
11 Oct 07
I would be grateful for any advice, help, or contributions to a probability issue I am trying to solve.
I have an extensive database of racing data that is focused on breeding. This includes probabilities for Sire, Dam Sire, and Grand Sire. The probabilities are based upon “Normal Distribution” and come from a base sample size of over 900,000 race performances.
I have the probabilities for the Sire producing a horse rated over anything from 70 as a 2 year old, to over 125 as a 4 year old plus over a specified distance. The same probabilities exist for the Dam Sire and Grand Sire.
What I am trying to achieve is a, purely statistical, probability of the Sire and Dam Sire producing a specific horse, based under the categories I have. I also have equivalent Impact Values for each probability.
I know the base theory would be Sire probability X Dam Sire probability. However, I just know this is not the correct approach, mainly due to the result.
Obviously adding the probabilities is incorrect as you could get in excess of 1.
At first I quite liked the following equation P (Sire & Dam Sire) = P (Sire) + (1- P Sire) (P Dam Sire) so if sire probability was say .2132 and Dam Sire .1003. This would give .2921. Equally, reversing it to Dam Sire and Sire would give the same result. However, the result seems too high.
The Dam Sire has an IV of less than 1 (0.95) so my assumption is that the Dam Sire should reduce the overall probability, the Sire has an IV of 1.27.
I hope the above makes some sense, the length of time I have spent trying to reach an answer might mean it sounds like gibberish.
Any help greatly appreciated.
I have an extensive database of racing data that is focused on breeding. This includes probabilities for Sire, Dam Sire, and Grand Sire. The probabilities are based upon “Normal Distribution” and come from a base sample size of over 900,000 race performances.
I have the probabilities for the Sire producing a horse rated over anything from 70 as a 2 year old, to over 125 as a 4 year old plus over a specified distance. The same probabilities exist for the Dam Sire and Grand Sire.
What I am trying to achieve is a, purely statistical, probability of the Sire and Dam Sire producing a specific horse, based under the categories I have. I also have equivalent Impact Values for each probability.
I know the base theory would be Sire probability X Dam Sire probability. However, I just know this is not the correct approach, mainly due to the result.
Obviously adding the probabilities is incorrect as you could get in excess of 1.
At first I quite liked the following equation P (Sire & Dam Sire) = P (Sire) + (1- P Sire) (P Dam Sire) so if sire probability was say .2132 and Dam Sire .1003. This would give .2921. Equally, reversing it to Dam Sire and Sire would give the same result. However, the result seems too high.
The Dam Sire has an IV of less than 1 (0.95) so my assumption is that the Dam Sire should reduce the overall probability, the Sire has an IV of 1.27.
I hope the above makes some sense, the length of time I have spent trying to reach an answer might mean it sounds like gibberish.
Any help greatly appreciated.
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I would have thought that it would more reliable to work this probability out by number crunching the data you already have.
Create a scatter chart based on the parents rating for all the horses you have data on and you should soon see how much correaltion if any there is and what kind of probability can be assigned and with how much margin of error, for any given coupling of ratings.
Sometimes the apple falls far from the tree.
Create a scatter chart based on the parents rating for all the horses you have data on and you should soon see how much correaltion if any there is and what kind of probability can be assigned and with how much margin of error, for any given coupling of ratings.
Sometimes the apple falls far from the tree.
At first I quite liked the following equation P (Sire & Dam Sire)[?] = P (Sire) + (1- P Sire) (P Dam Sire)
+ P(damsire) +(1-p(damsire))(p(sire)) all divided by two
simplifies
to
p(s) + p(ds) - p(s)x p(ds)
+ P(damsire) +(1-p(damsire))(p(sire)) all divided by two
simplifies
to
p(s) + p(ds) - p(s)x p(ds)
Gart and Escapee thanks for your replies.
Gart, I still just have the feeling the formula(s) we are quoting are not correct for the question, but I cannot explain why.
Partly, I guess, because I do not think the probability answer in this case should be as high as .2921. I was expecting around the .2 mark.
Escapee, either I have misinterpreted your reply, or I worded my question poorly. Anyway, I can ascertain the “probability” of a damsire/sire combination if it has past performance (I sound like somebody selling an investment), as I have the Average, Standard Deviation, and Low rating for the progeny. In this case, it gives an actual, based on past performance, probability of .1858.
However, I want to establish the actual statistical probability based upon their independent probabilities for three reasons.
Firstly, as in this case the sample size is to small (18 here), secondly I want to see if the actual results exceed, or fall below expectations, and lastly there just might not be any progeny from the combination in question and want to calculate the probability of such a cross succeeding.
Anyway, I will keep trying. Thanks again.
Gart, I still just have the feeling the formula(s) we are quoting are not correct for the question, but I cannot explain why.
Partly, I guess, because I do not think the probability answer in this case should be as high as .2921. I was expecting around the .2 mark.Escapee, either I have misinterpreted your reply, or I worded my question poorly. Anyway, I can ascertain the “probability” of a damsire/sire combination if it has past performance (I sound like somebody selling an investment), as I have the Average, Standard Deviation, and Low rating for the progeny. In this case, it gives an actual, based on past performance, probability of .1858.
However, I want to establish the actual statistical probability based upon their independent probabilities for three reasons.
Firstly, as in this case the sample size is to small (18 here), secondly I want to see if the actual results exceed, or fall below expectations, and lastly there just might not be any progeny from the combination in question and want to calculate the probability of such a cross succeeding.
Anyway, I will keep trying. Thanks again.
I don't think there is a valid formula for dealing with the probabilities you have derived. I would look at the average and standard deviation for dam and sire and combine them in some weighted manner and then apply the normal distribution function to the new numbers.
For example if the mean and standard deviations for dam and sire were 76 15 and 82 17 respectively and the weighting was 50% you could derive your probabilities from the normal distribution with mean 79 and standard deviation 16. Or is this what you are doing already?
For example if the mean and standard deviations for dam and sire were 76 15 and 82 17 respectively and the weighting was 50% you could derive your probabilities from the normal distribution with mean 79 and standard deviation 16. Or is this what you are doing already?
equimine, have you thought about using logistic regression ?
Bayes, thanks for that idea. I will try some test numbers.
I can calculate from my database actual means and standard deviations for Sire and Dam Sire, where they are the father and grandfather of actual progeny. For instance Danehill (S)/ Sadler’s Wells (DS) I have actual data for their progeny, and a decent sample size of 396. As opposed to Sadler’s Wells general dam sire sample size of 11,126!
Anyway, thanks will post how I get on.
Bettingquant,
I hadn’t thought of it, and to be quite honest “regression” techniques are not something I am that hot on (along with many other things
), but will look into it, cheers.
I can calculate from my database actual means and standard deviations for Sire and Dam Sire, where they are the father and grandfather of actual progeny. For instance Danehill (S)/ Sadler’s Wells (DS) I have actual data for their progeny, and a decent sample size of 396. As opposed to Sadler’s Wells general dam sire sample size of 11,126!
Anyway, thanks will post how I get on.
Bettingquant,
I hadn’t thought of it, and to be quite honest “regression” techniques are not something I am that hot on (along with many other things
), but will look into it, cheers.
A while ago I found a package called 'Tiberius' that might help you. It's quite easy to attach your data to it, select the appropriate variables as inputs (eg. Sire, Dam Sire, Grand Sire) select an output (eg. win/lose (represented by 1 or 0 in your data)) then you can use logistic regression and/or neural networks (amongst others) to estimate the probability with any given input values.
There's a free (restricted) version of tiberius, and a 30 day trial of the full package. I havent used this package for some considerable time though, as I didn't purchase the licence once my trial ran out.
There's a free (restricted) version of tiberius, and a 30 day trial of the full package. I havent used this package for some considerable time though, as I didn't purchase the licence once my trial ran out.
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