In our last post we looked at a recent scientific study that detailed out the importance of the maternal line, in particular the race performance of the dam of a yearling in terms of its influence on the outcome of the resultant foal. Unsurprisingly, the study found that a good stallion could generally not negate the heredity effect of a poor race mare but that a good race mare could negate the hereditary effect of a poor sire.

This finding is pretty much the same finding that pedigree statistician David Dink who has written extensively about it here, here and here, and a recent issue of Marketwatch where editor Ian Tapp tackled a similar concept looking at the production of race mares based on their racing class, in particular mares that had won their first start, and came to a similar conclusion - that racing class is at least as important as pedigree in broodmare selection, if not more so.

From a genetic perspective this isn't surprising. The 'bar' for being a stallion is now so high, the variance between stallions is lower, that is, the difference between stallions is minimal so their effect on creating difference between their offspring is reduced. Where the difference comes from is mainly due to the poor quality of selection that is applied to mares. That is, because we pretty much allow any mare, regardless of her racing merit, to breed, the variability of performance from the dam of the foal is much greater and subsequently has a greater impact on the outcome. As the studies above have shown, the quality of the dam as a race mare has a significant impact on the outcome, and as the industry as a whole selects harder and harder on stallions (with larger stallion books, etc), the variance in foals performance increasingly comes down to the effect of the dam.

This of course leads to the obvious question, how 'good' does a mare have to be for her race performance to have an effect on the outcome of her resultant foals?

Before we tackled that question, we needed to overcome one of the greater problems with this industry - a lack of a single unifying rating that sufficiently grades the race performance of each race mare in order to satisfactorily categorize the performance itself. I don't have a lot of time for the graded/pattern stakes system. It is poorly distributed (there are way too many stakes races in Ireland as an example), slow to adapt (it takes years for committees to drop races in class despite evidence that they are bad races) and probably too bountiful in relation to the number of horses and races being run (in particular in North America where the foal crop decline and small fields hasn't been reflected in a cutting of the number of stakes races so there is a dilution of quality going on).

Speed ratings such as Beyer or Equibase are limited to North America and I wanted something that could be applied in Europe and Australia also. Timeform came close, but not every mare is rated and it isn't easy to get a hold of without paying for it. Ideally the industry would have some type of Bayesian performance rating that was relative to all horses performance across all racing jurisdictions and updated frequently, but in the end I had to settle for the Class Performance Index (CPI), a rating produced by the Jockey Club Information Systems.

The CPI is a prizemoney index ranking which is calculated for each year and based on:

Horses of the same sex (i.e. only males compared to males and females compared to females)

Horses of the same age

Horses racing the same year(s)

Horses racing in the same countries

All of the criteria must match for the comparison to take place. To calculate a horse's CPI, the horse's average earnings per start is compared to the average of the average earnings per start of all like horses (i.e. if a horse's CPI is 5, then his average earnings per start is five times greater than the average of all like horses).

There are a couple of drawbacks to the CPI. Firstly, as it is calculated each year of racing, it is possible for a horse to have 3 or 4 ratings for each year over the career of a horse. The lifetime figure, the one that TJCIS publishes, is an average of this. So, if a horse is a superior two year old, but then has an ordinary three year old and four year old career, its overall rating gets dragged down to the average of the three ratings. Not ideal and there would be a better way to represent this than an average.

Secondly, while the CPI cleverly normalizes for a lot of influences, it is based on prize money, which itself is not normally distributed and can be skewed. That is, horses that finish 7th in a G1 race get no prize money but the winner of a crappy race on the same day does. If the total prize money of a race was redistributed from first to last in an equitable way it would be a significantly more accurate measure of performance across a population. That said, the CPI has the advantage of being calculated across all racing jurisdictions by the Jockey Club Information Systems so it overcomes the issue of a rating being internationally calculated which is more important and it also normalizes for a lot of the issues that an AEI or an APEX rating has with the distribution of prize money.

We got a hold of the CPI ratings for over 40,000 mares and the CPI ratings of their foals. In total we had just a little over 250,000 ratings (so each mare averaged about 8 foals) to examine which is more than enough to sufficiently describe a population. The CPI isn't normally distributed, that is there are a lot of ratings close to 0.00 and less the higher the CPI gets, this makes analysis of the CPI a little difficult.

So, the first thing that I did was to perform a Box-Cox Transformation on the CPI ratings, in order to get them more normally distributed and allow a more robust analysis of the data.

With the CPI ratings now more normally distributed, we could perform what is known as a Z-score or Standard Score on the data. What the Z-Score for each CPI would represent is how many standard deviations above or below the average of all CPI scores an individual CPI was.

The calculation of the Z-Score was done primarily to provide us with some 'bins' to compare groups of mares. I could have done this by manually selecting the number of bins that I wanted and calculating the frequency that each CPI appeared in each bin, but I liked the elegance of the standard distribution providing the bins themselves. At any rate, when I looked at the frequency that each Z-Score had it roughly fitted the standard distribution curve. If the data was distributed normally you would see 34.1% of all observations fall between 0.00 and 1.00 and 34.1% fall between 0.00 and -1.00. In our data we had 37.5% falling between 0.00 and 1.00 and 33.31% between 0.00 and -1.00 so it wasn't quite a perfect distribution, but it was very close.

Given that I now had the CPI scores roughly distributed in a normal distribution I was able then to establish the relevant CPI ratings for each of the bins as per above.

Probably the most interesting point taken from the chart above is that the average horse has a CPI of 0.68068. You would think that if the calculation of the CPI is based on a horse's average earnings per start is compared to the average of the average earnings per start of all like horses that the average CPI of all horses would be 1.00, but it is not, its 0.68068. I would say that this difference is due to the way the CPI is created as an average of their average CPI which I discussed above. Either way, we now have the cutoffs for each of the 'bins'.

What we also know now is that 85% of all the CPI observations fall from a CPI score of 0.00 (-6.00 SD) and 2.62250 (+1.00 SD). This means that only 15% of all CPI's are greater than 2.62250. We also know that only 2.38% of all CPI's fall above 10.3703. As I will later discuss, a horse with a CPI of 2.62 or greater is more than a useful horse so for my purposes, the CPI cutoff of 2.62250 serves as a marker for an 'elite' performer. Before you think I've gone crazy assigning 15% of the population as elite, just remember that the CPI is only generated for horses that race and given that only 65% of all horses get to the track, we are looking at about 10% of the entire population of horses.

The next step was to take a look at the population of mares, arrange their own performance into each of the bins and look at the average performance of their offspring in each bin but then I ran into the problem of stallion quality. Mares with higher CPI's (better race mares) are invariably bred to stallions that are 'better' and they also get better care of their offspring. This would put mares that had low CPI's at a disadvantage and make the race career effect a self fulfilling prophecy. To negate this somewhat I took a separate population of 1,000 mares that had been bred to elite sires at one point in their career (so they had at least been given the opportunity of a good sire) and mapped their own race performance and then the performance of their offspring into each of the bins that I described above.

Once I had this data it was then a matter of working out the Relative Risk of the offspring each of the groups of Dams as they appeared in groups 1-7 (non elite) and groups 8-12 (elite).

For each of the dams gathered by their Z-Score 'bin' we now have a Relative Risk of their production of elite runners. So, as an example, for Dam Group 1, which is mares that had a CPI between 0.00001 and 0.00081 as runners themselves, relative to other groups they represent a -25% disadvantage in terms of production over other groups. If you work your way through each of the groups you will see that it is not until we get to Group 8, that we get to a position where their own racing class (or lack of) doesn't influence the outcome negatively.

This finding is one of the central tenets to our sales selection process. In any given country, in any given year, there are literally thousands of yearlings to choose from, if you know that you have an advantage in confining your selection of yearlings to those whose dam has a CPI greater than 2.00, why would you look elsewhere?