Stallions, the Sexy Son and Selection

For another project that I am working on I just looked at some data on 82,073 yearlings, in particular the Generational Interval, or more commonly the average difference of ages between sire and dam and their offspring

Generational Interval ((HorseYOB-SireYOB)+(HorseYOB-DamYOB))/2

The Average Generational Interval of all 82,073 yearlings was 10.2 years. That is, on average the difference between the ages of the parents at conception worked out at an average of just over 10 years. Interestingly there was not much difference between the average sire-foal age difference and average dam-foal age difference. Breeders tend to send old mares young sires, vice versa.

The standard deviation for the dataset is 3 years which means that around 68% of matings have a generational interval between falling between 7 and 13 years ( 1 Standard deviation around the average of 10) and 95% will fall within 4 and 16 years (2 standard deviations). So it seems that any mare being bred to the ageing Galileo, who hits 22 this year, that is herself older than 11 will result in a foal that is an outlier found in less than 5% of the population.

What this also means is that foals that are getting ready to be born in 2020 having been mated in 2019, would have their 'genetic material' most likely coming from stallions and mares themselves born between 2015 (4 years) and 2003 (16 years). Again, there will be some exceptions to the rule like say Galileo, but generally speaking they will fall in that range as most stallions and mares are selected out of the breeding population unless they are top quality by age 16.

If we break these up into standard deviation cohorts, you'd have groups every 3 years that could be used to judge performance relative to one another. So stallions born between 2012-2014 wont have much in the way of reliable outcomes, but those born between 2008-2011 will have a graded stakes winner count that we can use to compare each stallions performance at any point in time.

This count would be, all other things being equal, relative to the stallions that they were competing with for mares at the same time. We readily account for a stallion being a first, second and even third season sire, but past that they are 'out in the wild' so to speak. We could rather easily look at the number of graded/group stakes winners a stallion has, and by normalizing the values found in each cohort (say a max-min normalization as there will be a lot of stallions with zero value for number of graded/group stakes winners) it would place the performance of the stallion relative to its peers.

It wouldn't get around the issue of 'opportunity' (i have previously discussed an ExpectedSW value for that for stallions), but it would be an easy, and more fair way to judge a stallion that many of the other metrics available. Jim Atkinson over at James Ortega Bloodstock has a very similar idea to the one that I mentioned above, but does manage to look at opportunity. He groups them by crop and looks at the average runner rating of the offspring of stallions, relative to the average rating of the mares that they have been bred to that created the offpsring. It leaves you something like below....

While I have been looking at this stallion data, and trying to get it into some type of usable format (like what Jim has done above), something struck me in terms of looking at all the stallions, the number of graded/group stakes winners that they had, and how it seemed to fit with mathematical theory, in particular R.A Fischer's "sexy son" hypothesis:

The “sexy son” effect–described by R. A. Fisher in 1915–is the idea that females will be favored to preferentially mate with males who exhibit conspicuous ornamentation if other females already happen to find this ornamentation attractive, simply because by mating with ornamented males they are more likely to have ornamented sons who will be more attractive to potential mating partners.

If we translate that over to commercial thoroughbred breeding, where matings are completed in a non-random way (that is, we as humans decide who to breed mares to), what breeders are ultimately valuing in a stallion is not just that he is a good sire, but that he has good sire-sons. How quickly a stallion can propel itself from being a good stallion, into an elite stallion relies heavily on three factors. These are:

1. The number of days from the day their first crop turns two, to their first Group/Graded Stakes winner

2. The number of days from the day their first crop turns two, to their first 5 Group/Graded Stakes winners

3. The number of days from the day their first crop turns two, to the day they have two Gr1. winning colts.

On the first point, these 'elite' stallions come out of the gates firing quickly. It is generally known that for all stallions, not just any stallion they have the bulk of their lifetime stakes winners in the first 5 to 6 crops, but what separates out the 'elite' sires is that they generally have a group/graded stakes winner early in their career. As an example, Elusive Quality had his first Graded stakes winner just 179 days into the two year old year of his first crop and while there are some elite sires that were a little slower out of the blocks than that, they are rare (Stormy Atlantic being one notable exception to the rule). Generally speaking, high class precocity is something that we value as an industry.

On the second point, the speed at which they sire their first 5 Graded/Group stakes winners is correlated to success, particularly their initial commercial success. The likes of Elusive Quality and Distorted Humor had their service fees rocket up quickly as they sustained the pressure while the likes of Malibu Moon and Indian Charlie took a lot longer to reach that point and as a result the trajectory of their service fees, and careers differed greatly.

Thirdly, those stallions who have taken a lot of time to get to two Group/Grade One winning sons, like Northern Afleet (3463 days), Grand Slam (3924) and Malibu Moon (5022) (not to mention stallions like Smoke Glacken who never had two Gr1 winning colts) have created a disadvantage for the survival of their genes through male line descent, with none of these stallions having any more than three sons at stud to sire stakes winners themselves (note: both Malibu Moon and Distorted Humor sired Gr.1 winning geldings but took some time to get colts to retire to stud).

Conversely, the likes of Stravinsky (458 days), Awesome Again (634), Elusive Quality (851) and Pulpit (1195) have been rewarded for the speed at which they have sired two Group/Grade one winning colts by having multiple sons retire to stud and give them the opportunity to maintain their genetics to the next generation. Some of these stallions get the coveted "sire of sires" moniker, some don't, but it is clear that the speed at which a farm managing a stallion can, once that stallion has proven himself, get his sons to prove themselves, ultimately helps the stallion.

The above is the manifestation of a derivative of the "Sexy Son" Hypothesis proposed by R.A Fischer. Similar to that theory, as we send mares to More Than Ready or Medaglia D'oro, and value these stallions when they appear as the sire of an unproven sire, not just because of their ability to sire a superior runner, but also because their sons can sire a superior runner. The ability for a stallion to sire a 'sexy son' drives a lot of the selection of stallions because they in turn produce elite runners and elite sire sons.

So how does this work in practice? We have already established that in the population of stallions that to be considered a statistically significant 'elite' sire you need to appear in the top 5% of all stallions (that top 5% is two standard deviations above the average) and from my data this roughly equates to 60 Lifetime stakes winners. Quite interestingly, in terms of what stallion material we take to the next generation, we rarely select outside of these elite stallions for our genetic material going forward. Once the stallion has proven himself 'elite' we immediately target his sons for genetic material, and rarely look outside that (horses like say Tiznow are rare events).

It is striking however that the 'sire of sires' concept seems to be an illusory correlation with being determined an "elite stallion", one very much reliant on an early retiring colt of a stallion making his own mark. The first two Grade One winning sons of Pulpit were Sky Mesa and Tapit (the third was Stroll) and both retired relatively early to stud and made an immediate impact, smoothing over the subsequent abject failures of the likes of Purge, Corinthian, Pyro, Ice Box and Power Broker, all Grade One winners that stunk the place up (not to mention the other sons as well). Just as the success of an elite sire requires him to sire a Graded/Group stakes winner early with his first 2YO runners, and getting to 5 Group/Graded stakes winners relatively quickly will sustain his career, having one of the first sons of the 'elite' stallion retire to stud himself come out early and look likely to reach the 60SW 'elite' level glosses over a lot of sins, and having two, like Sky Mesa and Tapit, places the industry moniker 'sire of sires' on his resume, even if his subsequent sons to retire to stud would have served the breed better if they had been gelded.

So what are the takeaways here?:

1. Using 'cohorts', stakes winners and a little bit of maths is an interesting and relatively easy way to rate a stallion. If you use Z-Scores, the ratings are relative to the populations so you can then compare one cohort to another and it is probably a decent way of measuring genetic merit relative to other stallions. So what you end up with is relative performances at stud for Distorted Humor (2.68 - more than twice the average), Scatmandu (0.02 - right on average) and Semoran (-1.20 below average) as examples.

2. Judging by what you see in sales catalogues, we heavily select for stallions that are two deviations above the average (elite stallions), moderately select for stallions that are one standard deviation above the average, and select against everything else. The bad stallions seem to disappear off the catalog page and out of the commerical population quickly as we select against them - we don't stand their sons and their daughters, unless they are good runners or very well related, aren't kept quickly in the commerical population. Conversely, the elite stallions in some cases we over value, especially sons of these elite stallions if they have already had a son retire to stud with success.

3. The concept of a 'sire of sires' is probably an illusory correlation. The industry seems to self select towards a narrow band of stallions in each cohort being considered useful for future generations, so the pool of stallions that have the potential to be 'sires of sires' is narrow, but there doesn't seem to be any correlation between being an 'elite' sire and being a 'sire of sires', Its most likely that only Pulpit and Elusive Quality have more than one son that themselves could be considered elite stallions. Stallion owners would be thinking twice about standing a son of Distorted Humor even though he is by far the best stallion in that cohort and stallion success looks an independent event.

Still some more work to do to bring some stallion ratings together that don't rely on prizemoney (as that is not-normally distributed anyway) and can be used worldwide, and while I am not a fan of the pattern/stakes system as a way of measuring the talent of individual horses, it is an easy framework to use in terms of valuing stallions and it seems that the industry at large uses it for selecting genetic material in each generation.