Dam Lines Unplugged
by Roger Lyons
In my last post about comparing the contemporary influence of competing dam lines, I explained that the measure of their influence (Dam Line Index, or DLI) is a function of 1) the number of SWs descending in direct female descent of the given dam (S) and 2) the average generational distance of the dam from those SWs (G). Or S / G = DLI. That function yields a measure that roughly reflects the relative influence of different dams of different eras.
I also mentioned that I go back only seven generations in search of any given dam–say, La Troienne–even though some contemporary SWs trace to La Troienne further back than that. Setting a maximum generational distance is important because it limits the extent to which the DLI is biased in favor of early-era dams. Going back eight or nine generations would increase the number of SWs descending from La Troienne more than it would increase the average generational distance.
Now, what I didn’t mention in that post is that there’s another factor related to that same bias: the historical limit that is set on the population of SWs surveyed. The tables published in my last post are based on SWs of stakes run from 1995 to the present. But, what if we lopped off the earliest five years and just used SWs from 2000 to the present?
Well, fewer of the more recent SWs would be traceable to older dams within the maximum seven-generational range. That means using only the more recent SWs tends to tilt the bias in favor of the later-era dams, just the opposite of what happens if you increase the generational distance of the survey.
Okay, I realize this is kind of wonkish, but, if you compare the rank order based on stakes run since 1995, here, with the alternate rank order based on stakes run only since 2000, here, you’ll get a sense of what is at stake in how these statistics are done.
The range of the alternate DLIs is compressed, such that La Troienne’s lead is diminished. Some of the later-era dams have displaced some of the earlier-era dams in the top spots. Helene de Troie, the dam of La Troienne and ranked 6th on the original list, is now ranked 23rd. Grey Flight, nowhere to be found on the original list, is now ranked 34th. Best in Show, the latest-born of all the top dam lines, at an average of only four generations removed, has edged up from 10th to 8th.
Even more indicative is that Urban Sea, to which I referred in my last post as ranking 362nd on the original list (not in the top-40 table), ranks 154th on the alternate list.
Basically, these two issues–how many generations are surveyed and how recent the pool of SWs–bear on the question of currency, and, to the extent that currency is valued above other considerations in the assessment of dam lines, less turns out to be more.
Posted by Roger Lyons on Thursday, October 28, 2010 at 1:36 pm.
Measuring Dam Lines
by Roger Lyons
Every few years, around November sale time, I survey female lines to see how their rankings have shifted over time. The terms “survey” and “ranking” require definition. This time round, I pulled out the winners of stakes, as compiled by WTC, that were run from 1995 to the present and tabulated every occurrence of every dam in the female lines of these SWs going back seven generations, along with the generational distance of each occurrence.
Then I crunched the numbers as usual to find out for each dam 1) how many SWs were descended from her and 2) the average generational distance of her occurrence in the female lines of those SWs. That’s all you need in order to get a rough idea of relative contemporary influence because, if you divide the number of SWs by the average generational distance at which the dam occurred in the female lines, then you end up with an index that you can use to rank the dams in a more or less valid way–based on the number of SWs per average number of generations removed. Let’s call it the Dam Line Index (DLI).
For example, La Troienne, which ranks highest among the 70,659 individual dams represented, occurs in the female line (within seven generations) of 298 SWs (since 1995) at an average of 6.42 generational removes. That means her DLI is 298 / 6.42 = 46.42, which is the number of SWs descended from her per generation.
The average generational distance is useful because it controls to some extent for the differential opportunity of mares of different eras. Best in Show, for example, which ranks 10th, occurred in the female lines of 78 SWs and at an average generational distance of only 3.79 generations. So, the index of her influence is 20.58 SWs per generation. That’s a lot less than La Troienne, but not that much less than Escutcheon, which has the second-highest rank, at 28.21 and an average generational distance of 6.38.
Now, there’s always going to be someone who says (without thinking) that seven generations is not enough since La Troienne occurs beyond the seventh generation of some contemporary SWs. That is an untenable position, though, because, if you extend that rationale across the population of dams (not just La Troienne), there can be no generational limit that will satisfy them all.
Besides, the method already has an inherent bias in favor of the older dams. Consider that Urban Sea, dam of sires Galileo and Sea the Stars, plus other high-class sons and daughters, ranks last (362nd) among dams with a DLI of at least 7.0. She is the dam of seven SWs, but has not had the advantage of subsequent generations through which to multiply her influence. She’s almost certainly bound to be better as a tail-female influence than she ranks now, and increasing the maximum generational distance of the survey would only serve to exaggerate the bias against her.
Click here to view the alphabetical list of top-40 dam lines and here to view the same list in rank order.
More about this topic in subsequent posts.
Posted by Roger Lyons on Wednesday, October 20, 2010 at 9:20 am.
Super Saver: a Minority Report
by Roger Lyons
In a recent post on the breeding behind Super Saver, Sid Fernando sets in relief three differing approaches to identifying pedigree factors that account for that horse’s ability to win the Kentucky Derby, including my own. Nobody does the historical color as well as Frank Mitchell, but, clearly, Alan Porter’s analysis, as endorsed by Andrew Caulfield in his TDN column of May 4, is at odds with my account in regard to the factors that it emphasizes.
I realize that Andrew’s analysis has the advantage of being the standard account. Its topical structure defines the prevailing pedigree analysis, including its center-stage placement of linebreeding as the main actor. Therefore, I offer my rebuttal as a minority report.
Linebreeding certainly does have a functional relation to performance, but I emphatically disagree with the presumption that its effects must be favorable, much less decisively so, just because it happens to be found in the ancestry of a Kentucky Derby winner. To take Super Saver’s performance as evidence of the benefits of linebreeding simply begs the question of its effects and, more broadly, of its functional relation to performance. Unless the standard account can establish a statistical relation between Super Saver’s linebreeding and his performance, then its analysis might as well be founded on a non sequitur, and I believe it is.
As Sid points out, Super Saver’s family began with “a simple nick between a La Troienne daughter (Baby League) and War Admiral.” The family continued to evolve on that same basis, each daughter having had her best production by the best stallion that afforded the best simple nick. The accumulating linebreeding, involving multiple strains of La Troienne, therefore, was a systematic consequence of that series of simple nicks. More broadly, linebreeding is a systematic consequence of the pedigree model of breeding. It’s not a formula for breeding great racehorses. Rather, it’s an inevitable consequence of the process.
So, is linebreeding a cause of superior performance or just an effect of pedigree breeding? The latter is evident from the genealogical record, but inferring a causal relation to performance requires populational evidence that not even the cheerleaders for linebreeding are able to provide.
Well, then, what can be inferred about it? We know what the effect of linebreeding is in a broad sense. Its purpose and effect is to establish a generational continuity between a new individual and its ancestry. The more linebreeding a pedigree has, the more likely is the individual representing that pedigree to express the traits conferred by ancestors to which it is linebred. But, if linebreeding is so effective at reproducing the traits that constitute a great racehorse, why is it that so many horses with linebreeding similar to that of Super Saver in distant generations are just no good?
I firmly believe that the prevailing pedigree analysis–the standard account of pedigree–misunderstands the way in which linebreeding is functionally related to performance. Let me explain by analogy.
A good melody consists of two fundamental elements that oppose one another at every musical level. In order to be recognizable as such, a melody must have continuity. It must have a certain repetitive rhythm. If sung, the words must rhyme. A refrain is very much a part of what we expect of a melody along this direction of its movement. However, the continuity of good melodies is subverted at every point and at every compositional level by the element of variation moving in the opposite direction. Each measure of a melody must be continuous with the last, but different from it. The lyrics rhyme by repeating the same sound, but enunciated in different words. The refrain interrupts and contrasts with the sequence of verses. A good melody arises from the tension between continuity and variation, the latter always playing a subversive role.
Breeding a good racehorse is just like that. Linebreeding mediates generational continuity. Its function is to specialize the new individual around qualities that are conferred by the ancestors to which it is linebred. At its best, it yields a physically coherent individual. However, the new individual must also be capable of a well-rounded performance. It must have the variety of typological possibility required by the prevailing conditions of racing. That’s the job of generational variation, which operates in opposition to linebreeding.
In the same way that musical variation subverts continuity in the making of a good melody, generational variation subverts the continuity established by linebreeding. This fundamental opposition between linebreeding and generational variation is what the advocates of linebreeding don’t get.
According to the numbers I have for Maria’s Mon as a sire (and other stallions as well), A.P. Indy, Supercharger’s sire, has just such a subversive relation to his own linebreeding to La Troienne. After all, Maria’s Mon hasn’t otherwise done that well with Buckpasser (10 superior runners from 156 mares through his 2007 crop, counting the three through A.P. Indy). If you take out the seven mares in descent of A.P. Indy, then Buckpasser’s strike rate falls to 7/149.
Nor has Maria’s Mon done all that well with mares in descent of Seattle Slew, another important source of La Troienne. If you take A.P. Indy out of Maria’s Mon’s strike rate of 5/46 with Seattle Slew, it drops to 2/39. In fact, all but one of those five superior runners were out of mares with Seattle Slew in tail-male descent. But, if you exclude A.P. Indy mares, the strike rate with Seattle Slew in tail-male descent is only 1/19. So, read very carefully how the standard account gets its numbers relating to the Maria’s Mon-Seattle Slew “nick,” including that restricted stakes winner thrown in for good measure, because there’s much at stake in it for the linebreeding hypothesis.
My numbers, by contrast, don’t suggest broadly favorable effects of linebreeing to La Troienne through the ancestors of A.P. Indy. What they suggest is that A.P. Indy’s influence very favorably disrupts effects of linebreeding that are otherwise not at all favorable to foals by Maria’s Mon. A.P. Indy provides a beneficial variation that combines with Maria’s Mon to yield a simple nick.
It’s quite possible, too, that Numbered Account, a key source of La Troienne also tends to subvert the La Troienne continuity. Maria’s Mon has a strike rate of 1/3 with daughters of Numbered Account through his 2007 crop, but her dam, Intriguing, otherwise has a strike rate of only 2/23. Maria’s Mon happens to work with Numbered Account, as far as can be determined, but not so much with her sire, Buckpasser, or with her dam.
As a matter of fact, the ancestors of Supercharger that have had the most favorable impact for Maria’s Mon through daughters have nothing whatever to do with La Troienne or with A.P. Indy. Maria’s Mon has a strike rate of 7/50 with daughters of Mr. Prospector, sire of Super Saver’s second dam. With daughters of Northern Dancer, sire of Super Saver’s third dam, Maria’s Mon has a strike rate of 5/34. These numbers, far from confirming that Super Saver’s performance is an effect of linebreeding, clearly suggest that it’s more likely an effect of generational variation. The influence of these important sires interdicts a linebreeding continuity that otherwise really hasn’t worked for Maria’s Mon.
In one pedigree after another, ranging across many different sires, the numbers say linebreeding is not the decisive factor. In fact, the numbers point to the ways in which atypical or variant strains subvert the effects of linebreeding. Such evidence trends toward the inference that Super Saver’s ability to win the Kentucky Derby is decisively affected, not by his linebreeding, but by the various directions in which his ancestry has deviated from its linebreeding to constitute a well-rounded individual–a horse with the speed, stamina, stoutness, and physical courage not only to withstand the rigors of training for that race, but also to win it.
We live in an era during which linebreeding has become ubiquitous in the population. All of the horses are linebred, and the functional relation of linebreeding to racing performance has already been taken too far. It’s too late to turn to the standard account for celebrations of linebreeding. In such an era, the successful breeder is the one who can identify useful variations with which to restore the residual aptitudes, the one who understands that linebreeding is the problem, not the solution.
Posted by Roger Lyons on Friday, May 7, 2010 at 12:21 pm.
All the Horses are Linebred
by Roger Lyons
Now I’ve heard everything. I didn’t get this at some obscure website specializing in pedigree correctness (PC for short, please) that hardly anybody reads. No, it came from none other than a Blood-Horse pedigree column, a publication that–well, obviously, I still read it.
It goes like this. The reason why La Troienne is such an important influence is that her sire, Teddy, traces four generations back to Ormonde, and her second dam, Lady of Pedigree, is by a sire whose second dam is Ornament, a full sister to Ormonde. In other words, she’s linebred through full siblings. That’s around the twelfth generation of contemporary horses, and, when mares with La Troienne are crossed with stallions whose pedigrees contain these two ancestors, we’re told, the foals will light up the tote boards.
Yes, good horses all have linebreeding within 12 generations, but so do all of the bad horses. The reason they’re all linebred is that they are all products of pedigree. You carve out a population of horses, define a range of performance that favors those horses, close the book around their ancestries, and call it pedigree. Then, 200 years later all of the descendents of those horses are linebred, especially as defined in broad strokes by its advocates.
Besides its role in signifying commercial value, pedigree is a set of rules enforced by the Jockey Club, and ubiquitous linebreeding is an historical consequence of the enforcement of those rules. The advocates of linebreeding conclude that it facilitates the breeding of good horses, but that is generally not what rules are about. Rather, rules pose a challenge to the playing of the game.
Suppose there were no rule in the game of basketball that says you have to dribble the ball, that you can’t just tuck it under your arm and saunter down court. Basketball would be much more boring and tedious than it is. The rules are meant to challenge the players, to make the game harder to play and more interesting to watch.
That’s exactly what linebreeding is in today’s thoroughbred racing and breeding environment. Racing and breeding without linebreeding would be like golf without the rough, sand traps, and water hazards. It would be like tennis without a net, like basketball without dribbling. Linebreeding and those pedigree patterns that are trotted out ad nauseum are the rough, sand traps, and water hazards of thoroughbred breeding.
If those distant ancestors of La Troienne were the key to Distorted Humor’s response to certain of her strains, then he would have a similar response to any expression of La Troienne’s influence. As I showed in a previous post, however, that is not the case. It’s not about some distant blood affinity. It’s about the variety of ways in which different descendents of La Troienne express her influence in regard to specific traits. By way of generational variation, some of those descendents contribute La Troienne’s influence in ways that are favorable to foals by Distorted Humor. Others contribute it in ways that are unfavorable to his foals, and those same ancestors interact with other stallions differently.
Any specific method of linebreeding will have harmful effects in a lot of pedigree contexts. Those who look at the twelfth generation and assume that everything they find there has some absolute value never notice the problems that have sprung up along the way, such as the negative effect mares in descent of Better Self (by Bimelech, a son of La Troienne) have on Distorted Humor’s foals, which I pointed out previously. Above all, no method of linebreeding has value in and of itself. Whether a method is beneficial or harmful depends on its pedigree context.
Jack Werk’s clients valued his advice so highly because he understood what so many pedigree consultants don’t get–to the extent that rules are in force, the onus is on making moves in the game. The hard part is to hit the jump shot off the dribble, to come up with a Lookin at Lucky amid the hazards of linebreeding.
Posted by Roger Lyons on Tuesday, April 27, 2010 at 11:56 am.