Sister Sarah Games the Fix
by Roger Lyons
My last post demonstrates the internal dynamics of the dam line index (DLI), with its seven-generation search limit and its survey of the last fifteen years of SWs (in the original analysis). Narrowing the survey parameter to SWs of the last 10 years confirmed the expectation that the number of SWs tracing to early-era dams would decrease substantially while their average generational distance would increase somewhat–a formula for declining DLIs of early-era dams relative to the late-era dams. Accordingly, the early-era dams moved down in rank as the late-era dams moved up, very dramatically in many cases.
But, as Greg Michalson comments, Sister Sarah (Abbots Trace-Sarita, by Swynford), an important dam born in 1930, proved non-compliant. She actually moved up in rank from eighth to sixth. The fix against her is strong statistical medicine, and, in order to game it, she would need to pick up a one- or two-generation advantage somewhere along the line over other older mares. Baby League, for example, born five years later than Sister Sarah, dropped from 14th to 18th.
Nothing proves a powerful rule like a notable exception, and Sister Sarah is–well–no exception. The numbers provide presumptive ground for suggesting that this family might be more capable than most other families of producing quality in old age. I can’t think of any other way Sister Sarah could beat the statistical fix I put her in.
Even her first generation suggests this. Her second-most substantial contributor to SWs since 2000–behind Sybil’s Sister (1943)–was her daughter, The Veil, born when Sister Sarah was 23 and the latest-born branch of the line. She’s represented within six generations (puts Sister Sarah in the seventh) by 26 SWs in the 10-year group, down from 36 in the 15-year group. The late coming of The Veil assured Sister Sarah a generational advantage over other mares of her era when the first decade of the 21st century rolled around.
Now, Sister Sarah’s daughter Lady Sybil was born in 1940 when the former was only ten years old. Even so, Lady Sybil retained a large proportion of SWs in the 10-year survey. Of the 22 that had Sister Sarah within seven generations of the 15-year group, 15 also qualified from the 10-year group. That’s the branch from which Workforce (2007) descends–his sixth dam Sister Sarah’s daughter, Lady Sybil.
Lady Sybil had a 1952 daughter named Esquire Girl, by My Babu, which produced Workforce’s fourth dam, Sounion (1961), by Vimy. At age 20, Sounion produced the 1981 filly Media Luna, by Star Appeal and the third dam of Workforce. By virtue of Sounion’s production of Media Luna in old age, Workforce and eight other winners of stakes run after 1999 descend from Sister Sarah within the seven-generation limit.
No doubt, such occurrences can be found along the branches descending from any great dam, but the numbers suggest that, more than is usual, descendents of Sister Sarah have been able to produce good producers late in their breeding careers.
Posted by Roger Lyons on Friday, November 5, 2010 at 9:24 am.
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.