Secretariat and ManO'War Revisited

Introduction

The might of Secretariat and ManO'War on display was nothing short of breathtaking, in particular with respect to the ages at which they ran.  Both, generally accepted as the century's best, ran as 2 and 3 year olds, and nothing more. The remaining greats ran beyond 3, and with the exception of Citation, ran their best at 4 or 5 when abilities peak. Not to be forgetful of Citation, his 3-yr. old season was nothing short of spectacular in that he ran 20 times in a space of 11 months at distances ranging from 6 furlongs to two miles. Not only did he complete the Triple Crown, but did so during the stretch of a record 15 straight wins that included multiple victories against older horses. Compare that to Secretariat's 12 and ManO'War's 11 at distances from one to one and five eighths in spaces of about 6 to 7 months. So why then were Secretariat and ManO'War selected as the century's best, with ManO'War as the singular best? Because as threes they demonstrated a precocity so far beyond the pale that one can only speculate on what they might have acheived as 4s or beyond.  ManO'War for instance in one of his races as a three ran one and one sixteenth miles carrying 138 lbs. while his nearest competitor at the finish in a field of 4 carried 118.  Not only did the colt win by a comfortable 1.5 lengths, but did so while setting a new track record. That was a demonstration not only of speed, but of raw strength. The horse was impervious to weight. In the handicapping world of the 1970's, only 5 year olds might have carried 138 pounds for that distance. Continuing, from the Belmont to his final race against three yr. olds, ManO'War's mean handicap weight ballooned to over 129 pounds and despite that the colt managed to set track records in 6 of those eight races, two of which were world marks. He was a star beyond his time. Secretariat, on the other hand, carrying 126 in the Kentucky Derby ran one of the great moves in racing history coming from last to first in a field of 13, running each successive quarter faster, and doing so coming anywhere from 3 to 6 wide around the turns. He not only set the track and Derby marks, records which still stand today,  but did so concluding the race's final quarter in an unprecedented 23 seconds flat. That was a demonstration of raw power, acceleration, and speed carried over a mile and a quarter that defies any other Derby performance in its long history. Perhaps the only thoroughbred that ran in similar fashion was the great Phar Lapp who, in a tremendous burst of power and speed distributed over a short distance, came from some seven to eight lengths back to first in the Agua Caliente's mile and a quarter and won pulling away. Phar Lapp however was a mature athlete running at that time in his 6th year. As threes, Secretariat and ManO'War dazzled the sporting world and injected life into an industry that was either fledgling or dwindling. As threes, they rewrote the books on what were considered the standards of the time, both setting track and world records along the way. So the question of how Secretariat and ManO'War might compare resurfaces time and again with assertions and proclamations that satisfy only a few. According to sources, the panel of seven assembled by Blood_Line in 1999 to rank the best thoroughbreds of the century actually had the two tied for first, but not for second which by one vote tipped the balance in ManO'War's favor. The panel expressed little accord over this selection. Can we stand yet another approach by which to estimate which of the two might have been the finer specimen in terms of athletic ability? Can we look beyond the charts, records, and eras to isolate and compare their abilities in order to form a finer judgment? Can we use winning times as the basis through which to examine their abilities? To do this, we must first find some way to show that thoroughbred athletic ability has improved over time through the breeding process for if athletic ability has not improved or improved minimally, then other determinants such as technological and environmental factors can be asserted as the major cause of mean differentials in winning times between those thoroughbreds that ran in ManO'War's generation and those that ran some 50 years later. If on the other hand thoroughbreds have significantly improved, then we might be in a position to compare the athletes and more specifically Secretariat and ManO'War in terms of abilities stripped of era-contingent differences that racing charts might contain. This paper will attempt to put this challenge to the test using simple descriptive measures to highlight similarities and differences between Secretariat and ManO'War and then defer to Statistical Regression Models to explore the deeper questions regarding athletic abilities and whether or not improvements to the breed have occurred.  If abilities have improved then a discussion of comparisons between Secretariat and ManO'War can ensue within the framework of quality. Questions hovering above and through them might then find another approach through which to engage the two; so let us begin with a canter through their performances to begin laying the foundation for this examination.

The initial survey will begin with a chart disclosing performance lines, the linear relationships between Secretariat's and ManOWar's three-year-old performances at classic distances with respect to time as a function of distance. Tables will follow that contain simple descriptive statistical comparisons of the racer's third year comparing performances by variables of weight, field size, post position, age and weight of opponents, distances raced, and track speeds. Inclusive in these tables is the cumulative number of foals born to their generation to the time when any records they may have set were broken. This array of variables will be repeated again in comparing the two only when track records were set.

In the second half of this paper, regression models for selected races will be constructed holding race, class, track conditions, weight, age, and distance constant. This approach will permit the projections of the finishing times of two of Secretariat's Triple Crown races, the Kentucky Derby and the Belmont Stakes, both for three-year-olds, into the past.

I). Comparisons at Three

 Chart I: Secretariat and ManOWar Performance Lines

This chart is interesting for many reasons. It displays five of ManOWar's key races and four of Secretariats all at classic distances. These races contain the best times, unadjusted for track speed, recorded at these distances. Of the five belonging to ManO'War, three were world marks, one an American and another a track record¹. The three world marks were at 9, 11, and 13 furlongs; the American was at 12, and the track at 10 (It should be noted that the 11 furlong race, ManO'War's Belmont Stakes performance, was run in a clockwise direction over a " fish-hook" shaped course which because of these atypical features disallows it from use in the later parts of this analysis). The mean rest time between these competitions and their preceding races was 2 weeks. Secretariat's races include one world mark and three track records. The world record includes one at 9 furlongs while the three track records are at 9.5 (Daily Racing Form time), 10, and 12 furlongs. (Note that the 12 furlong distance is a surface world record for dirt. Also note that Secretariat's 5th mark is at 13 furlongs which was not an official time but a clocking as he eased through the eighth immediately following the 12th furlong of his Belmont Stakes^{William Nack}. He accomplished a similar clocking easing through the same furlong immediately following the ManO'War Stakes on turf^{Raymond G. Woolfe Jr.}. Because both these times indicated his ability to run this distance at world record pace under race conditions, the best was selected to include as a data point for this chart.). Mean rest time between these races and their preceding ones was 3.1 weeks (again note that this large mean rest time value was greatly influenced by the 6 week pause in Secretariat's racing schedule incurred while recovering from a virus contracted at or before the Whitney Stakes). The X-axis variable is distance from 8 to 14 furlongs. The Y-axis for reasons of simplicity is the full time of each race in seconds less 100; for example, Secretariat's run at 9 furlongs was completed in 1:45.4 minutes, or 105.4 in seconds. Since all times for all the races in this chart were completed between the range of 100 to 200 seconds, subtracting 100 from each time was effected to simplify the scale. This adjustment does not change the vital dimensions of the performance lines; instead it has the effect of creating a smaller plot that can more easily be read. In the example above, to return Secretariat's time to minutes, simply add 100 to the time marked on the graph and convert to minutes. The pairs of numbers located next to the data points reflect the specific race distances and weights carried in those performances. Finally, the performance lines themselves are 'lines of best fit' or regression lines (trend lines) estimated and extending through the array of selected race times. As stated earlier, these same linear methods will be employed for the projections of racing times into the past.

The chart displays two performance lines that are remarkably similar. The most salient feature is the slope they share which is one of two important dimensions of interest, the other being the distance, or velocity, that separates them.  The latter metric will be addressed momentarily. The first, however, is confirmed by the equations located at the right that display slopes that are nearly identical: Secretariat's at 12.78x and ManO'War's at 12.983x. Slope in racing is a factor that calculates an estimate of the increased time required to run an extra furlong as a function of the increased distance and fatigue incurred when executing that run. Investigators have known that there is a linear relationship between distance and time that is applicable to human racing events. Here it is applied to Thoroughbreds⁹. The slopes these two lines share indicate that the durability these two exercised over these distances was remarkably similar; that is, both Secretariat and ManO'War were able to maintain strong speeds while experiencing less fatigue through the longer stretches. In fact, as their records confirm, in terms of time the longer the distance the greater the separation between them and their competitors. What differentiates the lines seems not to be the staying power but the gap, or estimated velocity, that separates them. This estimated mean difference of about 3.25 seconds reflects a number of considerations such as environmental factors, track surface depth and consistency, track speeds, weight, the racing technology of the day, field size, and finally the quality and abilities of the competitors themselves. It is this gap that is of interest here. Can it be explained primarily in terms of historical technological conditions, or can a significant portion be explained in terms of the quality of the specimens involved? The second half of this paper will attempt to answer this, but for the moment this brief review of their records will continue.

Table 1

The items of interest in this table are the records set and the duration of the records in terms of the number of foals born before they was broken. In the case of Secretariat for instance, a world record was set for 9 furlongs that lasted through 1988, or about 15 years. From the time that record was set to the time it was broken, some 664431 foals were dropped beginning with Secretariats own cohort extending to that generation that would have been at least three years old in 1988. For ManOWar's most enduring record, the Lawrence Realization where a 13 furlong world mark was set that stood for 36 years, (broken in 1956 by Swaps age 4 carrying 130 at Hollywood Park), the number of foals bred beginning with his cohort through 1952 was 201,014⁸. These many were required before an athlete talented enough to break the record emerged. In terms of foals, Secretariat's 15 year record for nine furlongs outlasted that of ManO'Wars' by a factor of 3 even as the 9 furlong distance was and continues to be a common event. Is this a minor datum that can readily be explained by the development of faster track surfaces and designs from the 1920s through the 50s? Or one that can be explained by the breeding of better horses, or perhaps a combination of both? Since ManO'War set the one and five-eighths record, only a small number have either equaled or broken it, that in itself a testament to his strength. Today there is only one race that runs that distance, the Gallant Fox which unfortunately has been relegated to a low grade winter race. The best classes simply don't run that distance and have not run it for some time which strongly suggests that today's crops are not bred with distance in mind. Yet, the best have run and continue to run 9 furlongs in both one and two turn contests and with that, only two horses in over 600 thousand, the four year old Simply Majestic carrying 114 pounds, and the four year old Gentlemen carrying 121, both on west coast tracks running 16 and 23 years later, have broken the record (www.horse-races.net/library/links-tbrecords.htm). That, too, is a testament of strength.

Secretariat's most enduring legacy, however, is his capture of all of the 1973 Triple Crown events in record time. The number of foals has exceeded 1.2 million since they were set and to the time of this writing, all but one remain intact. At the stakes level, all remain en force. Is this accomplishment a simple artifact that can be explained in terms of track technologies that in the last 30 years have failed to improve? Or has breeding simply reached an upper ceiling so that it is now rare if impossible to foal a specimen that stands apart from the rest? Or have foals actually improved with respect to speed but at the expense of durability so that sturdiness (and therefore longevity) has to be artificially induced through the use of deeper, slower tracks and experimental surfaces? These  issues plague today’s industry. It is the assertion of some that the dearth of great champions since Cigar is as much an effect of breeding practices as it is of track surfaces; in fact  the state of the surfaces reflects the quality of the breed.

I. Various Performance Measures

Mean Weight Carried by Age of Opponents

***from this point on , all measures are given with respect to dirt surface races only.

Table 2

The primary items to take from Table 2 are the weight differentials between ManO'War and his opposition vis-à-vis Secretariat's opposition against older competitors. Beginning with Secretariat, an average of about 3 pounds separated him from the best competition of the day, and that was against 4s and up. In the Marlboro Cup, perhaps an early forerunner to the modern Breeder's Cup and the race that pitted him against the finest dirt racers in the western hemisphere and perhaps the world, Secretariat carried 124 pounds giving scale weight to the rest of the field. In absolute weight, Secretariat carried 3 pounds less than his chief rival the 4 year old Eclipse winner and future Hall-of-Fame runner Riva Ridge, and two pounds less than the future Hall-of-Fame great Cougar, the 7 yr. old Eclipse winner from California trained by Charles Wittingham. Despite running primarily on turf, Cougar was a strong and proven winner on dirt through 10 furlongs. His come from behind stretch duel victory in the Santa Anita Handicap that year showcased his speed and determination when confronting younger formidable challengers. Secretariat, coming off a 6 week layoff for a virus contracted at the Whitney Stakes, and without a prep race, set the world record for the 9 furlong distance. In fact, the record was broken twice and possibly three times that day, first by Secretariat and then by Riva Ridge. Cougar in finishing a strong third may also have broken it. The 5-yr. old Kennedy Road, Canada's Hall-of-Fame runner, finished further back carrying 121 pounds. Secretariat also faced the 4 yr. old Eclipse winner Key-To-The-Mint who carried 126 lbs. and the 3 yr. old Annihilate 'Em who had just won the Travers Stakes. Quite an assembly of athletes.

ManO'War's record with respect to weight is indestructible. As a three that carried the weights of a five or six year old, the colt set a string of records in measures of time and margins of victory some of which still stand today. His estimated 100 length win in the Lawrence Realization stands today as the largest margin on record. Ignore the fact that with the exception of one race he competed solely against his age group; there simply was not a horse anywhere that could defeat him. He launched as from a cannon and all his competitors saw was his backside fading into the distance. In all of his races, the horse ran relentlessly from the start to the finish, his riders often holding him back to conserve his strength and energy for future events. Against threes the weights ManO'War carried ranged from 118 to 138 lbs., and on four occasions 130 lbs.or more. His record speaks for itself.

Weight by Distance by Age for Record Times at 9, 10, and 12 furlongs; Track Conditions fast

Table 3

At these classic distances, mean weights for these record times were somewhat close. ManOWar outcarried Secretariat at  9 and 10 furlongs by 2 and 3 pounds respectively, while Secretariat carried the largest differential at 12 furlongs.  

Mean Field Size When Records Set or Not Set

Table 4

Post Positions by Record Times

Track Conditions Fast; 0: record not set; 1: record set

Secretariat

 Post Position Groups (rows) by Records Set (columns)

            0     1    Total  Percent  Mean Wght

       +-------------+

     1 |    2     2  |     4    50.0   124.3

     2 |    2*    0  |     2    25.0   126

     3 |    0     1  |     1    12.5   124

     4 |    0     1  |     1    12.5   126

       +-------------+

 Total      4     4        8

 Percent   50.0  50.0          100.0

Table 5a

ManOWar

 Post Position Groups (rows) by Records Set (columns)

            0     1    Total  Percent  Mean Wght

       +-------------+

     1 |    2     7  |     9    81.8   125.4

     2 |    0     1  |     1     9.1   138

     3 |    1     0  |     1     9.1   126

     4 |    0     0  |     0     0.0   0

       +-------------+

 Total      3     8        11

 Percent   27.3  72.7          100.0

Table 5b

* Secretariat in the one mile Gothom Stakes at Aqueduct equaled the track record from this position.

Mean (Wght by Distance by Field Size By Post)  when Records Set

Track Condition Fast;  0: Record not set; 1: Record set

Table 6

The track speeds were fast for all of these tables thus disallowing track condition as a factor when considering performance. Some of  the important points to consider come from Tables 5a and 5b. Secretariat carrying not more than 126 pounds set records from virtually all post groupings. The colt demonstrated a capacity to win and set records from virtually any position, whether from post 10 in a field of 13 in the Kentucky Derby or post 1 in a field of 5 in the Belmont. These performances demonstrated his strength and endurance over long and short distances. How can one forget the final race, the Canadian International at Woodbine, where he started from post 12 in a field of 12 and dueled with Kennedy Road for the first 7/8s of a 13 furlong distance. At the mile mark, Secretariat burst from the field as if from the starting gate to open a 12 length lead by the eighth pole, eventually winning by 6 1/2. This particular race was only his second turf run and despite competing under adverse weather conditions, came to within less than a second of the track record. This was another performance demonstrating strength, speed and endurance over a long distance. Tables 5a and 6 bring the horse's 3 yr. old season in terms of post position and record times into focus  The column labeled "0" represents races where records were not set, and "1"  where they were set. The rows numbered 1 through 4 represent post position groupings: "1",  the first 3 positions, "2",  positions 4 through 6, "3",  positions 7 through 9, and so on. The intersection of the row and column is the number of times records were or were not set at the particular post group identified by the row heading. Thus, for Secretariat, at group position 1, two races were ran that resulted in 2 records; though a track record was equaled in the second grouping, no new records were set; one was set in the third and another in the fourth. Overall, with the exception of the second, 4 records were set from the first through the fourth groupings demonstrating Secretariat's strengths in handling a variety of post positions and field sizes. He set records in races from 9 to 12 furlongs and on multiple surfaces: carrying 126 in the Kentucky Derby which began in the 4th grouping; carrying 124 pounds in the Marlboro Cup, the record set starting with the 3rd group; and 126 in the Belmont Stakes, one of two set from the first grouping. He was strong opening from any post and set records trailing or leading the field. The horse demonstrated great versatility in his approach to any given race, reminiscent of the great Pharr Lapp.

Table 5b misrepresents ManO'War's abilities in that it shows that he set records from only the first and second groupings. It cannot be forgotten that few challenged him in his 3 yr. old season. The horse ran once in the third grouping, the Preakness Stakes at 9 furlongs, in a field of 9 launching from position 7. Carrying 126 pounds he won by 1.5 lengths but with a speed figure of 97. It was the first race of his three year old season and the champion never ran that slow again. ManO'War set records through all the distances competed in, from 8 to 13 furlongs, while carrying weights ranging from 118 to 138 lbs.. As for contesting larger fields, the horse's two year old season provides ample evidence of a capacity to win from a variety of positions while carrying weights of up to 130 pounds.

Table 6 recapitulates the preceding 2 tables.

Are there weaknesses that can be extracted from this survey? None, at least no apparent ones. Secretariat's losses never  resulted from deficiencies in his mental or physical constitution. Instead, his losses can be traced to human factors: in the Wood Memorial, the trainer failing to inform the rider of an abscessed mouth; in the Woodward, the failure to have him prepped. Proof for these assertions lies in the fact that Secretariat never lost when he was sound and prepped. For those races he was 8 for 8 on all surfaces setting records in 4 of the 6 contests on dirt. The Whitney may have been the only defeat that could not have been avoided in that Secretariat contracted a virus that escaped detection. He followed this with 4 weeks of recovery and 2 weeks of training before starting in the the first running of Marlboro Cup. The only questions that arise occur when considering his ability to carry weight. How might the champion have handled 131 lbs or more? Of course that cannot be answered with any certainty but judging from his pedigree, one can speculate: for instance, if Secretariat inherited great endurance and speed from his sire and dam, he might also have inherited good weight bearing capacity. His sire Bold Ruler was an excellent carrier  winning races bearing 130 to 136 pounds as a three and a four year old, and for distances of up to a mile and a quarter. As a four, he never carried less than 130 pounds while winning five of seven races against the likes of Gallant Man. Still, seeing is believing and the point is moot. What can be said is that in the 1973 Belmont Stakes, while carrying 126 pounds, Secretariat near sprinted one and a half miles and crossed the finish line in full stride. If this is seen as nothing more than anecdotal, one might then consider the observation that the mean weight differential in his dirt races against stronger older competitors was negligible and but for one, Prove-Out in the Woodward, a long distance race he was not in training for, he defeated all of them.

If there was any weakness in ManO'War's constitution it might be said that his headstrongness made him difficult to handle. This was in fact no weakness for it made him relentless in his competitions. He ran hard from the start etching into stone his legendary will to win.

The question now arises as to how these two might compare against one another. The following section explores this.

II.) Modeling

Introduction

As stated previously, ManO'War's record is indestructible, yet selected the century's best by the Blood-Horse Panel by one vote*. He lost one in twenty-one, and none as a three. Other thoroughbreds recorded similar records, some undefeated, yet ManO'War's performances stretch across time from a time when heroes were in demand in post-war America. As the Equine species was indispensable to exploring and settling the Western Hemisphere, horses have always held a special place in the hearts of Americans.  ManO'War filled that space as he set the tracks afire and helped build a racing industry that today is worth billions. Some have called him the Babe Ruth of the sport. How then could he have been selected the century's best by one vote, and that vote over the one horse Secretariat that had a record containing five losses?. Could it be that Secretariat's performances rivaled those of ManO'War? That Secretariat's performances also were  legendary? That he, like ManO'War, came into the world when heroes were in demand; when something was needed to counterbalance the news of the day, the numbers lost in foreign wars, the national scandals uncovered and exploited. Those that selected Secretariat as the century's second best must have held his abilities in great deference. None of the panel saw ManO'War run, all they had for review were old grainy black and white films. What they did have were the written records left by those who did, and they are indestructible. But what they also had were the opinions of some who saw both Secretariat and ManO'War run, like those of  the aged Charles Hatton who died in 1975, the greatly respected turf journalist who observed and studied the New York racing scene from the days of ManO'War; and the late Hall-of-Fame trainer Holley Hughes who trained a Kentucky Derby winner in 1916. These and others declared Secretariat the most capable they had ever seen. These opinions may have influenced some of the panelist's choices, simply adding to what they had personally witnessed in their careers. What is remarkable is that a horse who was never heavily handicapped was selected so close to ManO'War, and this over others that had been strongly handicapped throughout their careers and who may have set many more records.  Secretariat was given the benefit because his performances were just as dramatic.

*note: according to sources, the panelist whose vote tipped the balance placed Secretariat in 14th place.

The Model 

In earlier sections of this paper, queries were posited regarding whether or not breeding practices had improved the quality of specimens, and that if so, then perhaps faster recorded speeds might be explained, at least to some degree, in terms of such improvements. Most likely, breeders would like to think so: that because of improved knowledge and of the availability of better stallions and mares, improvements in foal quality have occurred which can be measured where owners and trainers would like them to be measured, on the track. Historically, the introduction of strong European blood-lines into the American breed from the 20s through the 40s bettered the odds that such improvements would result. In theory, faster, stronger horses were foaled. Much like playing the odds in Las Vegas but there is more. In an article posted at thorographs.com/archive/gettingfaster.htm, investigator Jerry Brown asserts Thoroughbreds have improved and draws from an article entitled "The Genetics of Thoroughbred Horses" written by Dr. Patrick Cunningham, professor of animal genetics at Trinity College Dublin. The article appeared in Scientific American in May of 1991 and in it, Timeform ratings for the use of determining the racing abilities of horses were introduced. Timeform ratings were developed by British mathematician Phil Bull in 1948 and are considered, according to Mr. Brown, the best method used when analyzing the performances of horses in Great Britain and Ireland. Mr. Brown and his colleagues used Timeform ratings to analyze the performances of over 31,000 3 yr. old colts that raced between the years 1961 and 1985. Their findings concluded that roughly 35% of performance could be attributed to inherited factors, while the remaining 65% plus or minus could be assigned to other factors such as training, nutrition, etc....Using the instruments of Timeform ratings and Thoro-Graph points, Mr. Brown estimated that the inherited quality of racehorses in his country improved by about 1.5 percent from 1982 to the time his article was published³. 

This paper will not seek answers to these same questions but will test the notion of inherited contribution through the breeding methods of the time as a means to estimating the effect of factors other than inheritance on finishing times in a sample of races . Should the results prove statistically sound, then the percentages of contribution can be applied to estimate projected times into the past. One might then be able to say that a time of X in a race in 1973 might translate into a time of Y in 1920. One might also be able to find trends in the analysis that could be useful in addressing the premise of improvements to the breed over time; however, quantifying such improvements as Mr. Jerry Brown did will not be attempted.

Regression models will be used to analyze the historical samples of two races, the Kentucky Derby and the Belmont Stakes. These were selected for two reasons: first, several variables can be held constant:

            1. track;

            2. sex;

            3. age;

            4. track surface;

            5. distance;

            6. course direction and shape;

            7. weight carried;

            8. class of horse;

            9. stakes grade;

            10.  the time of the year; and finally

            11. the sequence of the races, in that the Belmont follows the Derby after a period of five weeks.

And second, that because these races have been run since the early part of the century, they have been accessible to the greats of the past.  This historicity makes comparisons between individual performers possible.

Regression models test independent against dependent variables and derive equations that quantify effects. If a correlation is detected between the variables, these models will transform that correlation into a coefficient of effect that quantifies the influence. Simple models test one independent variable, but that variable should have some theoretical basis for its use otherwise the model will not reveal anything of interest. Generally, regression models are used to test some theory that a causal relationship exists between two phenomena. Specious relationships can exist, but investigators can detect them.

The two variables for these models are:

Dependent y: the times the races were run in; and

Independent x: the number of foals foaled for the age cohort performing in the races.

The equation of estimate:  T_yr = constant + bx + e  where T_yr is the dependent variable, the constant is the y intercept when x is equal to 0, b is the beta coefficient of estimate (influence), x is the independent variable and e the error term.

The Dependent Variable and Its Parameters

This variable for the two races will be their finishing times, the times they were completed in: for the Kentucky Derby the times from 1920 through 1973 and for the Belmont 1926 through 1973 (in 1926 the Belmont was changed from an 11 to a 12 furlong event).The specific races selected will be controlled for track speed, that is, only those run on fast tracks. These times will be trimmed according to the following format:

1. Kentucky Derby times: since the races on fast tracks were, with the exception of one, run equal to or greater than 2 minutes but not equal to or greater than 3, the times will be trimmed to the seconds exceeding 2 minutes. The 1964 record of 2 minutes flat will be represented as 0, and Secretariat's record as -0.6. The number of races run on fast tracks through this time period is N= 37, or 68.5 percent of the total number of races.

2. Belmont Stakes times: The same criteria apply: times will be represented as seconds exceeding 2 minutes. The number of races run on fast tracks through this time period is N = 37, or 77 percent of the races. The years 1963 to 1967 were excluded because the races for this period were run at the Aqueduct racetrack.

The information for these races was gathered from the Churchill Downs netsite located at www.Churchilldowns.com; also from the New York Racing Association who supplied the charts for each Belmont Stakes race for the time period in question. These charts contain the race track conditions as well as all the additional information for each event to include the thoroughbreds that ran, whether or not records were set, the size of the field, post positions, etc....  I am grateful for the NYRA's assistance; they have aptly demonstrated their policy of open-doors to a public that is endeared to their program.

The data in tabular form is located in the Appendix.

The Independent Variable and Its Parameters

The independent variable includes the natural logarithm of the number of foals foaled between and including the years 1917 to 1970. These figures represent those crops that produced 3 yr. old competitors in 1920 through those that produced 3 yr. old competitors in 1973. In 1920, the figure was 1680, the foal count born in 1917, some of which ran in 1920. Those that ran in 1973 were foaled in 1970, and so on.  This variable contains only those crops born 4 years prior to those races ran on fast tracks in the Kentucky Derby and Belmont races.

The number of foals is what is known as a proxy variable, much the way educational level is often used as a proxy (correlated link) to income levels in social and economic studies. This count will test the success of the breeding industry in producing a quality stock, the theory that when a good number of good sires are bred to a number of good mares good specimens will result. If this proves accurate, then we should see a measurable contribution of the variable to the finishing times the sample of races have been run in; it should correlate to any trends in performance in terms of time over the period of years in question. If a weak correlation is detected, then breeding is not contributing, or only marginally,  and other factors can be asserted as the primary cause of better finishing times. The first part of this section will test for correlations between the foal counts and the races between 1920 and 1973 regardless of track conditions for the Kentucky Derby. This will be the first test of the hypothesis that a relationship exists between annual foal counts and racing times. Before continuing it must be added that this variable has certain weaknesses associated with it. The independent variable is being tested as a proxy to the quality of breeding as determined by race times. Even if a well correlated relationship exists, what is to say that this factor is not in fact a product of other forces, such as improvements in the nutritional practices of the day, or better  nutrition, environment and training? What is at question is whether or not the independent variable is actually a proxy to developmental influences after the foalings, and not to genetic qualities at birth due to improved  breeding methods. More than likely, the foal count as a proxy variable encompasses all these dimensions. Disaggregating them is what Jerry Brown and his team attempted to do. At best, this initial analysis is testing the hypothesis that breeding methods as approximated by the independent variable is contributing to quality outcomes, but if so, the degree of contribution may be somewhat clouded amongst other variables not in this study. In the end, as will be seen, it is the capability of the specimens on race day on the track in  year 'X' that is being tested against non-biological factors as causes to racing times.

1.) The Kentucky Derby

As stated earlier, due to weaknesses within certain dimensions of the independent variable, the natural logarithm of the counts is used in place of the raw figures. This transformation produces a more robust distribution of the data which approaches required apriori assumptions. Conversions of this type are not uncommon, occurring where issues of Distributional Normalcy exist. Being that this variable is one that may be impacted by other forces in the environment, forces of an economic or social nature such as the presence of national war, economic recession or depression, or other  forces that can adversely impact the underlying demand distribution of the industry and thus distort its natural probabilistic features, transforming the data is suggested. Using the natural logrithm of the data is more of a 'fine-tuning' operation that should not disturb the underlying theoretical questions involved. The data for this variable along with the logarithmic transformations can be found in the Appendix.

The dependent variable, the distribution of times the races were completed in, did not display any serious weaknesses in its internal dimensions and thus was not transformed.  The raw times, though,  were trimmed to the seconds and fractions of seconds of each race that either equaled or exceeded two minutes; or as in the case of Secretariat, was less than two minutes. The following graphs displaying the probability plots and the correlations between the variables were computed with the statistical software Systat.

Probability Plots of Variables for the Kentucky Derby

Though not perfectly linear, the plots show strength and normalcy between the variables. These plots cover all the Kentucky Derby races within the historical time period. N = 54.

Correlation

Pearson correlation matrix

                      TIME     NL_FOALS

 TIME                1.000

 NL_FOALS           -0.655        1.000    N=54

Unfortunately, the data points for all the 54 races within the oval did not show but their direction and strength is apparent. For the Derby, an inverse correlation of .655 exists between the natural logarithm of the foal count and the time the races were completed in; that is, as the foal count increases, the time races are competed in declines. This first measure suggests that there is a relationship of better than moderate strength between the proxy independent variable and race time, and that perhaps breeding methods did produce effects that made a positive contribution to the outcomes of the races.  How great a contribution? Other methods are required to estimate that answer. 

Continuing onto the next phase, the Regression Model will now be addressed. For this part, only those races that took place on fast tracks will be considered which will reduce the sample universe from 54 to 37 races. This is done for a number of reasons: the first to reduce the number of factors other than breeding that is contributing to the outcomes of races; and second to focus only on those races where the participants could offer their best performances. Off tracks would slow performance and thus affect time. Other factors under control are listed in a previous section. One important factor not under control is field size. If competitors are forced to run wide around turns in order to avoid traffic jams and rail traps, time and endurance will be affected in that more distance and therefore more time and energy will be required for the finish. This variable will have to be included in that portion for factors other than breeding that affects outcomes. The results for the Kentucky Derby model follows.

Kentucky Derby Regression Results

Data for the following results were selected according to:

      (TRACK SPEED = Fast)

Dep Var: TIME   N: 37   Multiple R: 0.721   Squared Multiple R: 0.520

Adjusted squared multiple R: 0.506   Standard Error of Estimate: 1.085

Effect         Coefficient    Std Error     Std Coef     Tolerance     t           P(2 Tail)

CONSTANT                        16.484                    2.232        0.000      .                          7.387     0.000

NLOG of FOALS           -1.534                    0.249       -0.721             1.000           -6.156    0.000

                             Analysis of Variance

Source             Sum-of-Squares   df  Mean-Square     F-ratio       P

Regression                44.611     1       44.611      37.899       0.000

Residual                  41.198    35        1.177

Durbin-Watson D Statistic     2.127

First Order Autocorrelation  -0.104

Three statistics are of importance: the Multiple R, the Squared Multiple R, and the Standard Error of Estimate. Another finding of importance is the P(2 Tail) which contains the odds of obtaining the coefficient values where no difference (or effect) exists between the variables.

The Multiple R value, .721,  is the correlation between the variables with the additional control of Track Speed. Like the value obtained without this control, it too depicts an inverse relationship as attested to by the negative coefficient value 'NLOG of Foals'. This value, though, is stronger than the .655 obtained when track speed was not controlled; in other words, not only were horses turning in better performances on drier surfaces, a result surely to be expected, but perhaps they were also providing a 'cleaner' view of their true strengths thus improving the correlation between the independent and dependent variables. This takes us to the next value of import, the Squared Multiple R.     

Squaring the correlation R gives the Squared Multiple R value of .52 which represents the estimated percentage of contribution the independent variable, in this case the proxy variable Nlog of Foals, gives to the dependent variable, Time. The independent variable accounts for  about 52 percent of the variation in the differences that result when the equation of estimate and its results are compared to the actual times the races were run in. In layman's terms, breeding as represented by the proxy variable Foals is accounting for or contributing about 52 percent of the explanation of time and from this we deduce that about 48 percent of time is attributed to factors other than breeding, such as track design, surface composition, depth and consistency, start gates, field size, post position, race strategy, etc.... How do these figures square with Mr. Browns figures of .35 and .65 percent respectively? They are expectedly stronger and should be for the following reasons: the number of horses that ran in the Derby for the period in question was about 775; the number of Foals foaled for the same period and age cohort was about 465,000. The percentage of the former to the latter is about .17% for a rate of about 2 per 1000; approximately 2 of every 1000 thoroughbreds foaled ran in the Derby from 1920 to 1973. If only colts are considered, the rate adjusts to roughly 3 colts for every 1000. Selecting only races where the track speed was fast, the number 775 is reduced to approximately 500. Those running in the Derby were and are simply the best or near best of their age group and consequently their average individual contribution is greater. These numbers, however, cannot answer specific questions of a biological nature such as how much cohorts genetically improved; but if race times improved, and they did, one can conclude that these specimens contributed to it. What can be said is that on average, according to this model, Derby times improved by about 4 seconds over the years in question; if these horses contributed 52 percent to that improvement, then horses improved by approximately two seconds.

The P values column populated with zeros indicates that the likelihood or probability of having the two coefficient values of 16.484 for the constant and -1.534 for the effect of the independent variable upon Time where no true effect exists approaches zero. The P values suggest that a true non-spurious effect exists. 

The value attributed to other factors, the value of .48, will, along with the equation of estimate, become important in projecting times into the past, that part of this paper reserved for last.

2.) The Belmont Stakes

Data for the Belmont will be presented in the same order followed by a brief discussion of the results.

Probability Plots of Variables

Foals for the period appear relatively normal while time betrays some anomaly along the left tail. Regression methods, though, have been known to be resistant to bias as long as deviations are not pronounced. As for the correlation between the variables, please refer to the Appendix where all the pertinent information can be found.

Belmont Stakes Regression Results

Data for the following results were selected according to:

(TRACK SPEED = Fast)

Dep Var: TIME   N: 37   Multiple R: 0.586   Squared multiple R: 0.344

Adjusted squared multiple R: 0.325   Standard error of estimate: 1.451

Effect         Coefficient    Std Error     Std Coef  Tolerance     t   P(2 Tail)

CONSTANT                        47.146                            4.110                                0.000      .                                  11.472            0.000

NLOG of FOALS           -1.962                           0.458                                  -0.586           1.000                    -4.279            0.000

Analysis of Variance

Source             Sum-of-Squares   df  Mean-Square     F-ratio       P

Regression                38.554     1       38.554      18.314       0.000

Residual                  73.681    35        2.105

The item to review here is the Multiple R Square value of .344. Approximately 34 % of Belmont time can be attributed to the quality of the horse. The Belmont is a different race that requires more strategy and pacing than the other Triple Crown events. It is known as the Jockey's race in that the rider plays a more pronounced role in its development and outcome. The 34 percent figure falls more in line with that of Jerry Browns' perhaps because typical derby distances in Europe are 1.5 miles, therefore racing strategies may be similar. There is more horse in the American mile and a quarter runs because a larger number can more naturally run that distance while at the 1.5 mile distance, a divergence takes place: the longer distance so dramatically alters the conditions that other factors dominate the outcome. All the coefficients are, as in the Kentucky Derby, statistically significant. According to this model, Belmont times did improve over the 46 year spread by about 4.3 seconds, and Belmont horses contributed about 34 percent to that gain, or 1.46 seconds (note that if Secretariat is excluded from the data set, improvement is reduced to .98 seconds or approximately 1 second).

III) Time Projections

The equation of estimate, T_yr = constant + bx + e,  introduced earlier, expresses a relationship between Time and Foals, the proxy to quality of the cohort. The equation written in model form appears

T_yr = constant + b(Nlog_Foals_yr) + e.

The Kentucky Derby

Before calculating the Time projections,  Secretariat's times for both the Derby and the Belmont will be removed from the data sets. This is done so as not to include his performances in the projections for 1973. The new model for the Kentucky Derby excluding Secretariat's figures is as follows:

Data for the following results were selected according to:

      (TRACK_COND$= "Fast")

Dep Var: TIME   N: 36   Multiple R: 0.694   Squared multiple R: 0.481

Adjusted squared multiple R: 0.466   Standard error of estimate: 1.062

Effect         Coefficient    Std Error     Std Coef Tolerance     t   P(2 Tail)

CONSTANT            15.556        2.263        0.000      .       6.875    0.000

NL_FOALS            -1.424        0.254       -0.694     1.000   -5.617    0.000

                             Analysis of Variance

Source             Sum-of-Squares   df  Mean-Square     F-ratio       P

Regression                35.616     1       35.616      31.553       0.000

Residual                  38.378    34        1.129

Durbin-Watson D Statistic     2.140

First Order Autocorrelation  -0.082

Using the model to estimate the  Kentucky Derby time for 1973, substitute the coefficients of the regression model into the equation as follows:

T₁₉₇₃ = 15.556 - 1.424(Nlog_Foals₁₉₇₃)

where  (Nlog_Foals₁₉₇₃) is the natural log of the number of American three year olds in 1973 that were foaled in 1970. The number foaled in 1970 was  24,361 and the natural log of that number is 10.10.  Inserting 10.10 into the equation and solving gives a predicted value of  1.2 seconds for the winning Kentucky Derby time in 1973. Adding that time to two minutes, the minimum, gives a predicted time of 2:01.2, or  T₁₉₇₃ =2:01 1/5.

Doing the same for T₁₉₂₀ gives the following equation:

T₁₉₂₀ = 15.556 - 1.424(Nlog_Foals₁₉₂₀) 

where the number of three year olds in 1920 foaled in 1917 was 1680; the natural log of that number is (Nlog_Foals₁₉₂₀) = 7.426. Substituting 7.426 into the equation and solving gives a predicted value for the Derby in 1920 of 5 seconds or T₁₉₂₀ =2:05.

This is where  individual performances adjusted for factors other than ability can be projected into the past.

Using the expression

Y = (T₁-T₂) (1-R²)

where Y is the estimate of time in seconds attributed to factors other than ability, T₂ is the estimated time of the race to be projected, T₁ is the estimated time of the race ran in the ealier part of the period, and R² is the correlation R squared derived from the Regression Modeling, Secretariat's Derby time can be projected to the year 1920 by adding Y to his real time in 1973:

KD_Sec_{192 0} = KD_Sec₁₉₇₃  + Y.

The estimated time for 1973 (T₂) is 2:01.2 while the time estimated for 1920 (T₁) is 2:05. Subtracting these two gives a difference of 3.8 seconds. 

The Multiple R Squared (R²) for the KD Regression Model is .48. Accordingly, Foals explains about 48 percent of the variation in times run on fast tracks through the years in question. Subtracting this figure from 1 leaves .52 as the unexplained, those factors other than ability that contributed to the outcomes of the races.  Multiplying the 3.8 second differential by .52 gives 1.976 seconds, or that portion of the differential explained by factors other than ability (Y). We can adjust individual performances for the KD in 1973 by this amount and offer estimated projections in 1920 KD terms. Hence, we will slow Secretariat's time of 159.4 (KD_Sec₁₉₇₃) by adding 1.976 (Y). The resulting projected time is 2:01.376, or by way of this model, Secretariat's time in 1920 (KD_Sec_{192 0}) would have been approximately 2:01 2/5s rounded (or 2:01 1/5 without rounding). Information is lacking as to whether this figure would have been a record of some sort, but it can be compared to ManOWar's best time for that distance at Saratoga. ManOWar's best time at that distance was 2:01 4/5s achieved at the Travers Stakes on a fast track carrying 129 lbs. where he raced two others and set a record. It is not possible to say if Saratoga was a slower track than Churchill Downs in 1920; but consideration, too, must be given to the statements that ManOWar was restrained in the race. Consideration must also be given to the fact that Secretariat, starting from post 10 and carrying 126, came from last to first against a larger field of 12. Giving 10 to 12 lengths to the leaders in the opening quarter and loosing substantial ground through both turns, he ran the final quarter in a sensational 23 seconds taking the laurel by two. In truth, Secretariat's time for the 1 1/4 run may have been close to a second faster, or near world record pace given the path he ran¹⁰ (the standing world record in 1973 for dirt courses was 1:58 1/5). This model suggests that Secretariat's mark would have edged the figure that ManOWar set.

Using the Standard Error of Estimate to calculate a 95% confidence interval for the projected times in 1973 and 1920 gives the  values a plus or minus 2.2:  2:01.2 +- 2.2 for 1973 and 2:05 +- 2.2 for 1920 respectively. Both Secretariat's and ManOWar's times reside outside the fastest boundary point of the confidence interval for 1920.

The Belmont Stakes

Performing the same operations for the period 1926 through 1973, the equation of estimate derived for the Belmont Stakes model excluding Secretariat's performance is

T_yr = 43.174  - 1.506(Nlog_Foals_yr) + e ^{see appendix}.

Substituting 10.10 in for the Nlog_Foals  for the year 1973 gives 2:27.96 or 2:27 4/5  as the  projected time for 1973. Substituting 7.426  in for the year 1920 gives  31.97 or 2:31 4/5  . The difference between these two times is  4 seconds. Multiplying this differential by .755, the percentage of the time explained by factors other than ability gives 3 seconds.

Adding this figure to Secretariat's Belmont time of 2:24 gives a projected estimate for the year 1920 of 2:27.00. This time would have been 1 4/5 seconds faster than ManO'War's 1.5 mile time in the Jockey Club Stakes which was also run at Belmont. In that race, ManO'War, carrying 118 pounds, ran against one other competitor and set a record. With an additional eight pounds, could he have performed as well as Secretariat? Seven days earlier, in the Lawrence Realization also ran at the Belmont track, he carried 126 for one and five-eighths and set a world mark. In that race, ManO'War could have hit the 1.5 mile mark about three fifths of a second faster than recorded (this figure was interpolated mathematically using the Excel software). Secretariat's time still would have bettered the Lawrence interpolated figure by 1 1/5th of a second. Rest time between these races and their preceding ones was a non-factor as both had at least two weeks along with workouts (that is, between ManO'War's Lawrence Realization and the previous race and between Secretariat's Belmont and Preakness Stakes). This model suggests that Secretariat performed better at the 1.5 mile distance . (As an aside, one cannot confidently extrapolate ManO'War's Belmont Stakes performance to one and a half miles due to the pattern and course direction of the day. In 1920, according to the charts for that period, the Belmont was run in a 'European' style, clockwise and in a 'fish-hook' pattern as has been described, partly run on the training course and finishing on the main track. In 1921, Grey Lag would be the first to win the Belmont Stakes in the counterclockwise format we are familar with today.).

Using the Standard Error of Estimate to calculate a 95% confidence interval for the projected times in 1973 and 1920 gives the values a plus or minus 2.8:  2:27.8 +- 2.8 for 1973 and 2:31 4/5 +- 2.8 for 1920 respectively. In this case, Secretariat's time resides outside the confidence intervals for both 1973 and 1920; and as with the previous projection, ManOWar's time also resides outside the interval for 1920.

IV). Conclusions

Secretariat was selected second to ManO'War in part because he never carried more than 126  pounds. Based on his performances, one might estimate his capacities; for instance, Secretariat's Belmont performance in terms of weight, carrying 126 pounds, is not atypical of the great carriers in history. Forgo through his five-yr. old campaign ran three 1.5 mile races and in only one of them carried a weight greater than 126 pounds, 134 in the Suburban Handicap of 1975. Kelso, another great work horse, in all of his mile and a half campaigns only once carried more than 126, 129 pounds as a five.  Reviewing the history of world marks for this distance on dirt shows that not one of the record setters carried greater than 126 pounds. Furthermore, of the 3 thoroughbreds older than 3 years of age that set records for this distance, each carried less than 126⁷. This provides some indication of a bearing capacity in Secretariat that was never tapped. He simply did not have the opportunity to demonstrate his strengths in this area and this may have been why the Blood-Horse Panel gave him some benefit: that judging from his performances, in particular the Belmont, it was safe to conclude he had strong weight-bearing capability. It is this writer's assertion that had Secretariat carried 10 to 12 lbs more in the Belmont, and spotted the rest of the field 15 to 20 lbs,  in addition to winning he still would have challenged the track record. And again, in the Kentucky Derby, had Secretariat carried 5 to 6 more pounds, the star champion still would have been first to the finish line. ManO'War, on the other hand, was a proven carrier. As a three, he shouldered weights that only fours and above carry today.  With ManO'War, there is nothing left to speculation.  Handicapping officials often  probed the depths of his endurance searching for a bottom they would never find. Despite being assigned large imposts, ManO'War always had something left at the finish, enough to keep him lengths ahead of the competition. He expended little effort in his victories.

In terms of ability, it has been shown that both these  specimens carried the large heart factor¹³, and both inherited great conformation and athleticism through their pedigrees. Speed wise, though ManO'War was strong through the first sixteenth, beyond this point both shared explosive potential through the remaining quarters. Secretariat clocked quarters from 22 to 22 2/5 seconds in the Belmont Stakes and Marlboro Cup achieving velocities from 60 to over 62 feet per second. In workouts he ran splits approaching 63 ft/sec. Conformation wise, at three, ManO'War's frame was near that of Secretariat’^{see appendix}. Both had long strides measuring up to or through 27 feet (Whereas it has been reported that ManOWar's stride ranged from 24.5 to 28 ft^5a. , Professor George W. Pratt of MIT who has studied horse gait described Secretariat's stride, estimated from 24 to 27 feet^{see appendix}, as highly productive, producing great extension and efficiency^{2, 12}.). This is what set ManO'War apart from his 1920 contemporaries. Officials had to apply strong handicaps to make his races competitive for the fields he competed against were simply of a different class. Certain European blood lines had yet to be injected into the American stock, lines that would foal the likes of Gallant Fox  and  Whirlaway, and which would eventually produce such sires as  Northern Dancer  and Bold Ruler ^{7, 10}. But once those lines were injected, by 1970, mean abilities had improved thus narrowing the differentials between Secretariat's contemporaries and himself. As this paper shows, Secretariat competed against fields better than those ManO'War faced. It is conceivable that ManO'War might not have been quite as effective had he raced in 1973, and by the same token, Secretariat might have been just as successful as ManO'War against his level of competition in 1920. Mathematical models might offer some insight into exploring this statement. In the final analysis, those who assert that one was without argument the greatest, or 'the horse of the millennium', or that the other was 'suspect', or beatable, need to look beyond the strengths and weaknesses of  the records. They need to look into things the wins and losses don't show; they need to look beyond the racing charts and the rhetorical verbiage of the apologists. Should they do this, they will discover these two are far closer than any record demonstrates, near indistinguishable in their performances. The performance lines in Chart I assert that where distance and weight were equal or near equal, an uncanny resemblance exists between them. The gap separating the two lines was explored using projection models for two races, with the results suggesting racing times within fractions of one another.  The various tables following the chart highlight times and records some of which have stood for years. Both set official and unofficial world marks from 9 through 13 furlongs carrying 126 or near 126 pounds.; for example, Secretariat was clocked easing through the 10th furlong following the Marlboro Cup distance in 1:57.8⁶, an unofficial world record for a mile and a quarter that Spectacular Bid would equal 9 years later, as a four year old. Bid's official record still stands today. Secretariat  was also clocked easing through the 13th furlong following the Belmont Stakes at 2:37.6^{William Nack, SecretariatThe Making Of A Champion,2002}, an unofficial world record that broke Swap's one and five-eighths mark by close to one second. In truth, Secretariat stands closer as ManO'War's equal or possible better, but not merely as one of the greats since ManOWar. His Belmont performance stands as the benchmark of excellence at the true classic distance of one and a half miles carrying the true classic weight of 126 pounds. It can be argued concordantly with Walter Farley in his semi-fictionalized account of ManO'War entitled 'ManO'War' that the original Big Red was never allowed to extend himself, that he was always held in check and that if he had been allowed to run  many of his records might still stand. Farley also states that by the early 60's, tracks through the years had sped up by a near two seconds through the mile (approx. a fifth per furlong) and speculated on what he might have accomplished had he ran in the1960s or later⁵. If the two second figure or just a little faster is a good estimate, then we know that of the factors explored other than ability that contribute to race time, track speed (the track variant) would be the primary component. If we were to slow Secretariat's times by about 2 seconds (or even a fifth through 12 furlongs), he would have generated a wider margin of victory in the 1920 Belmont than the model in this paper predicts. Recall that 3 seconds was added to his 1973 outcome, a race in which he was never extended, a race after which his rider commented "he was running easy". In the end, we return to the question posed at the start, the question which initiated this project: which of the two was the finer specimen, the better athlete? Ceteris paribus, this analysis suggests Secretariat, but perhaps we cannot be sure. Models contain degrees of uncertainty. Nor can we be sure how Secretariat and ManO'War would rate against one another in actual competition: ManO'War's long and powerful stride against Secretariat's large and relentless form. Intangibles such as "the determination to win under the toughest circumstances" interplay, but are difficult to measure. The physical attributes of the specimens have a substantial say. What is certain is that these two stand apart from the rest and this because of what they showed the world as threes. Not only did they pass the great tests unique to their eras, but they did so while demonstrating strength, courage, and abilities far beyond their age.

Abstract