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 3yr. 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 power
and energy so far beyond the pale that one can only speculate on
what they might have achieved 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 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
The initial survey will begin with a chart disclosing
performance lines, the linear relationships between
Secretariat's and ManOWar's threeyearold performances at
classic distances with respect to time as a function of
distance. Tables will follow containing 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
threeyearolds, 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
record^{1}. 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 "
fishhook" 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
Xaxis variable is distance from 8 to 14 furlongs. The Yaxis
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 Thoroughbreds^{9}. 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.




Best
Times 














Distance Furlongs 
9 
9.5 
10 
12 
12 
13 


Track 

Pimlico 
Churchill
Downs 


Woodbine 


Age of Comp 
3 and up 
3 
3 
3 
3 and up 
3 and up 


Track Cond 
fast 
fast 
fast 
fast 
firm 
firm 

Secretariat 
Wght 
124 
126 
126 
126 
121 
117 


Field Size 
7 
6 
13 
5 
7 
12 


Post 
7 
3 
10 
1 
3 
12 


Time 
01:45.4 
01:53 
01:59.4 
2:24 
02:24.8 
02:41.8 


Surface 
dirt 
dirt 
dirt 
dirt 
turf 
turf 


Record Set 
w 
t 
t 
w^{@} 
course 
 


Record Still in Effect 
t 
 
t 
w 
 
 


Foals dropped against original record**/ Year
Broken 
613,135/
1988 
764,568/ 1991 
1.2
mil * 
1.2
mil * 
812,776
/ 1992 
 











Distance Furlongs 
8.5 
9 
10 
11 
12 
13 


Track 
HdG 
Aqueduct 






Age of Comp 
3 
3 
3 
3 
3 
3 


Track Cond 
fast 
fast 
fast 
fast 
fast 
fast 

ManOWar 
Wght 
138 
126 
129 
126 
118 
126 


Field Size 
4 
2 
3 
2 
2 
2 


Post 
4 
1 
1 
1 
2 
2 


Time 
01:44.8 
01:49.2 
02:01.8 
02:14.2 
02:28.8 
02:40.8 


Surface 
dirt 
dirt 
dirt 
dirt 
dirt 
dirt 


Record Set 
t 
w 
t 
w 
a 
w 


Record Still in Effect 
 
 
 
 
 
 


Foals dropped against original record** / Year
Broken 
17,199/ 1927 
3630/ 1921 
111,717/ 1946 
252,009/ 1961 
17,199/ 1927 
201,014
/ 1956 











^{@}dirt
surface world record 








** estimate as of 2002 ^{8 } three year olds bred^{} 















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, 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 664,431
foals were dropped. This figure begins with Secretariat's own
cohort and extends 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 201,014^{8}.
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 fiveeighths
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 fast west coast tracks running
16 and 23 years later, have broken the record (www.horseraces.net/library/linkstbrecords.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
Dirt Surface Only *** 
Secretariat 
ManOWar 
Mean wght carried all races as a
3 
124.4  126.6 
Number of races against 3s only 
7  10 
Different 3 yr. olds
ran against 
24  15 
Mean wght carried against 3s
only 
126  127.3 
Mean wght of opponent 3 yr. olds 
120.9  115.8 
Number of races against older 
3  1 
Different older horses ran
against 
10  1 
Mean wght against older horses 
120.7  120 
Mean wght of older horses 
123.1  126 
***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 visàvis 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 probably 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 HallofFame inductee Riva Ridge. Secretariat also
carried two pounds less than the future HallofFame great
Cougar. Despite running primarily on turf, Cougar, trained by
Charles Whittingham, 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, 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 5yr. old
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
Weight
by Distance Against 3s 
Secretariat 
ManOWar 
9 furlongs    126 
10 furlongs  126  129 
12 furlongs  126  118 
Weight by
Distance Against Older 
Secretariat 
ManOWar 
9 furlongs  124   
10 furlongs    120 
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
0: record not
set; 1: record set 
Secretariat 
ManOWar 
0 
5.7  4.7 
1 
7.5  2.5 
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
Secretariat 
Mean Distance 
Mean Wght 
Mean Field Size 
Mean Post Position 
0 
1.1 miles  124.25  5.75  4 
1 
1.27 miles  125.5  7.75  5.25 
ManOWar 
Mean Distance 
Mean Wght 
Mean Field Size 
Mean Post Position 
0 
1.1 miles  130.7  4.7  3.3 
1 
1.27 miles  125.1  2.5  1.9 
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
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 received little attention. He followed this with 4 weeks of
recovery and 2 weeks of training before starting in the the
first running of the 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
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
headstrong 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 query.
II.) Modeling
Introduction
As stated
previously, ManO'War's record is imperishable, yet selected the
century's best by the BloodHorse Panel by one vote*. He lost
one in twentyone, 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 postwar
*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 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 bloodlines 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
This paper will
not seek answers to these same questions but will test the
notion of inherited contribution through era contingent breeding
methods 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
And second, that
because these races have been run since the early part of the
century, they have been accessible to the finest performers 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 sound investigations 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 for they aptly
demonstrated their policy of opendoors 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. Those that ran in 1973 were foaled in
1970, and so on. This variable
contains only those crops born 3 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 nonbiological factors as causes to racing
times.
1.) The
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 distort its natural probabilistic features,
transforming the data is suggested. Using the natural logrithm
of the data is more of a 'finetuning' 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
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
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 through turns in order to
avoid traffic jams and rail traps, time and endurance will be
affected in that more distance and therefore more time 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.
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
SumofSquares df MeanSquare Fratio P
Regression
44.611 1 44.611 37.899 0.000
Residual
41.198 35 1.177
DurbinWatson 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 Time, the
dependent variable. The independent variable accounts for about 52 percent of the variation in
the differences that result when the equation of estimate and
its predictions are compared to the actual times the races were
run in. In laymans' terms, breeding as represented by the proxy
variable Foals is accounting for or contributing about 52
percent to the outcomes 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, racing
strategy, etc.... How do these figures square with Mr. Browns
figures of .35 and .65 percent respectively? They are larger and
should be for the following reasons: the number of horses that
ran in the
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 nonspurious 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
Data for the
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.
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
SumofSquares df MeanSquare
Fratio
P
Regression
38.554 1 38.554 18.314 0.000
Residual
73.681 35 2.105
The item to review is the
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
Before
calculating the Time projections, Secretariat's
times for both the
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
SumofSquares df MeanSquare
Fratio
P
Regression
35.616 1 35.616 31.553 0.000
Residual
38.378 34 1.129
DurbinWatson 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:
T_{1973 }= 15.556  1.424(Nlog_Foals_{1973})
where (Nlog_Foals_{1973})
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
T_{1973 }=2:01 1/5.
Doing the same
for T_{1920 }gives the following
equation:
T_{1920 }= 15.556  1.424(Nlog_Foals_{1920})
where the number
of three year olds in 1920 foaled in 1917 was 1680; the natural
log of that number is (Nlog_Foals_{1920})
= 7.426. Substituting 7.426 into the equation and solving
gives a predicted value for the
This is where
individual performances adjusted for factors other than
ability can be projected into the past.
Using the expression
Y = (T_{1}T_{2})
(1R^{2})
where Y is the estimate of time
in seconds attributed to factors other than ability, T_{2
}is the estimated time of the race to be projected, T_{1
}is the estimated time of the race ran in the ealier part
of the period, and R^{2} 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_Sec_{1973 }+
Y.
The estimated time for 1973
(T_{2}) is 2:01.2 while the time
estimated for 1920 (T_{1}) is 2:05.
Subtracting these two gives a difference of 3.8 seconds.
The Multiple R Squared (R^{2})
for the KD Regression Model is .48. Accordingly, Foals explains
about 48 percent of the variation in times ran 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 1:59.4 (KD_Sec_{1973})
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
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 2.0: 2:01.2 + 2.0
for 1973 and 2:05 + 2.0 for 1920 respectively. Both
Secretariat's and ManOWar's times reside beyond the fastest
boundary point of the confidence interval for 1920.
The
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 4/5s
as the projected time for
1973. Substituting 7.426 in for the
year 1920 gives 31.97 or 2:31 4/5s . 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
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 2.6: 2:27.8 + 2.6 for 1973
and 2:31 4/5 + 2.6 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. Secretariat's
In terms of ability, it has been shown that both these specimens carried the large heart
factor^{13}, 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 a powerful potential through the
remaining quarters. Secretariat clocked quarters from 22 to 22
2/5 seconds in the Belmont Stakes and Marlboro Cup achieving
velocities of 60 feet per second or better. 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 lengthy 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 energy 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 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 existed 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. Secretariat was clocked easing through the 10th furlong
following the Marlboro Cup distance in 1:57.8^{6},
an unofficial world record for a mile and a quarter that the
four year old Spectacular Bid would equal 9 years later. 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 fiveeighths 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