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 
01:53.4 
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 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 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 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 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