Because of all the discussion about Secretariat times for the Preakness
I decide to model his Kentucky Derby race and the Belmont race using
my Energy Program (EP). I then took both models and did an estimate
for his Preakness race. The EP tries to model the three energy source
used for running: phosphates, glycogen, and oxygen. I started with
a version of the program similar to the Breeder Cup models (posted before
BC94).
I spent a number of hours running various variables to model both races.
The Kentucky Derby was difficult to model. I had to change the level
of phosphate energy to allow for distribution later in the race. All
other variable were the same. From running these models I believe Secretariat
had a bad start in the Derby and was allowed to stay further back then
he normal would.
For gate distance I review a video tape I have for the Belmont and Preakness
and estimate the gate distance. I also made estimates for the track
resistance (mu=.019 for Churchill, and mu=.018 for Belmont and Pimilco).
Kentucky Derby Model: Gate=30 ft from timing pole, time given in seconds
1/2 3/4 1mi 11/4
Actual Time 47.40 71.80 96.20 119.40 <-seconds
Secretariat 48.80 *72.90 96.25 119.40 <-est base on lengths**
EP Model Est. 49.05 71.55 95.05 119.40
Model Error> +.25 -1.35 -1.20 0 *Posted as 71.90 sec
corrected 2/5/95
Belmont Model: Gate=60 ft
1/2 3/4 1mi 11/4 11/2
Actual Time 46.20 69.80 94.20 119.00 144.00 <- seconds
Secretariat 46.20 69.80 94.20 119.00 144.00
EP Model Est. 46.05 69.95 94.40 119.15 144.10
Model Error -.15 +.15 +.20 +.15
Preakness Estimates: Gate=40 ft.
1/2 3/4 1mi 13/16
Recorded Time 48.20 71.40 95.60 114.40
Secretariat 48.20 71.40 95.60 114.40 (DRF 113.40)
EP Kentucky Derby 48.40 70.70 94.00 112.05 <-seconds
EP Belmont 46.40 70.30 94.75 113.30
Because of the problems I had modeling the Kentucky Derby, I believe
the Belmont was a better representative race for Secretariat. If that
is the case then his time would be 113.30 or 1:53.30 for the Preakness.
This is only .10 seconds off the handed time for the race.
If Secretariat ran the Belmont with the same EP profile as he did the Derby
his time would be:
1/2 3/4 1mi 11/4 11/2
EP Estimate 47.90 70.20 93.50 117.60 142.25 <-seconds
He would have won by almost 40 lengths.
** I use and adjustment other then 5 lengths equal 1 second for calculating
Secretariat times.
Larry
From: saroman@ix.netcom.com (Steve Roman)
Subject: Secretariat: Time, Distance, and Fatigue
Comments: Derby Message #3327
Following up Larry Wellman's fascinating mathematical
modeling of Secretariats Triple Crown, I am posting a
study of my own that appears in an article I wrote in 1983
entitled THE RELATIONSHIP BETWEEN TIME, DISTANCE, AND
FATIGUE: EVIDENCE FOR A RECORD-BREAKING PREAKNESS. The
methodology is based on a prior observation that a log-log
plot of time vs. distance for American records on turf and
on dirt from 5 to 12 furlongs yields a virtual straight
line with correlation coefficients in excess of 0.9999.
The equation derived from the plot allows for the
calculation of any time at any given distance. In every
case, the calculated time is within 2/5 of a second of the
actual time.
Using this technique we evaluated Secretariats Preakness
in three ways. Table 1 uses the best recorded times of
Seattle Slew, Affirmed, and Secretariat as 3yos through the
Belmont Stakes, but excluding the Preakness. The results
show that Seattle Slews and Affirmeds Preakness were
both within 2/5 of a second of the predicted value. The
predicted time for Secretariat is 1:52.3, certainly closer
to 1:53.2 than to the official 1:54.2.
TABLE 1. FINAL TIME OF PREAKNESS PREDICTED FROM BEST
STRAIGHT LINE DETERMINED BY BEST THREE-YEAR-OLD FORM
THROUGH THE BELMONT STAKES.
SEATTLE
DISTANCE SLEW AFFIRMED SECRETARIAT
8f 1:33.2(6)
8.5f 1:42.3(4)
9f 1:47.2(1) 1:48.0(5)
10f 2:02.1(2) 2:01.1(2) 1:59.2(2)
12f 2:29.3(3) 2:25.4(3) 2:24.0(3)
9.5f(predicted) 1:54.3 1:54.4 1:52.3
9.5f(actual) 1:54.2(7) 1:54.2(7) 1:54.2 or
1:53.2(7)
SLOPE 1.14731 1.04800 1.06893
INTERCEPT 0.93758 1.03544 1.00596
CORR. COEFF. 0.99955 0.99975 0.99981
(1) Flamingo Stakes
(2) Kentucky Derby
(3) Belmont Stakes
(4) San Felipe Handicap
(5) Santa Anita Derby
(6) Gotham Stakes
(7) Preakness Stakes
Table 2 uses the fractional times for the three Triple
Crown winners in each leg of Triple Crown races. Note the
very high correlation coefficients for the Derby and the
Belmont (all exceeding 0.9999) for each of the runners.
>From the data we can also project the time for
Secretariats final 3/16 mile. In the Derby it is :17.2
sec. In the Belmont it is :18.3 sec. In the Preakness,
Seattle Slew and Affirmed retain a >0.9999 correlation
coefficient. However, a 1:54.2 Preakness for Secretariat
lowers his correlation coefficient to below 0.9999.
1:53.2, on the other hand, corresponds to a more likely
correlation coefficient of 0.99995. The projected final
3/16 in a 1:54.2 race is :18.4 sec while for a 1:53.2 race
it is :17.4 sec. Based on the final 3/16 of the Derby and
the Belmont, it is unlikely that Secretariat ran a final
3/16 slower in the Preakness than he did in the Belmont
which is 5/16 of a mile longer. This further supports the
faster Preakness.
TABLE 2. FRACTIONAL TIMES/BEST STRAIGHT LINE PARAMETERS FOR
TRIPLE CROWN RACES
KENTUCKY DERBY
SEATTLE
DISTANCE SLEW AFFIRMED SECRETARIAT
4f :45.4 :46.4 :49.2
6f 1:10.4 1:11.3 1:13.0
8f 1:36.0 1:35.4 1:36.2
9.5f
10f 2:02.1 2:01.1 1:59.2
12f
SLOPE 1.06982 1.03623 0.96354
INTERCEPT 1.01692 1.04694 1.11363
CORR.COEFF. 0.99999 0.99997 1.00000
TIME FOR FINAL 3/16 MILE: :17.2(3)
BELMONT STAKES
SEATTLE
DISTANCE SLEW AFFIRMED SECRETARIAT
4f :48.2 :50.0 :46.1
6f 1:14.0 1:14.0 1:09.4
8f 1:38.4 1:37.2 1:34.1
9.5f
10f 2:03.4 2:01.3 1:59.0
12f 2:29.3 2:26.4 2:24.0
SLOPE 1.02420 0.97701 1.03555
INTERCEPT 1.06968 1.10924 1.03978
CORR.COEFF. 0.99997 0.99992 0.99998
TIME FOR FINAL 3/16 MILE: :18.3(3)
PREAKNESS STAKES
SEATTLE
DISTANCE SLEW AFFIRMED SECRETARIAT(1) SECRETARIAT(2)
4f :45.3 :47.3 :48.1 :48.1
6f 1:10.0 1:11.4 1:11.2 1:11.2
8f 1:34.4 1:36.1 1:35.3 1:35.3
9.5f 1:54.2 1:54.2 1:54.2 1:53.2
10f
12f
SLOPE 1.06141 1.01416 0.98800 0.99034
INTERCEPT 1.01950 1.06703 1.08029 1.08557
CORR.COEFF. 0.99998 1.00000 0.99987 0.99995
TIME FOR FINAL 3/16 MILE: :18.4(4) :17.4(4)
(1)Official final time.
(2)Daily Racing Form final time.
(3)Calculated from equation for best linear fit of data.
(4)Actual time from 3/16ths pole to finish.
Finally, Table 3 projects a final time based on the earlier
fractions (Table 2) for all of Secretariats Triple Crown
races and for the Preakness of Seattle Slew and Affirmed.
A 1:53.2 for Secretariat in the Preakness results in all
five races being within 3/5 of a second of the predicted
time. 1:54.2 is a full 1 2/5 sec slower than the
projection.
TABLE 3. FINAL TIMES OF CLASSIC RACES PREDICTED FROM BEST
STRAIGHT LINE DETERMINED BY EARLY PACE(1)
PREDICTED ACTUAL
HORSE RACE FINAL TIME FINAL TIME
Secretariat Kentucky Derby 1:59.3 1:59.2
Secretariat Belmont Stakes 2:23.2 2:24.0
Secretariat Preakness Stakes 1:53.0 1:54.2 or
1:53.2
Seattle Slew Preakness Stakes 1:53.4 1:54.2
Affirmed Preakness Stakes 1:54.3 1:54.2
(1) Calculated from early fractions only, excluding final
time.
Actually, folks, the issue here is not whether Secretariat
broke the Preakness record. Everyone involved at the time
*knows* that he did. The whole mess is nothing more than a
bureaucratic screw up.
--
Steve Roman
"Creator of the Dosage Index"
Fulshear, Texas
Date: 6 Feb 95 09:33 EST
From: wellman (Larry Wellman)
Subject: re: Secretariat: Time, Distance, and Fatigue
In-Reply-To: Message of 5 Feb 1995 11:53
Comments: Derby Message #3357
Steve Roman wrote:
Belmont Stakes, but excluding the Preakness. The results
show that Seattle Slews and Affirmeds Preakness were
both within 2/5 of a second of the predicted value. The
predicted time for Secretariat is 1:52.3,*** certainly closer
to 1:53.2 than to the official 1:54.2.
Thanks for the feedback.
I also have a second model of Secretariat's Kentucky Derby and Belmont
which I did not post on 4 Feb.
I found a typing error in my 4 Feb post, correction shown below.
Kentucky Derby Model: Gate=30 ft from timing pole, time given in seconds
1/2 3/4 1mi 11/4
Actual Time 47.40 71.80 96.20 119.40 <-seconds
Secretariat 48.80 *72.90 96.25 119.40 <-est base on lengths**
EP Model Est. 49.05 71.55 95.05 119.40
Model Error> +.25 -1.35 -1.20 0 *Posted as 71.90 sec
Kentucky Derby #2 Model:
EP Model Est. 48.40 71.85 95.55 119.45
Model Error -.40 -1.05 -.75 +.05
Preakness Est. Using Derby Model #2
1/2 3/4 1mi 13/16
EP Model 47.90 71.15 94.65 112.40
(17.75 seec)
This second model is closer to your estimate of 1:52.60.
For reference:
Belmont Model #2 1/2 3/4 1mi 11/4 11/2
Secretariat's 46.20 69.80 94.20 119.00 144.00
EP Model Est. 45.95 69.95 94.45 119.20 144.20
Model Error -.25 +.15 +.25 +.20 +.20
Preakness Est. Belmont #2
1/2 3/4 1mi 13/16
EP Model 46.45 70.75 95.45 114.20
(18.75 sec)
This time is closer to the official time.
Conclusion: All four model show Secratariat's time for the Preakness
to be faster then the official time.
This kind of reminds me of the quote:
"A man with two watches does not know the time".
Larry