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