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Thoroughbred race times distances and variability
T H O R O U G H B R E D R A C E TIMES, D I S T A N C E S A N D VARIABILITY J a m e s R. R o o n e y
RESULTS
SUMMARY Linear regression shows an almost perfect correlation for race distance versus time for different race courses, turf and dirt, over distances from 2 furlongs to 4 1/8 miles. There is less variability a m o n g track record times for sprint races as compared to distance races. This decreased variability for sprint races correlates indirectly with greater fatigue in such races.
INTRODUCTION In the continuing study of the factors involved in the causes of lameness and breakdown in Thoroughbred racehorses, a fuller understanding of the normal is the basis for reasonable understanding of the normal. The process of racing per se is an obvious factor of importance. Track geometry, surface characteristics, horse quality and condition, level of competition, rider skill, human intentions, etc. commingle to form a process of extraordinary complexity. In previous reports j- 6 an epizootological approach has been used to begin sorting out the effects of race length, season of the year, track surface conditions, turns, etc. on the frequency of lameness and breakdown. MATERIALS
AND
METHODS
Race record times for different race distances at seven race courses in North America were examined. Turf course records were available for four of the seven tracks, a Records were available for the usual race distances between four furlongs and two miles, and one track provided records from two furlongs to four and one-eighth miles. All distances were converted to meters for statistical evaluation by linear regression and Spearman's rank correlation analysis 7 a Data was obtained from the Daily Racing Form. Author's Address: Dept of Vet Sci, Univ of KY, Lexington, KY 40505 172
AND
DISCUSSION
1. The results of regression analysis for distance versus record times for dirt courses are summarized in Table 1 and for turf courses in Table 2. All records and distances, dirt and turf, were, then, combined, n = 157, providing, T=21.46+
07s
r2=0.98
It is apparent, as might be expected, that there is a near perfect correlation of distance and record times without regard to track or surface. It is also apparent that the constant, a~, is nearly the same whatever the track or surface, while the constant, ao, represents, at least in part, t h e " s i g n a t u r e " o f the specific race course. That these results have generality beyond horse racing is shown by the regression for human track records over the distances 100 to 30,000 meters b; that is, T = - 6 2 . 3 3 + .18
r E = 1.00
2. The standard deviation (S.D.) of the means of the record times for the usual race distances, 4 furlongs to 2 miles, for the seven tracks were calculated. The results are summarized in Figure 1. The S.D. tends to increase with the length of race. The Spearman correlation coefficient was statistically significant, r, = -.86, ranking distance, shorter to longer, versus S.D., largest to least. Therefore, the shorter the race, the less variation of record times a m o n g tracks and, conversely, of course, the longer the distance the greater the variation. This suggests that the time for shorter races is less dependent upon the specific track, being more dependent upon race distance per se. Obviously, then, track character (geometry, surface, etc.) becomes more important for race time as the distance increases. These are intuitively plausible results. The velocity drop during the last segment of races, a measure of fatigue as reported previously ~, is also shown in b Encyclopedia Americana, Int. Ed., 1977. Vol. 26, p. 900. EQUINE VETERINARY SCIENCE
F i g u r e 1. I n s p e c t i o n suggests a generally inverse r e l a t i o n s h i p b e t w e e n velocity d r o p a n d t h e S.D. (rs=-.59, a statistically significant inverse correlation). This r e l a t i o n s h i p is p r o b a b l y i n d i r e c t ; t h a t is, b o t h t h e v e l o c i t y d r o p a n d t h e S.D. a r e r e l a t e d t o race l e n g t h p e r se r a t h e r t h a n directly to e a c h o t h e r . W h i l e t h e s e results d o n o t directly relate t o t h e c a u s e s o f l a m e n e s s , t h e y d o p r o v i d e a m o d e s t l y objective b a c k g r o u n d f o r u n d e r s t a n d i n g t h e v a r i a b i l i t y o r race times, d i s t a n c e s a n d fatigue.
TABLEI L i n e a r R e g r e s s i o n o f D i s t a n c e vs. T i m e , D i r t C o u r s e s
T:ao+als ( T : time; s = distance)
Track 1
2 3 4 5 6 7
REFERENCES
1. Rooney, J.R. The relationship of length of race to fatigue and lameness in Thoroughbred racehorses. J. Eq. Vet. Sci. 2: 98, 1982 2. lbid The relationship of season of the year to lameness and breakdown in Thoroughbred racehorses. Ibid, 2: 174, 1982. 3. lbid The relationship of sex to breakdown in Thoroughbred racehorses. Eq. Vet Data 4: 132, 1983. 4. ibid Track condition in relationship to fatigue and lameness in Thoroughbred racehorses, lbid, 4: 134, 1983. 5. Rooney, J.R. and Genovese, R.L. A survey and analysis of bowed tendon in Thoroughbred racehorses. J. Eq. Vet. Scl. 1: 49, 1981. 6. Rooney, J.R. and McCue, M.C. Further studies on breakdown in Thoroughbred racehorses. Eq. Vet Data 4: 133, 1983. 7. Volk, W. Applied Statistics for Engineers. McGraw-Hill, NY, 1958.
ai .07 .08 .07 .07 .07 .07 .06
a,, -9.61 -24.73 -11.13 - 17.05 - 19.31 -14.98 -9.72
r2 1.00
1.00 1.00 1.00 0.98 0.99 1.00
r 2 = correlation coefficient a ° and a I are constants in the linear regression equation. These were calculated from the linear regression equation, T = a 0 + al x s
TABLE 2 Linear Regression for Turf Courses
Track A B C D
ao -13.41 -17.05 -9.36 -11.99
aI .07 .07 .06 .07
r2 0.99 1.00 1.00 1.00
FIGURE 1
s
g 6
5
5
~
4
4
0
3
3
o=
e~ 2
2
-~
1
;~
=a
0
\1.01 4, Volume 3 Number 5
S.D.
4.5,
~.68 5,
5.5,
6,
6.5,
~ 7,
lm,
17°,
11/16, 1i/8, 13/16, 11/4, 11/2',
IS/8,
13/4,
2m 173
RESULTS
SUMMARY Linear regression shows an almost perfect correlation for race distance versus time for different race courses, turf and dirt, over distances from 2 furlongs to 4 1/8 miles. There is less variability a m o n g track record times for sprint races as compared to distance races. This decreased variability for sprint races correlates indirectly with greater fatigue in such races.
INTRODUCTION In the continuing study of the factors involved in the causes of lameness and breakdown in Thoroughbred racehorses, a fuller understanding of the normal is the basis for reasonable understanding of the normal. The process of racing per se is an obvious factor of importance. Track geometry, surface characteristics, horse quality and condition, level of competition, rider skill, human intentions, etc. commingle to form a process of extraordinary complexity. In previous reports j- 6 an epizootological approach has been used to begin sorting out the effects of race length, season of the year, track surface conditions, turns, etc. on the frequency of lameness and breakdown. MATERIALS
AND
METHODS
Race record times for different race distances at seven race courses in North America were examined. Turf course records were available for four of the seven tracks, a Records were available for the usual race distances between four furlongs and two miles, and one track provided records from two furlongs to four and one-eighth miles. All distances were converted to meters for statistical evaluation by linear regression and Spearman's rank correlation analysis 7 a Data was obtained from the Daily Racing Form. Author's Address: Dept of Vet Sci, Univ of KY, Lexington, KY 40505 172
AND
DISCUSSION
1. The results of regression analysis for distance versus record times for dirt courses are summarized in Table 1 and for turf courses in Table 2. All records and distances, dirt and turf, were, then, combined, n = 157, providing, T=21.46+
07s
r2=0.98
It is apparent, as might be expected, that there is a near perfect correlation of distance and record times without regard to track or surface. It is also apparent that the constant, a~, is nearly the same whatever the track or surface, while the constant, ao, represents, at least in part, t h e " s i g n a t u r e " o f the specific race course. That these results have generality beyond horse racing is shown by the regression for human track records over the distances 100 to 30,000 meters b; that is, T = - 6 2 . 3 3 + .18
r E = 1.00
2. The standard deviation (S.D.) of the means of the record times for the usual race distances, 4 furlongs to 2 miles, for the seven tracks were calculated. The results are summarized in Figure 1. The S.D. tends to increase with the length of race. The Spearman correlation coefficient was statistically significant, r, = -.86, ranking distance, shorter to longer, versus S.D., largest to least. Therefore, the shorter the race, the less variation of record times a m o n g tracks and, conversely, of course, the longer the distance the greater the variation. This suggests that the time for shorter races is less dependent upon the specific track, being more dependent upon race distance per se. Obviously, then, track character (geometry, surface, etc.) becomes more important for race time as the distance increases. These are intuitively plausible results. The velocity drop during the last segment of races, a measure of fatigue as reported previously ~, is also shown in b Encyclopedia Americana, Int. Ed., 1977. Vol. 26, p. 900. EQUINE VETERINARY SCIENCE
F i g u r e 1. I n s p e c t i o n suggests a generally inverse r e l a t i o n s h i p b e t w e e n velocity d r o p a n d t h e S.D. (rs=-.59, a statistically significant inverse correlation). This r e l a t i o n s h i p is p r o b a b l y i n d i r e c t ; t h a t is, b o t h t h e v e l o c i t y d r o p a n d t h e S.D. a r e r e l a t e d t o race l e n g t h p e r se r a t h e r t h a n directly to e a c h o t h e r . W h i l e t h e s e results d o n o t directly relate t o t h e c a u s e s o f l a m e n e s s , t h e y d o p r o v i d e a m o d e s t l y objective b a c k g r o u n d f o r u n d e r s t a n d i n g t h e v a r i a b i l i t y o r race times, d i s t a n c e s a n d fatigue.
TABLEI L i n e a r R e g r e s s i o n o f D i s t a n c e vs. T i m e , D i r t C o u r s e s
T:ao+als ( T : time; s = distance)
Track 1
2 3 4 5 6 7
REFERENCES
1. Rooney, J.R. The relationship of length of race to fatigue and lameness in Thoroughbred racehorses. J. Eq. Vet. Sci. 2: 98, 1982 2. lbid The relationship of season of the year to lameness and breakdown in Thoroughbred racehorses. Ibid, 2: 174, 1982. 3. lbid The relationship of sex to breakdown in Thoroughbred racehorses. Eq. Vet Data 4: 132, 1983. 4. ibid Track condition in relationship to fatigue and lameness in Thoroughbred racehorses, lbid, 4: 134, 1983. 5. Rooney, J.R. and Genovese, R.L. A survey and analysis of bowed tendon in Thoroughbred racehorses. J. Eq. Vet. Scl. 1: 49, 1981. 6. Rooney, J.R. and McCue, M.C. Further studies on breakdown in Thoroughbred racehorses. Eq. Vet Data 4: 133, 1983. 7. Volk, W. Applied Statistics for Engineers. McGraw-Hill, NY, 1958.
ai .07 .08 .07 .07 .07 .07 .06
a,, -9.61 -24.73 -11.13 - 17.05 - 19.31 -14.98 -9.72
r2 1.00
1.00 1.00 1.00 0.98 0.99 1.00
r 2 = correlation coefficient a ° and a I are constants in the linear regression equation. These were calculated from the linear regression equation, T = a 0 + al x s
TABLE 2 Linear Regression for Turf Courses
Track A B C D
ao -13.41 -17.05 -9.36 -11.99
aI .07 .07 .06 .07
r2 0.99 1.00 1.00 1.00
FIGURE 1
s
g 6
5
5
~
4
4
0
3
3
o=
e~ 2
2
-~
1
;~
=a
0
\1.01 4, Volume 3 Number 5
S.D.
4.5,
~.68 5,
5.5,
6,
6.5,
~ 7,
lm,
17°,
11/16, 1i/8, 13/16, 11/4, 11/2',
IS/8,
13/4,
2m 173