The caller introduced himself as Steve Scharff and didn't waste time with small talk. "I have the answer," he announced. The tone of his voice indicated that he meant he had The Answer, the solution to the mysteries of handicapping.
"Write this down," he instructed, and I wrote it down. "V3 equals C times minus-E to the V1 power, where E is a universal constant with the value of 2.7l8, plus . . . "
As my head was spinning, I assumed that my caller was another one of the many brilliant crackpots who become fascinated by the racing game and start looking for mathematical certainties in a game where formulas do not work. But as I listened to his explanation, I began to realize that Scharff had dealt brilliantly with one of the most subtle and complex problems in handicapping--the effect of the early pace of a race on a horse's final performance.
The problem is so subtle, in fact, that I refused to accept its existence for most of my life as a horseplayer. I believed that horses were measured by the final time of their races. If an animal ran three quarters of a mile in 1:11, that time defined his ability. Whether he had engaged in a tough speed duel and covered the first half mile in 44 seconds, or whether he had been restrained and run the half in 46 seconds did not matter. He was a 1:11 horse, and he was superior to a rival who had been running in 1:11 1/5.
I clung to this neat, simple philosophy for many years, until a mountain of evidence piled up to contradict it. Nothing could have demonstrated the shortcomings of this simplistic approach better than the major 2-year-old races at Saratoga, the Hopeful Stakes for colts and the Spinaway for fillies.
In the Hopeful, three horses looked virtually even on the basis of final time (after adjustments to take into account the speed of the track on the day they had run). These were the fractions and final times of the contenders: [TABLE OMITTED]
Once I would have viewed this race as indecipherable. By now I was beginning to realize that Copelan was the vastly superior horse. Pax in Bello had earned his final time by racing close to a slow pace. Victorious had rallied after the leaders had engaged in a speed duel. But Copelan had earned his 1:10 4/5 time the hard way, battling for the lead at a fast pace that would have caused a lesser horse to collapse. In the Hopeful, Copelan blew his opposition away by more than three lengths and paid $8.60.
The next day's Spinaway Stakes was similar. Four of the fillies in the field were even on the basis of final times, but one of them, Share the Fantasy, had earned her final time by battling for the lead in fast fractions. She won by nearly five lengths and paid $15.40.
It had occurred to me that there might be some way to evaluate horses' fractions mathematically, to express Copelan's superiority over Pax in Bello with some kind of a sophisticated figure. But the difficulties seemed insuperable. While it may be easy to compare two front-runners on the basis of their early fractions, how does one compare their performance with that of a stretch-runner? I had no idea -- until the phone call from Steve Scharff.
Scharff, a 27-year-old New Yorker, did five years of graduate study in mathematics and physics; his special interest was general relativity. He teaches statistics and probability in college. When he started taking an interest in the racetrack, he naturally looked for a way to apply his mathematical expertise.
He perceived that the most efficient way for a horse to run is by maintaining a fairly even rate of speed thoroughout, decelerating slightly toward the end. But the more a horse deviates from this ideal pattern, running a very fast fraction somewhere, as Copelan did, the more impressive his performance is. What Scharff did was to calculate the horse's average speed for each quarter of a race and add those figures together to produce his speed rating.
Compare, for example, two horses who run six furlongs this way: [TABLE OMITTED]
Horse A covers the first two furlongs in 23 seconds; 2/23 equals .0869 furlongs per second. He covers the next two quarters in 24 seconds each; 2/24 equals .0833 furlongs per second. Adding 869, 833 and 833, his rating is 2535.
Horse B covers the first two quarters in 22 seconds each; 2/22 equals .909 furlongs per second. His rate for the final quarter is 2/27, or .740 furlongs per second. His rating (calculated by adding 909, 909 and 740) is 2548, clearly superior to Horse A despite their identical final times.
This is, in fact, a considerable simplication of Scharff's calculations. To evaluate fractional times with precision, a handicapper must deal with different distances and different track contours; he must take into account the effect of turns in slowing horses' rates of speed. Scharff's formula attempts to do all this, although the mathematics of it are beyond me. Even so, I sense that he may have made a significant contribution to the art of handicapping. Even if he has not found the all-encompassing Answer, he may have found a lower-case answer to a very difficult question.