Tomorrow I'm off to the annual meeting of the Southern Economic Association in San Antonio. I organized a session titled "Economic Issues in the Equine Industry" and it includes papers by Brian Chezum (St. Lawrence), Ann Gillette (Kennesaw State), and Jill Stowe (U of Kentucky).

My paper is co-authored with Ryne Marksteiner, a Rhodes undergraduate. Below is a very brief summary.

The Effect of Age on Thoroughbred Racing Performance
The purpose of this study was to find the peak age for a thoroughbred’s racing performance and determine the rates at which a horse’s speed (as measured by Beyer speed figures) increases to its peak and declines past it. A horse’s speed figures may vary widely over the course of a career. The average speed figure for the Breeders’ Cup Juvenile, the Kentucky Derby, and the Breeders’ Cup Classic, are 100, 109, and 117, respectively, indicating substantial improvement with age. The differences between the speed figures indicate that for a 1¼ mile race, the typical Kentucky Derby winner would finish six lengths ahead of the typical Breeders’ Cup Juvenile winner and 5½ lengths behind the typical Breeders’ Cup Classic winner.

The dataset is composed of 202 male horses that are at least six years old and have made at least 45 starts. The table below groups horses into 24 categories based on age and shows the average difference between the speed figure a horse earned in a particular race and that horse’s career mean speed figure. For example, 95 horses made 231 total starts when they were less than 2½ years old. Speed figures for the horses running in these 231 races average 17.5 points below their career mean speed figure. This difference translates into seven lengths for a 6 furlong race. The speed figure difference is negative but smaller in size through age 3¼ years. Every category between 3¼ years and 5¾ years has a positive difference, indicating that horses typically run faster than their career mean between these ages. The peak difference occurs between ages 4¼ and 4½ when horses run 5 points faster than their career mean (two lengths faster for a 6 furlong sprint and three lengths faster for a one mile route). Beyond age 6¼, the speed figure differences are once again negative, because a typical horse is past his peak age and is consequently slowing down. Horses older than 9 years run an average 7.2 points slower than their career mean and 12.2 points slower than the peak age category. According to the table, horses improve by 22.5 points as young two-year-olds to the middle part of their four-year-old year and then decline by 12.2 points over the next five years. In sprint races this translates to a 9 length improvement to the peak and a 5 length decline. In route races it is a 14 length improvement to peak and a 7½ length decline. % Career Top SF is the percentage of horses that earned their career highest speed figure when they were the age of the corresponding category. 3% of the sample earned their best figure as a two-year-old. This increases to 22.9% as a three-year-old, 32.3% as a four-year-old, and 21.0% as a five-year-old. 79% of all horses in the sample earned their top speed figure below the age of six. Top SF is the best figure run by any horse in the corresponding age category.






(note: 20 is typo. It is meant to be >9)

The model assumes that horses have quadratic improvement up to the age of peak performance and experience a quadratic decline in racing ability past that age. Ray Fair in "Estimated Age Effects in Baseball" in the Journal of Quantitative Analysis in Sports (vol 4, p1-39) develops a model for aging effects in baseball that is used here for race horses. Peak age is estimated to be 4.38 years. At age 2 a horse is predicted to be 28 points slower than at peak age. The improvement over the first two years is dramatic and the subsequent decline is more gradual. Predicted speed figure by age for the mean ability horse is depicted in the figure below.