Estimated Age Effects in Athletic Events and Chess

Abstract

Rates of decline are estimated using record bests by age for chess and for various track and field, road running, and swimming events. Using a fairly flexible functional form, the estimates show linear percent decline between age 35 and about age 70 and then quadratic decline after that. Chess shows much less decline than the physical activities. Rates of decline are generally larger for the longer distances, and for swimming they are larger for women than for men. An advantage of using best-performance records to estimate rates of decline is that the records are generally based on very large samples. In addition, the age range is large. In this study the age range is 35 to 100 for swimming, 35 to 98 for track and field and running, and 35 to 94 for chess. The estimates also do not suffer from traditional forms of selection bias.

Acknowledgments

The author is indebted to William Sudderth and to the referees for helpful comments, to Linda Honikman for help with the road racing data, to Suzanne Rague for help with the swimming data, and to Oxana Marmer for research assistance.

Notes

¹Baker, Tang, and Turner (2003) is an example of a study using percentage rates of decline.

²For high jump the measure of performance is distance and for chess the measure is rating, where, unlike for time, larger is better than smaller. For simplicity, the following is written assuming time is the measure, but the switch to distance or rating is straightforward. Again, because of the use of percentages (logarithms), it does not matter whether the measure is in units of time, distance, or rating.

Notes. Sprint = 100-, 200-, and 400-m track. Run = all running except 100-, 200-, and 400-m track. M50 = 50-m and -yard swimming events, men. M100 = 100-m and -yard swimming events, men. M200 + = all other swimming events, men. W50 = 50-m and -yard swimming events, women. W100 = 100-m and -yard swimming events, women. W200 + = all other swimming events, women. HJ = high jump.

³For ease of comparison, the R _k values in Table 1 for the high jump and chess are reciprocals of the actual values.

⁴For example, the 10-year rate of decline for end age 50 is 100 (R ₅₀/R ₄₀ − 1). These rates were computed using unrounded values of R, not the values rounded to two decimal places in Table 1.

⁵The age factors are, however, smaller for M200 + versus M100 for ages 90 and 100, but this may be due to small sample problems at the very old ages.

Notes. M = meters; K = kilometers. M events are track, K events are road racing.

LCM = long course meters; SCY = short course yards. FR = free; BA = back; BR = breast; FL = fly; IM = individual medley.

Note. See notes to Table 1.

⁶Because of the collinearity between the estimates of k*and δ mentioned above, the following discussion focuses on the 10-year rates of decline in Table 1 rather than on the individual estimates of k* and δ.