# ON THE EFFECT OF AN AGE TO A RESULT OF AN ATHLETE

by
Aimo Niemi, Turku 1997

Introduction. It is well known that talent, age and exercise are the three most important factors, which affect the result of an athlete. The aim of this study is to find out the effect of the age alone. To do this the WR results of 43 events were analyzed using the records of September 1. 1997. Altogether the material comprised over 500 single records of the athletes of ages 25-95.

Method of the analysis. The method of the analysis was as follows. From the WR results of an event a mathematical formula was looked for, which would best explain the aging effect of the records. When over one hundred two parameter formulas were tested, the best fit was always obtained with the formula

(1) time = r25/[1+(25/b)³ -(age/b)³ ].

In the formula r25 is a result of an imaginary athlete of age 25. Other records of the event were then compared to this time resulting a normalized scale, which allows the comparison of different events. Table 1 gives examples of the procedure and pictures 1 and 2 show graphically the same thing. The values of the parameters r25 and b and their mathematical error estimates are given in the table 2. Using these values a normalized record set was created and then the hole sample was analyzed. Again over one hundred equations were tested and the best fits were studied. This time the top of the list was very even showing only marginal disparity between different formulas. When some of the most exotic were passed, the best fit to the sample was found with the formula

(2) y² = (z-age)*(z+age)/s² , z = 98.22 ± 0.23, s = 94.02 ± 0.40.

Picture 3 shows the result graphically. In it the shape of the line is defined by the parameter z whereas parameter s fixes the scale of the y axis. If needed, we get y=1 exactly with age=25 by using values z= 98.22, s=94.99 or with sufficient accuracy to most practical purposes

(3) y² = (98+age)*(98-age) / 95².

Discussion. The result obtained confirms well the two previous analyses, which the author has made with two completely different data sets. Altogether nearly 1600 data points have been used and so far, within the error limits, the result obtained has always been the same. This shows that formula (2) describes the aging effect very well and allows thus a simple method to compare the results of the athletes of different ages. Even the comparison of different events is possible, if formula (3) is used together with the parameters r25 from the table 2.

As an example suppose an athlete A, age=50, has got a time 1860 sec in men's 10 km running and athlete B, age=80, time 105 sec in men's 100 m breaststroke. Using formula (3) we calculate the aging index for A and B and get y=0.8872 for A and y=0.5958 for B. Multiplying the results of A and B with these values we get the age-adjusted results 1650.2 and 62.59. These are the results A and B would be capable, if they both were 25 years old. From table 2 we find the corresponding reference times 1621.9 and 63.26 sec (r25), which means that B is better than A. His time is 1.1% better than reference time whereas A's time is 1.7% slower.

TABLE 1. WR97 results of men's 100 m breaststroke and 10000 m running. Actual times are in seconds and normalized speeds are those obtained, when compared to the result of an imaginary athlete age 25.
age100 M BRST10000 M RUNNING
time speed time speed
25 63.26 1 1621.9 1
25-30 64.11 0.9867 - -
30-35 65.65 0.9636 - -
35-40 65.67 0.9633 1637.48 0.9905
40-45 69.79 0.9064 1710.88 0.9480
45-50 72.96 0.8671 1802.56 0.8998
50-55 72.38 0.8740 1861.90 0.8711
55-60 77.87 0.8124 1949.86 0.8318
60-65 80.56 0.7852 2054.88 0.7893
65-70 86.06 0.7351 2082.80 0.7787
70-75 91.05 0.6948 2303.69 0.7040
75-80 97.55 0.6485 2523.40 0.6427
80-85 106.92 0.5917 2669.86 0.6075
85-90 132.18 0.4786 3263.00 0.4971
90-95 188.18 0.3362 4300.78 0.3771

TABLE 2. Least square solutions of the parameters r25 and b in the formula WR97 = r25 /[1+(25/b)³ -(age/b)³ ]
eventr25[sec]b [year]
men's running 100 M 10.14 ± 0.20 116.01 ± 1.34
200 M 20.38 ± 0.32 113.28 ± 0.89
400 M 44.45 ± 0.50 107.59 ± 0.41
800 M 104.72 ± 1.78 108.50 ± 0.39
1500 M 209.24 ± 3.25 106.90 ± 0.29
3000 M 463.72 ± 4.89 107.90 ± 0.39
5000 M 771.71 ±12.65 106.98 ± 0.31
10000 M 1621.91 ±27.38 108.12 ± 0.64
MARATHON 7363.64 ±72.51 103.15 ± 0.58
men's swimming 50 M FREE 22.98 ± 0.30 114.19 ± 0.84
50 M FLY 24.44 ± 0.37 104.64 ± 0.69
50 M BACK 27.20 ± 0.48 110.72 ± 0.86
50 M BRST 29.67 ± 0.23 115.39 ± 0.76
100 M FREE 51.12 ± 0.70 111.12 ± 0.70
100 M FLY 56.57 ± 0.67 101.81 ± 0.42
100 M BACK 59.72 ± 0.80 108.53 ± 0.54
100 M BRST 63.26 ± 1.37 106.04 ± 0.69
200 M FREE 114.70 ± 1.34 110.56 ± 0.56
200 M FLY 131.77 ± 3.10 103.27 ± 1.48
200 M BACK 131.47 ± 1.87 108.15 ± 0.56
200 M BRST 143.48 ± 2.70 108.19 ± 0.74
200 M I.M. 126.22 ± 2.86 104.04 ± 0.58
400 M FREE 247.59 ± 3.21 110.07 ± 0.90
400 M I.M. 282.16 ± 3.70 106.40 ± 0.70
800 M FREE 516.82 ± 6.90 110.26 ± 0.94
1500 M FREE 1006.13 ±14.87 111.52 ± 0.77
women's swimming 50 M FREE 27.00 ± 0.31 114.17 ± 0.73
50 M FLY 28.09 ± 0.35 99.14 ± 0.33
50 M BACK 31.24 ± 0.27 109.74 ± 0.85
50 M BRST 34.10 ± 0.34 108.42 ± 0.62
100 M FREE 58.97 ± 0.62 108.95 ± 0.68
100 M FLY 65.56 ± 1.95 98.21 ± 1.23
100 M BACK 68.07 ± 0.85 106.99 ± 1.02
100 M BRST 76.20 ± 0.69 106.67 ± 0.73
200 M FREE 128.09 ± 1.58 103.79 ± 1.17
200 M FLY 144.61 ± 3.01 95.54 ± 1.13
200 M BACK 146.92 ± 2.33 106.64 ± 1.23
200 M BRST 167.88 ± 1.37 106.73 ± 0.65
200 M I.M. 149.14 ± 2.06 104.55 ± 0.96
400 M FREE 273.51 ± 2.79 105.50 ± 0.75
400 M I.M. 318.46 ± 5.12 104.18 ± 1.08
800 M FREE 561.90 ± 6.33 104.91 ± 0.53
1500 M FREE 1067.08 ±16.04 103.91 ± 0.65