## 01 January, 2018

### Age factors

One important question that all master athletes ask themselves is how fast will their performances decline with age. Because decline they do. Once a athlete is past his prime (which is situated around an age of 25-30) performances start waning. The rate varies enormously from one individual to another but the tendency is there. A look at the men's long jump world records is telling. From a 8.95 m world record, held by a 28 years old, we arrive at 1.78 m for a 100 year old athlete. (Women's records follow the same tendency, declining, in the case of long jump, from a 7.52 m by a 26 year old athlete to 1.28 m for a 92 year old one).

What is most interesting is that the rate of decline is constant. When one considers the whole population of master athletes it looks as if every year between 40 and 80 is bringing an 8 cm loss in performance. (By the way, this appears to be equally true for men and women). The straight line of the graphic is indeed passing through the world record points for the 40-80 age bracket and is very close to the curve of best fit already for ages of around 30 and all the way up to 90. Of course, when it comes to individuals the corresponding evolution curve may have different rates but we expect it, barring accidents along the way or premature death, to have a universal behaviour starting from zero at birth and reaching zero again at some hypothetical maximal life span that should be around 120 years.

Given that the decline in performance as a function of age is perfectly regular, one can try to adjust the performance, correcting for age. This is exactly what the World Masters Athletics association is doing with the famous age factors. How does the empirical age factor compare with one that would be based on the straight-line decline model? In the figure below I give such a comparison. The basic formula is
$$F={b\over a-A}$$
where F is the age factor, A the age in years and a,b two parameters to be determined by the best fit. In the case of men's long jump the result of the fit of the empirical data by the formula above is excellent and leads to the values b=95 and a=126.

Similar results hold for all athletics disciplines. A more detailed analysis can be found in my publication "Scoring athletic performances for age groups", New Studies in Athletics 24 (2009) page 63.

Age factors can be proposed also for young athletes, below 20 years of age but I am not going to address this question here. However an almost linear progression appears to be true also for junior athletes. In the case of men's long jump the world record goes from slightly over 3 m at age 5 to over 8.5 m at age 19. This is a slightly less than 40 cm progression per year. Thus young athletes appear to speed up roughly five times faster than old athletes slow down.