The entire performance–age curve for timed sports is concave and can be approximated by an expression of the form
P(t) = a(1 ‒ e‒*bt ) + c(1 ‒ e*‒*dt *), which reaches its maximum when
tm=1b+dln⁡(abcd).t_m = \dfrac{1}{b+d} \ln \left( \dfrac{ab}{cd} \right).
For men’s running events, performance peaks at an average age of 26, ranging from 23.3 for the 100 m to 31.6 for the marathon. The graph below shows how speed changes with age in the men’s 100 m, with the points representing the best performances in each age group.