i-Race 2009: Fun, Fitness, For All

Race model

We first looked at running distance (5K, 10K, half-marathon, full-marathon) with the world records plotted for each for different ages on a 3-D graph (International Athletic Association keeps this data). This data was smoothened using the stochastic frontier function The function was refitted for both the sexes (pooled data). This gave a 5th order polynomial in age, 5th order polynomial in race distance, 1st order polynomial in sex, and two cross-terms. This gives us the ability to theoretically predict the world record for any distance, and any age, and for men or women. Note that for "unusual" distances and age combination (say, age 48, 7.283 km, female), there is no world record recorded (and most likely, ever possibly of being recorded). But our model can give this number: 24.533 minutes (We get results within 3% of existing world records when we feed actual data.)

We then took another plot of race distances versus the heights and weights of the world's best athletes for those distance. This was fitted as a logarithmic curve. y = A*ln(x) + B. One for men, one for women. So for any race distance, we could get the weight, height and therefore BMI of the theoretical world record. Knowing our runner's height and weight, we can adjust the world record holder's weight for the runner's height. The runner may be much heavier than the theoretical world record holder (TWRH). So we adjust the best performance proportionately, as the runner has to lug more weight around than the TWRH person.

The race model is complete and all of you can check YOUR theoretical best performance for the race distance of your choice by following the calculator link.