Risk and reward

Today, the Tour de France begins three gruelling weeks of sun, scenery and summits, but what’s the key to winning in this elite world of small margins? How about appetite for risk? Ian and Javi are leading the breakaway.

Read more: https://www.maths.ox.ac.uk/node/72427

#shorts #maths #tourdefrance

How do you win the tour to France? In 2018, I co-authored a paper in which we looked at this question. And the idea is that a cyclist should ride in a group of cyclists called the Pelon to shield themselves from the wind and use less energy, but then make a strategic breakaway at a particular point to win the race. But what we didn’t look at in this paper was the chance of crashing. And this is crucial because at best a crash means that a cyclist loses time, but at worst it means that a cyclist would have to withdraw from the race altogether. So we decided to build a new mathematical model, one that not only balances energy and aerodynamics, but also factors in crash risk. Whilst cycling in the pelatin offers significant energy savings through drafting, it also carries a higher crash risk. Breakaway riders mitigate that risk but face different challenges like fatigue. Our model captures this trade-off by introducing an objective function. And within this objective function, we have the probability of crashing and the time gains that you have by making the breakaway. And we can tune this objective function according to the particular cyclist. For example, a cyclist that wants to win the entire tour defense would like to minimize crashing, whereas a stage hunter that wants to win a particular stage might be happy to take more risks. Importantly, our objective function can capture the fact that crashing is often much more significant for a cyclist than gaining a time advantage. Our model predicts that there is an optimal power that you should cycle at in order to make a breakaway. And the model also tells us if that breakaway will be successful or if the pelon will catch up and the cyclist will end up losing the race. One of the more surprising results we found is that it is possible to win a race using less energy than the average rider in the pelatin, provided you’re willing to assume a high enough level of risk. Nowadays, elite cycling isn’t just about physical performance. It’s about timing and strategy as well. And small differences such as the precise time in which a breakaway is attempted can be the difference between winning or losing a race. Our model offers a structured way of turning race day instincts into something quantifiable. That clarity can make a real difference for how things plan, react, and race.