The Tour de France, which finishes this weekend, is regarded as one of the world’s toughest cycle races. Winning it is a psychological as well as a physical test.
The 113th edition of the world’s greatest cycling race finishes this weekend. The Tour de France is a team event that also has awards for individual riders. Even people who do not follow the Tour de France will be familiar with the iconic and much-coveted yellow jersey given out to the rider who completes the three-week tour the quickest cumulative time.
From an outsider’s point of view, however, perhaps the most intriguing questions about the Tour have nothing to do with the overall winner and more to do with understanding why riders repeatedly do things that seem irrational. Almost every day a small group of cyclists will attempt to break clear of the peloton (the main group of riders) despite knowing that they are unlikely to keep ahead of the pack and win the day’s stage. Why?
You would be forgiven for thinking that the most important science for understanding bike racing is biology: aerobic capacity, lactate clearance and muscle fibre composition all help determine how much power a rider can produce and for how long. If not biology, then surely physics? Cyclists must contend with gravity on the climbs and inertia whenever the pace changes.
Where the big bucks meet physics
When it comes to bike racing, cyclists act in response to the incentives they face. For a select few this might be personal glory, but this doesn’t explain the actions of the vast majority who will never win a grand tour.
Running a pro cycling team is not cheap, so teams rely on sponsors for financial support. In return, sponsors expect their brands to be highlighted to the Tour’s global TV audiences.
The most obvious way to do this is to go after the famous yellow jersey in the Tour’s general classification (GC), which determines the overall winner. But there are other prize jerseys to be won too: green for the points classification (for winning the spring stages), polka dots for the King of the Mountains (the best rider in the hill-climbing stages), white for the best young rider, plus daily awards for the stage winner and the most combative rider. One of the best ways to go about winning the latter is by getting into a breakaway.
You might think that the best riders would just get into the breakaway every day and win the race that way, providing non-stop coverage for their sponsors in the process. But that would be to neglect the very significant impact of air resistance. Walking around we barely notice its effect, but at 25mph (40km/h), professional cyclists can’t help but feel its drag.
Riders at the front of a group bear the brunt of the physical effort of cutting through the air, effectively shielding the riders behind them. By riding in a big group – the peloton – the hard work can be rotated. There is an incentive for everyone, even across rival teams, to cooperate because everyone benefits from sharing the aerodynamic burden.
So riders trying to get off the front of the peloton are penalised. A lone rider must do all the work, while even a small group has to spend far more time exposed to the wind than riders back in the bunch. The probability of a breakaway staying out is low. Even if it succeeds, only one rider can win. With the odds stacked against them, why do riders still go?
Game theory
Understanding these seemingly irrational actions is where game theory comes into its own. The primary motivation is the TV coverage afforded to the sponsors of the teams with a rider in the move. This provides the incentive team directors need to compel their riders to get into the breakaway. According to game theory, incentives dictate the actions of the “players”.
Despite the escapees’ best intentions, it is typically within the power of the peloton to pull back any breakaway. Indeed, breakaways containing any of the major yellow jersey contenders will usually not be allowed to escape in the first place. The risk is simply too great for the other GC contenders, so their teams will come to the front of the peloton, riding hard to pull them back.
But riders who are not a threat in the overall race may be allowed up the road. If it is a flat stage, one that the big sprinting contenders are interested in winning, then their teams will work together towards the end of the day to absorb the breakaway, giving their star performers a chance to battle it out for victory.
Even when a breakaway looks likely to hold off the charging peloton, game theory has one more nasty trick to pull. While the incentive at the start was for all the escapees to work together, as the finish approaches the calculus changes. In a sport where second is the first loser, former comrades turn back into competing individuals.
Riders stop taking turns doing the hard work at the front as they conserve energy for the finish. Those who do find themselves leading are forced to watch for attacks from rivals hoping to steal a march on the rest.
While finishing ahead of the chasing pack would be a better result for everyone than being caught, each rider has a personal incentive to save energy for the finish. The premium on winning over placing high means that the group slows, the peloton closes in, and everyone in the breakaway loses in what game theorists would call a tragedy of the commons.
The complexities thrown up by the incentive structures of grand tour cycling can be best understood through the maths of games, explaining why, from this cerebral and calculating angle, the sport is often referred to as “chess on wheels”.