To Kick or Not to Kick: Decision making for elite runners
Game theory has been applied to countless activities and sports, with each round of the game ending with scoring a point or winning the game. In track and field distance races, game theory acts as a continuous sequence of decisions made by runners, not to achieve the fastest times, but to achieve the best position in the group. For championship races, the magnitude of the winning time rarely matters, instead athletes are more focused on strategically maneuvering their way through the pack of runners over long distance races (1,500 to 10,000 meters), making sure they are in the best position or can power through to the end. In these races, large packs of runners often form from the beginning to the middle of the race, with most runners “sitting” instead of running at their fastest possible speed, saving their energy for a late “kick” at the last lap or few hundred meters to surge to the finish line. This type of strategic running does not guarantee a win by any means, but oftentimes can allow slower runs to creep to the front and reach a podium finish.
Jordan Wheeler from the University of Nebraska describes this situation in a field with N runners with two players, each with the strategy to Lead or Not Lead the race. He considered two types of models: a normal static and simultaneous game with a traditional payoff matrix, and an Extensive-Form Model which represents the game as being both dynamic and sequential. Using this Extensive model, graphs are formed by edges corresponding to specific strategies taken, connecting player nodes, and each node resembles a new round being played with a certain payoff at the end. This extensive model is useful for modeling racing because the runner reacts to another’s strategy throughout multiple rounds (or laps). The decision to lead or not to is important because the leader often dictates the pace, but has to push through some air resistance, while non-leaders can sit in the back and save energy, and this payoffs can be substantial when decisions to move around the pack are being made continuously over several laps.
This type of decision making is integral in strategic racing compared to all out or record breaking racing, because the main goal is to win or place highly in the race. Therefore, this type of racing requires payoffs involving a player’s remaining energy or VO2 max, which directly correlates a runner’s energy expenditure based on their oxygen consumption. Wheeler also found that Not Leading runners used 7.5% less energy due to less air resistance, demonstrating a quantitative payoff for these different strategies, and how they may affect one’s chances of winning. This research into game theory within racing is important because it shows decision making in games that are not necessarily turn-based (like tennis or chess), and the payoffs accumulate over a race lasting 4-30 minutes. Also, this can be used to guess an athlete’s current running shape or confidence level, as those who are not leading are likely not to be as fit or are counting on a last minute kick to pass other people. On the other hand, some runners may train to have above average sprinting speed, so that in distance events they are able to consistently out-kick any other runners who were not leading. Ultimately, the final payoff from this continuous Extensive game is the final positions of each runner within the race.
Source:
https://jordanmwheeler.com/work/school-work/Papers/ChampionshipStyleRacing_GameTheory.pdf