If you have ever been to a cross country race, or a track meet, you know endurance running is boring. Runners can be going very slow and it’s hard to know how impressive it is, especially the races that take 20+ minutes. Recently championship races are getting harder and harder to watch, races that had audiences that spanned outside the running community. Specifically, I’m talking about races such as the olympics, D1 nationals or the IAAF championship. The short answer: the races have been getting slower. The confusing part is that the runners are not getting slower, just these races. The type of running that is leading to these slow races is “Strategic Running”
Strategic running is referring to the a method of running that focuses on winning. This is when you conserve your energy until the end of the race and right before the end you sprint (This is called kicking). This strategy doesn’t guarantee you the win but it gives you the best shot. It certainly will always beat someone running an honest race. When everyone in the race runs strategically, the race becomes very slow. We saw this in the 1500m at the last olympics, which was the slowest olympic 1500m in history.
We’re all familiar with the alternative choice to strategic running. Running as hard as you can for the whole race (honest racing). This strategy leads to world records and incredible performances, the problem is strategic running doesn’t win. Runners can still kick and usually do. These are the runners the hold the WRs and win the race. It only takes one or two runners in a race to make it “honest.” A couple runners start the race at a fast pace and the other racers will have no choice but to keep up. These races are exciting suspenseful, and awesome, but they’re getting rarer and rarer.
The game theory model we are going to create is one that uses two runner’s decisions in the race; runner1 and runner2, with two options; kick or honest. The utility will be as follows; 1st = 4u, 4th=1u, Fast Time(At least one runner chooses honest) = 1u, Same Strategy = 3u. We’re making the assumption that if you run honest, and get kicked down, you will get kicked down by 3 runners and get 4th. It would be more fitting to have an uncertain outcome for “same strategy” , but for simplicity we gave it 3u.
|HONEST||(3+1) = 4u, (3+1) = 4u||(1+1) = 2u, (4+1) = 5u|
|KICK||(4+1) = 5u,(1+1) = 2u||3,3|
Any economist can tell that the nash equilibrium is for both runner to kick, leading to that slow boring strategic race I’ve been talking about. Before I move on, let me explain why. If a runner runs honest it is the optimal choice for the other runner to kick; allowing the kicker to win and have the fast time. If a runner kicks it is still optimal for the other runner to kick and give themselves the best opportunity to win. This kind of decision making is leading to slow races. This last olympics Matthew Centrowitz won the 1500 meter in the slowest time ever to win the olympics. Mo Farah won the 10,000m run and the 5,000m at the London olympics using the kick strategy as well. Both of these runners ran slow races, but they won the gold medal.
World records are still being broken, just not at championship races like the olympics. That is because of the weighted utility. These races have utility focused winning(like our model), think about how much utility you have from getting a gold medal. The lesser known races have a lower utility for winning but the same utility for fast times. The shift incentives honest races. However, until olympic athletes start making tough choices we’re stuck with these slow races.