Not all sports have strategic elements. There is not much strategizing in the 100-meter dash. You just run as fast as you can. That’s all there is to it. I have also never heard of a 100-meter racer employing a strategy coach. Mental coaching, yes, physical coaching, of course, yes, but strategic coaching, no. It is just not necessary. All they would say is: “Try to run as fast as possible” and you don’t need to pay someone to give you this kind of advice. There is probably also not much strategic concern in the long jump, the high jump, pole vaulting, and javelin. I guess there is little strategic thinking in most of athletics. But there are also lots of sports, even within or close to athletics, that do have a substantial element of strategic consideration.

Take the so-called “sprint” race of track cycling. The main rules are as simple as those of the 100-meter dash. To quote from a reliable source, “two riders race off over three laps to see who is fastest.”

The first time I watched such a race at some Olympics, I expected, now I know somewhat naively, that the race would be simply a cycling version of the 100-meter dash. The two cyclists would come out flying and race as fast as possible until one of them crosses the finish line. This is not what happens. What happens is that at the crack of the starting pistol essentially nothing happens. The two racers amble off, almost going as slowly as possible. You can see this for yourself. The front “racer” meanders around, sometimes veering left (or down the track, as the track is slanted) and sometimes veering right (or up the track). The other rider carefully mimics these movements. Sometimes they almost come to a standstill. This goes on for quite some time and all this time the front “racer” constantly turns their head to look back to check up on their opponent. At some, ex-ante unclear, point in time, one of the two, finally and suddenly, starts to pedal as hard as possible, with the other racer trying to catch this moment and trying to start pedaling as hard as possible as well. Finally, the race deserves its “sprint” name. 

Why don’t we see what I expected to see, that both cyclists race off as fast as possible from the start? Well, the reason is that this is simply, in the language of game theory, not a Nash equilibrium. When your opponent does race off as fast as possible, you do not want to do the same. What you want to do, this is the best response behavior as game theorists would call it, is that you go fast, yes, but behind the other cyclist, in their slipstream. Because of the physical advantage that this gives you, you do not have to exert quite as much effort as the front cyclist does, and after you have been in the slipstream for about two of the three rounds, you can come out of it with an even higher speed and overtake your opponent just before the finish line. More often than not, with that strategy, and if your opponent just races as fast as possible, you will come out on top.

Because of this, nobody just races off like that. I wonder if the current way the race pans out is what the original inventors of the sport had in mind. I wouldn’t be surprised if the original inventors were quite as naïve as I in thinking that the two cyclists would simply race as fast as possible. I could imagine that, for a while, the cyclists would even have done this. Imagine two very unevenly matched cyclists. The stronger of the two could then probably win simply by going as fast as possible. The slipstream effect is not THAT strong. It only becomes an issue, I would think, when the two cyclists are pretty similar in their athletic ability, and, thus, only when the sport becomes quite competitive. I couldn’t find any good source for the history of this event, but there are some indications that it took a while for the currently observed behavior to unfold. First, the sport has seen occasional rule changes: at some point, rules were added that cyclists are not allowed to stop completely or go backward or put their feet on the floor. These are indications that a Nash equilibrium had gradually established itself (because perhaps of a higher degree of competitiveness and a certain (slow?) learning) in which the competitors did that. The rules were then introduced because otherwise, the sport would have become too boring. Perhaps there were races that instead of the minute or so that a race should last, took hours to complete, because none of the racers was willing to start the race properly, thinking they would lose the advantage by doing so.

Second, another sprint event, the individual pursuit, was introduced, quite a bit later if I understood this correctly, that can also be seen as a rule change. In this case, however, with both kinds of races remaining (somewhat) popular. The individual pursuit is very much like the sprint race, except that the two cyclists start from opposite positions (half a track apart) from each other. Slipstream effects cannot come into it now.

In any case, the sprint race is actually quite interesting to watch, mainly because it has interesting strategic considerations. I guess what we are seeing is pretty close to Nash equilibrium behavior. Moreover, this Nash equilibrium behavior is quite complex. As it also probably strongly depends on the relative strengths of the two competitors, it is also somewhat varied. You don’t get the same predictable outcome in every race. All this, I believe, explains why the track cycling sprint event has remained a (reasonably) popular and Olympic event, despite or perhaps even because it has such strong strategic considerations that seem in strong contrast to the perhaps originally intended pure athletic nature of the competition.