a mathematical justification of Why Jank trick shots are good

Some players in the badminton community like to look down upon what they see as “jank” shots or bad form. By the end of this post, I hope to convince you through game theory concepts that we should actually encourage more exploration of jank shots, and give our opponents a nice round of applause when they pull one off (while secretly plotting on how to counter their next attempt).

Game theory attempts to model strategic games in way to characterize their nature. One important concept to describing games is the Nash equilibrium, under which neither player can unilaterally play their strategy differently such that the player can do strictly better in the game. (However, it may be the case in general that both players change their strategies at the same time, and suddenly one or both players can do strictly better.)

Specifically in two-player, zero-sum games like badminton where only one player can win, Nash equilibrium are also Pareto optimal. This just means that no player can do better without the other being worse off. Then, if you can find a winning Nash equilibrium for you, you should play it!

I enjoy talking about the “best” or “optimal” badminton playing style. I personally think Kento Momota’s 2018-2019 performance could be characterized as such. Because his defense-counter attack style was so strong, other players could either choose to lose by attacking or to lose by rallying and eventually getting tired. Momota did not have a strong incentive to play all-out attack, other than against Anthony Ginting or other strong attacking players. Therefore, we could argue that Momota’s play style was close to a Nash equilibrium.

But badminton is interesting because the game is extremely complicated, both in terms of variance of factors… wind conditions, temperature, shuttle speeds, the mental and physical conditions of players, the different amounts of pressure to win at the Olympics, etc., and even individual actions are all different. The shuttle is never in exactly the same place, the angle and the position of the body is always different, and every molecule on every shuttle cock is unique.

In addition, Nash equilibriums are quite strict in definition. As soon as we show the smallest strategy shift that yields a better outcome, we no longer have an equilibrium. And one such tiny strategy shift is the jank shot.

No one expects it. Maybe YOU don’t even expect it when trying to play it. But when it goes over, your opponent(s) are often so confused that you either straight up or subsequently win the point. If you claim to have an optimal strategy, I would throw in a 1-2 jank shots per game. If my success rate is high and you don’t expect it, I have conquered your impenetrable optimal strategy with my Trojan Horse of chaotic racket movement.

But fear not, just devote enough mental focus to countering it and shut down that bs next time. If I play it too often, you can easily exploit me, or just relish in the loss of shot consistency from me having to do crazy bs every time.

So if you want to become a better badminton player, play jank shots! It’s a tiny game theory-approved exploit that just happens to teach us more about the beautiful chaos of badminton.

-M

Side Note: It has been proven that all finite games (finite sets of “pure” strategies and finite number of players) have a Nash equilibrium. But badminton pure strategies and actions are infinite.