Dominant Strategy in Olympic Artistic Gymnastics Scores
This past summer, many people tuned in to watch the Tokyo Olympic games. One of the most popular sports people tune into is Women’s Artistic Gymnastics. In the sport of gymnastics, gymnasts compose routines that maximize both their difficulty and execution scores in hopes to score higher than their competitors. Difficulty scores have no cap on how high it can go while execution scores are given from a scale from zero to ten, the two scores are added together to get a final score. The pandemic allowed an extra year of practice and more time for athletes to add more difficulty in order to make their routines competitive. With training videos and previous competitions, top gymnasts commonly know what skill/difficulty others will do and will try to add skills to raise difficulty but also make sure the skills can be executed cleanly.
We can use the concept of dominant strategy in the sport of gymnastics because of the way gymnasts react to each other. The definition of dominant strategy was established in class as a strategy that is the best response by Player 1 to any strategy of Player 2. Take the example below of two popular vaults gymnasts commonly perform: double twist (worth 5.4 difficulty) or an Amanar (worth 5.8 difficulty) .
- A can consistently do a double twist with perfect execution for a score of 15.4 every time.
- A can do an Amanar for a score up to 15.4, but it can be lower sometimes since it is not consistent. A will also get nervous B does it too, so the execution isn’t as clean and will get a 15.0 instead.
- B can perform under pressure and consistently gets 14.9 for a double, 15.5 for Amanar.
To maximize Athlete A’s score: if Athlete B chooses to do a double twist, then Athlete A should do a double twist since it is the most consistent and guarantees a good score. If Athlete B chooses to do an Amanar, Athlete A should still choose to do a double twist to maximize their own score. Here, doing the double twist is the dominant strategy for Athlete A. In real life, the double twist is a lot more consistent than an Amanar which is why it is the most popular vault at the Olympics. It has the perfect balance of difficulty and clean execution for many gymnasts. Of course, ideally, an athlete has a strictly dominant strategy such that no matter what the difficulty an opponent chooses, they have a competitive routine that wins. This is why Simone Biles is a huge name in the sport. She has a strictly dominant strategy of high difficulty and clean execution that no other athlete matched for the past 8 years.
Dominant strategy plays a huge role in constructing smart routines and innovating new skills. When opponents are increasing their difficulty, an athlete also has to increase theirs to keep up. This is why in the sport of gymnastics and other sports like ice skating and snowboarding, skills get more dangerous and innovative as time progresses. This phenomena is really similar to the arms race discussed in Ch 6.2 in the textbook. Athletes need to keep increasing their skills to be evenly matched with others in the same sport.
Sources:
Astor, Maggie. Olympic Gymnastics: What is a Cheng? A Double-Twisting Yurchenko? New York Times, 2021.
Easley, David, and Jon Kleinberg. Networks, Crowds, and Markets: Reasoning about a Highly Connected World. Cambridge University Press, 2019.