We present each swimmer’s chances of winning the gold medal at the Tokyo Olympic. Statistical methods based on computational simulations were used in order to estimate the probability of winning the gold medal for each swimmer. Results from 2018 were considered in the calculations. The more recent the result is; the more impact it has on the probabilities.
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The method was determined by observing results from 2014 to 2016 and comparing them to what in fact occurred at the 2016 Olympic, in order to find the most suitable probability distribution. Of course, these probabilities will change, depending on how swimmers will swim until the Tokyo Olympic. The probabilities will be updated on a regular basis.
The approach here is to determine the probabilities in an empirical fashion. If you have a coin and you don’t know the chances of tails and heads, you can toss the coin, let’s say, 1,000 times. If you get 512 tails and 488 heads, the estimated probabilities are 51.2% and 48.8%, respectively.
So we don’t know what’s the chance of, let’s say, Simone Manuel, winning the 50 freestyle. Manuel could swim the event 1,000 times, as well as her adversaries, and we could count how many times she would win to estimate her winning probability. Obviously, this can’t be done. In this condition, we simulate the possible outcomes in a computer program using a statistical method.
How do we do that? Let’s go back to 2016. Manuel inwards in Rio with a 24.33 from the US Olympic Trials. In Rio, she managed to a 24.09. Cate Campbell came in with a 23.84, and in Rio, she went 24.15. And so on. I conducted the calculations and realized that, compared to the times registered from 2014 until the Olympic 2020, the times of the top swimmers in the Tokyo Olympic present a specific pattern of variability, well explained by the so-called normal distribution of probability.
Using the very same pattern of variability, it is possible to simulate the possible outcomes for Tokyo. Manuel has a 23.97 from 2019. So, her time for Tokyo Olympic is simulated according to that pattern of variability. In 1,000 trials, let’s say that her simulated times are 24.08, 23.90, 24.18, 24.01, 23.79, 23.89, etc. Her times will float around 23.97 with some erraticism. We do the same for every other swimmer.
Let’s say that, in 1,000 trials, Manuel has the best time of all swimmers in 800, so she has an 8% chance of winning. The same technique was shown in all events, according to the respective pattern of variation. In relays, the sum of the times of the dissolute swimmers of each country in each round of simulation was considered.