Statistical Analysis: How Fast is Adam Peaty’s World Record?

Courtesy: Daniel Takata

A couple of days ago, Adam Peaty became the first man to break 57 seconds in the 100 breaststroke as he delivered an incredible 56.88.

He is also the only swimmer to ever break 58 and he has the 17 fastest performances of all time.

No one else has ever swam under 58.29 in the event.

I think I don’t need to explain why this record is one of the most legendary ever.

But what if there would be a swimmer capable of a similar performance in the 100 freestyle? Or in the 200 fly?

To imagine that, I conducted a statistical analysis using a methodology called Extreme Value Theory.

It is based on a scientific paper I wrote with Ligia Henriques-Rodrigues, a professor of the Department of Statistics at São Paulo University, called “Swimming performance index based on extreme value theory” published in the International Journal of Sports Science & Coaching*.

Basically, I took the times of the 150 best performers in each event and modelled the data in order to determine the probability of an specific time be exceeded.

Using Extreme Value Theory, we can determine the theoretic probability distribution of such data – this distribution is called Generalized Pareto distribution.

We now can evaluate the probability of Adam Peaty‘s world record being exceeded in the universe of the 150 best performers of all time. This probability equals to 0.3%.

Similar analysis can be conducted for other events. For example, the probability of Ryan Murphy‘s world record in the 100 backstroke being exceeded equals to 0.91%.

We now can evaluate the time in the 100 backstroke which leads to a probability of 0.3% to be exceeded. This would correspond to the time that matches Adam Peaty‘s world record. Such time is 50.49.

The same analysis is conducted for every other individual male event.

The stronger the time, the less the probability of exceedance.

The probability of the Peaty’s world record to be exceeded is, of course, very small.

What would be the time in the 100 freestyle, or in any other event, to match such probability?

The times are listed below (male events only).

Event    56.88 equivalent World Record
50 free 20.53 20.91
100 free 45.71 46.91
200 free 1:41.72  1:42.00
400 free 3:35.59 3:40.07
800 free 7:25.93 7:32.12
1500 free 14:09.87 14:31.02
50 fly 21.88 22.27
100 fly 48.94 49.82
200 fly 1:49.97 1:51.51
50 back 23.21 24.00
100 back 50.49 51.85
200 back 1:49.60 1:51.92
50 breast 25.86 25.95
100 breast 56.88 56.88
200 breast 2:02.54 2:06.67
200 IM 1:52.51 1:54.00
400 IM 3:59.90 4:03.84

It is really interesting to observe how fast the swimmers would have to be in some events to match Peaty’s record.

It would take 45.71 in the 100 freestyle.

3:35.59 in the 400 freestyle.

50.49 in the 100 backstroke.

2:02.54 in the 200 breaststroke.

And 3:59.90 in the 400 individual medley.

How many years will we have to wait until swimmers are capable of performing like this?

Adam Peaty is truly ahead of our time.

*Daniel Takata Gomes, & Ligia Henriques-Rodrigues (2019). Swimming performance index based on extreme value theory. International Journal of Sports Science & Coaching, 14(1), 51-62.

About Daniel Takata Gomes

Daniel Takata is editor of Swim Channel Magazine from Brazil, has a PhD in Statistics and is a college professor. He also works as a swimming TV commentator on SporTV and holds a website dedicated to sports analytics, Esportístico (www.esportistico.com.br).

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Charge

Can I give this 1000 likes?

Great analysis, Daniel!

Peaty is unhuman

Absolutely ends the debate

Richard

This is really cool— I’m curious whether the 150 swimmers are all-time performers, or active swimmers, or performances in the last year, etc. Specifically, if this includes supersuited swims, that would be even more impressive than I originally thought.

Richard

Never mind, I just saw best performers of all time, which I assume means it includes non-textile swims— that’s truly otherworldly

Facts

Gotta update that 200 fly world record!

Philip

Peaty = 100 breast GOAT.

To be so dominate in a 100 race is unprecedented.

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