Adam Peaty’s Project Immortal: A Mathematical Review


This article originally appeared in the Spring 2022 issue of SwimSwam Magazine. Subscribe here.

In 2016, peated adam won his first Olympic gold medal by winning the men’s 100 breaststroke in Rio de Janeiro. In the process, he set a new world record with 57.13, finishing more than 1.5 seconds ahead Cameron van der Burgh, silver medal. By then Peaty was the predominant swimmer in a single event and already one of the greatest swimmers of all time.

In 2017, he and his trainer Mel Marshall launched “Project 56”. He wanted to enter 56-second territory at a time when much of the world still couldn’t believe someone had broken 58. Said and done. At the 2019 World Championships in Gwangju, Peaty set a 56.88, which is the world record to date.

Having won his second Olympic gold medal in this event in Tokyo last year and unbeatable in the 100m breaststroke since 2014, Peaty is still setting very ambitious challenges. Now he’s considering what he and Marshall call “Project Immortal.” In his own words, “Making a time that can never be beaten – the next three years are how we do Project Immortal.”

Peaty has been in a league of his own since he first broke the 58-second barrier in 2015. He set world records few believed possible in our time. Now he wants to go beyond that and set a time that can never be beaten.

An impossible goal?

Sad news for him: it is unlikely to happen. Probably in 300 years swimmers will be setting times so fast that we can’t even imagine today – just like 56.88 would have seemed insane 40 years ago. You would think that one day someone would be able to swim the 100 meter breaststroke in 53 seconds.

In fact, it was calculated. In 2020, a very interesting scientific article was published in the Journal of the Royal Statistical Society, one of the most renowned journals in statistics. It’s titled Ranking and other properties of elite swimmers using extreme value theory, by Harry Spearing, Jonathan Tawn, David Irons, Tim Paulden and Grace Bennett, of Lancaster University. The researchers sought to estimate the limits of human performance using statistical data and methods, and they concluded that the ultimate world record in the men’s 100m breaststroke is 53.81.

This should be Peaty’s goal in his “Immortal Project”. And, obviously, that sounds crazy. We propose another objective (still ambitious, however). What date could he pass on to never see anyone beat him? In other words, a world record that would last as long as Peaty lived.

A new “Immortal Project”

The graph below shows the times of the world’s fastest swimmers in the men’s 100m breaststroke by year since 1960. We can see a clear downward trend, which is not surprising.

The world’s fastest times in the men’s 100m breaststroke over the years

Of course, the breakdown pattern was more dramatic in the early years. Then it started to stabilize, as shown by the dotted line. The line represents an exponential function, obtained by a mathematical procedure called nonlinear regression, and it is the best approximation of the data in mathematical terms.

(Note: World peak times in 2008 and 2009 have been adjusted to remove the effect of now-banned high-tech wetsuits, using statistical methodology detailed in SwimSwam Magazine’s 2021 Olympic Snapshot.)

This approach is a simple way to get an idea of ​​the ultimate world record, since it converges to a time limit. In this particular case, the function indicates a time limit of 53.99, which is very close to the ultimate world record estimated by the scientific paper of 2020. Moreover, we can estimate the world record of a year given. This is the link with the “Immortal Project”.

Since our goal is to estimate a world record that could last peated adam lives, we can perhaps think that 80 years from now, a world record that Peaty would set now would not be equaled until the year 2100.

For those who are interested, the mathematical function is:

time = 53.99 + 13.81 × e –0.021 × year

Where e = 2.7183 is a number called Euler’s number. It is as important in mathematics as π – this one, you may know him. (In this formula, the year is defined so that 1960 is year 0. So 2022 is year 62 and 2100 is year 140.)

Interestingly, by this function, the world record today would be 57.83, which is very close to the best time of the second fastest performer in history – 57.80 by the Dutch swimmer. Arno Kamminga. This seems reasonable since peated adam is really an outlier.

In 2100, the estimated world record is 54.72. Over the past 60 years we have seen the world record drop by 10 seconds. It is natural that over time the rate of improvement will decrease. In the next 78 years, according to this projection, the record will be bettered not by 10 seconds, but by two seconds. And yet, 54.72 seems beyond our imagination.

This is our suggestion for a target time for Peaty. It would be an immortal world record as long as he lived.

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