Courtesy: Daniel Takata
A few days ago, I presented a statistical analysis of Adam Peaty‘s 100 breaststroke world record.
I used Extreme Value Theory, which is a branch of statistics which deals with extreme values, or rare values.
Using the times of the 150 best performers in each event, I modeled the data and concluded that Peaty’s world record is the more extreme among all men’s world records.
In other words, Adam Peaty’s 56.88 in 100 breast is the greatest current world record in men’s events.
And, to match this time in other events, 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, for example.
But what about women’s events?
Some say that Katie Ledecky‘s 800 and 1500 world records are the greatest among women’s records.
In the 800, Ledecky’s world record is 8:04.79, and no one else has ever swam under 8:14.10 in the event.
In the 1500, the world record is 15:20.48, and the second performer ever is at 15:38.88.
Others say that no record can match Sarah Sjostrom‘s 50 butterfly.
Her world record is 24.43, and no other woman has ever swam under 25.07.
Using Extreme Value Theory, I can compare these records not only with the second best performer of all time, but with a population of world class swimmers, and determine how extreme these records are.
I took the times of the 150 best performers in each event and modeled the data in order to determine the probability of these world records be exceeded.
We can determine the theoretic probability distribution of such data – this distribution is called Generalized Pareto distribution.
We now can evaluate the probability of Ledecky’s 800 world record being exceeded in the universe of the 150 best performers of all time. This probability equals to 0.465%.
Ledecky’s 1500 world record probability is 0.301%.
And Sjostrom’s 50 fly world record probability is 0.593%.
For illustration, the probability of Katinka Hosszu‘s world record in the 400 individual medley being exceeded equals to 1.151%.
And Regan Smith‘s 200 backstroke is 0.891%.
In these terms, the 1500 free world record is the greatest among the current women’s world record in swimming.
And what would be the time in the 100 freestyle, or in any other event, to match Ledecky’s probability in the 1500?
The times are listed below (women’s events only).
| Event | World Record | 15:20.48 Equivalent |
| 50 Free | 23.67 | 23.1 |
| 100 Free | 51.71 | 50.72 |
| 200 Free | 1:52.98 | 1:51.75 |
| 400 Free | 3:56.46 | 3:54.69 |
| 800 Free | 8:04.79 | 8:03.22 |
| 1500 Free | 15:20.48 | 15:20.48 |
| 50 Back | 26.98 | 26.18 |
| 100 Back | 57.57 | 56.77 |
| 200 Back | 2:03.35 | 2:01.80 |
| 50 Breast | 29.40 | 28.60 |
| 100 Breast | 1:04.13 | 1:02.80 |
| 200 Breast | 2:19.11 | 2:14.82 |
| 50 Fly | 24.43 | 24.16 |
| 100 Fly | 55.48 | 54.51 |
| 200 Fly | 2:01.81 | 1:59.52 |
| 200 IM | 2:06.12 | 2:03.70 |
| 400 IM | 4:26.36 | 4:22.16 |
It would take 50.72 in the 100 freestyle.
3:54.69 in the 400 freestyle.
2:01.80 in the 200 backstroke.
1:59.52 in the 200 butterfly.
And 4:22.16 in the 400 individual medley.
Unfortunately Katie Ledecky couldn’t swim the 1500 in the last World Championships.
But her world record stands as the greatest of women’s events.
And certainly one of the greatest of all time.
One could ask, how can we compare Ledecky’s record with Adam Peaty’s 100 breast record?
In fact, the probability of Peaty’s world record being exceeded in the universe of the 150 best performers of all time equals to 0.291%.
Remember the probability associated with Ledecky’s record is 0.301%), which means that Peaty’s record is a little bit more extreme than Ledecky’s.
Hence Peaty’s world record is the greatest current world record, among all men and women’s swimming events. But just by an inch.
To match Peaty’s record in women’s 1500 freestyle, it would take 15:20.09 – very close to the actual world record of 15:20.48.
In the following table we can see the times that would match Peaty’s record in every swimming event. Note that the times in women’s events are almost as fast as the times that would match Ledecky’s record, which means that Peaty’s 100 breast world record is almost as extreme as Ledecky’s 1500 world record. These two records are truly in the same difficulty level.
Women’s events
| Event | World Record | 56.88 Equivalent |
| 50 Free | 23.67 | 23.09 |
| 100 Free | 51.71 | 50.62 |
| 200 Free | 1:52.98 | 1:51.72 |
| 400 Free | 3:56.46 | 3:54.59 |
| 800 Free | 8:04.79 | 8:03.09 |
| 1500 Free | 15:20.48 | 15:20.09 |
| 50 Back | 26.98 | 26.17 |
| 100 Back | 57.57 | 56.74 |
| 200 Back | 2:03.35 | 2:01.75 |
| 50 Breast | 29.40 | 28.58 |
| 100 Breast | 1:04.13 | 1:02.77 |
| 200 Breast | 2:19.11 | 2:14.75 |
| 50 Fly | 24.43 | 24.14 |
| 100 Fly | 55.48 | 54.49 |
| 200 Fly | 2:01.81 | 1:59.47 |
| 200 IM | 2:06.12 | 2:03.64 |
| 400 IM | 4:26.36 | 4:22.06 |
Men’s events
| Event | World Record | 56.88 Equivalent |
| 50 Free | 20.91 | 20.53 |
| 100 Free | 46.91 | 45.71 |
| 200 Free | 1:42.00 | 1:41.72 |
| 400 Free | 3:40.07 | 3:35.59 |
| 800 Free | 7:32.12 | 7:25.93 |
| 1500 Free | 14:31.02 | 14:09.87 |
| 50 Back | 24.00 | 23.21 |
| 100 Back | 51.85 | 50.49 |
| 200 Back | 1:51.92 | 1:49.60 |
| 50 Breast | 25.95 | 25.86 |
| 100 Breast | 56.88 | 56.88 |
| 200 Breast | 2:06.12 | 2:02.54 |
| 50 Fly | 22.27 | 21.88 |
| 100 Fly | 49.50 | 48.94 |
| 200 Fly | 1:50.73 | 1:49.97 |
| 200 IM | 1:54.00 | 1:52.51 |
| 400 IM | 4:03.84 | 3:59.90 |
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).
Did you take into account that there are less 1500 swimmers?
Sure Katie’s record is greater, but Sarah’s world record is more untouchable. Katie has a great chance of rebreaking that 15:20, but there is no way Sarah is getting back to 24.4 form this late in her career. Truly a once-in-a-lifetime swim back in 2014.
This touches upon the way the distribution was fitted. It probably included the performances by Ledecky, Peaty, and Sjostrom. However, taking their performances out and fitting the distribution can yield the likelihood that someone ELSE will break their records. This may be a more accurate measure of how great their records are.
The other article states that the probability of Peaty’s world record being exceeded is 0.03%, whereas this article states that it is 0.291%. So which is it?
Actually I typed it wrong in the other article. It is 0.3%, rounded from 0.291%. My mistake, sorry. Thank you!
Would be interesting to use the swimrankings.com database and project, based on previous event trajectories, what times swimmers would have been expected to reach in their off events (but didn’t because they stopped swimming the event to specialize otherwise). E.g. What could Michael Phelps have gone in the 200BR? or What could Penny Oleksiak or Taylor Ruck have gone in the 200IM?
One have no basis to compare the records in swimming disciplines that have different level of development in competition. The results in well developed competition reflect to some degree the biological abilities of swimmers. The competition where a few are swimming tells practically nothing about limits. For instance, it is almost absurd to compare of how outstanding records are in female swimming from 1960s-1970s and in nowadays. The record holders were changing more frequently in the pass than now. The records life longevity is some other factor that has to be taken under consideration.
I love Peaty,,,but I worship Ledecky. Her 1500 which is part of this discussion was done during mid-season preparation. Her first 800 was 8:11+ and her latter 800 was 8:10+. The second best 800 by a
female is 8:14.1. She is the all time best in the 400, 800 and 1500 by ridiculous margins and is among the best ever in the 200 as well. She is the human being goat!
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Daniel – can you re-run this analysis for the women’s 200 fly, removing Liu Zige’s 2:01.81? (Make it her Beijing winning time, 2:04.18).
I would be very curious to see how much that affects the Peaty/Ledecky-level swim time.
If Ledecky had swum 1500 free in Rio, she would have swum 15.10-15.15.