# Analysis: Ledecky vs. Sjostrom, Which is the Greatest Women’s World Record?

August 05th, 2019

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.

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

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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Oldbay

Would love to see more of these with NCAA, SCM and relay records!

Bee Pea

Absolutely. Dressel’s 17.6 in SCY 50 free would be great to see

Charge

Is there a database of all historical NCAA swims like FINA has?

PK Doesn't Like His Long Name

The women’s 200 fly stands out as somehow getting adjusted too much here-given that there’s only one swim faster than 2:04.69 since 2010, I’m surprised that 2:01 would get adjusted down 2 more seconds to match 15:20 or 56.88. If you compare it to all performances that weren’t from the year 2009, where would it stand?

Steve Nolan

I was thinking the same thing – we already think of 2:01 as pretty otherworldy (because it is) so it being 1:59 is just bonkers.

If anything I feel like that 200 fly record might be more of an outlier than Sjostrom’s 50 fly. (Which for all I know this article said I’m bad at reading leave me alone.)

tea rex

One problem with comparing the 150 fastest times across events: the 1500 historically has been swam much less than other events. Elite (female) distance swimmers might race it 2-3 times near peak performance in a year – and often 0 or 1 time in Olympic years. Meanwhile, a good 50 flyer could race it 2-3 times in a single meet. So, Ledecky’s 1500 may be statistically more of an outlier, but I think her 800 is more impressive because the all-time performers go a lot deeper in that event.

PK Doesn't Like His Long Name

The number of times an event gets raced in terms of one meet is less important when considering performers and not performances. A person swimming a 15:45 once vs swimming a 25.2 50 fly 3 times is going to be the same thing. I do agree that the number of instances of high level 800s vs high level 1500s on the female side (and a similar deal on the male side) makes the 800 record more impressive, in comparison.

Josh

True he’s using performers but I think most agree the distance events have less performers especially 1500.. still makes it statistically less likely to be broken per this math but yeah question is whether this accurately defines “greatest”

Tea rex

Ah, I didn’t read carefully enough – it is performers, not times. Still, a lot more swimmers will attempt the sprints in their career than the 1500.