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Meng Lu <lumeng3@gmail.com>
Aug. 7, 2012

  1. Data
  2. Variables
  3. Analysis
    1. Distribution of performance improvement indicators
    2. Sub-sample of great performance improvers
    3. Performance improvement v.s. age
  4. Swimmers who achieved good performance improvement in 400m IM over the 2011-2012 period
  5. Swimmers who gained better performance improvement than Ye Shiwen over the 2011-2012 period
  6. References

16-year-old Chinese swimmer Ye Shiwen swam more than 5 seconds faster than her personal best in women's 400m individual medley (IM) in London 2012 Olympics, winning her a gold medal. This performance received high exposure to media and mixed comments, even controversy. For example, the prestigious scientific magazine Nature published a news report titled "Why great Olympic feats raise suspicions -- 'Performance profiling' could help to dispel doubts" [1] and immediately raised great attention and a great number of reader comments. In the following, I analyze short-term performance increase of top swimmers in 400m IM during 2011 and 2012, and attempt to contrast that to Ye Shiwen's, using Fédération Internationale de Natation (http://www.fina.org) data [2]. I hope to bring some data perspective to the issue.

Data

The FINA 40m IM data sets contains the 300 fastest race times recorded in 2011 and 2012 respectively, and for male and female swimmers, respectively. It turns out there are 195 female and 191 male swimmers who have both a 2011 time and a 2012 time, which will be used in the following analysis.

FINA data has two pool course sizes: long course (LC) and short course (SC) however the latter is different from the Olympic standard pool size. We'll include SC times in the analysis for comparison, but will keep it separate from LC times.

Here is the first 10 rows from the data sets for "women's 400m IM, LC":

time name country event date event event city event country qualify for
4:28.43 Ye, Shiwen CHN 28/07/2012 2012 Olympic Games London GBR OQT
4:31.27 Beisel, Elizabeth USA 28/07/2012 2012 Olympic Games London GBR OQT
4:32.20 Zheng, Rongrong CHN 08/01/2012 National Spring Championships2 2012 Nanning CHN OQT
4:32.67 Miley, Hannah GBR 03/03/2012 British Gas Swimming Champs 2012 London GBR OQT
4:32.83 Hosszu, Katinka HUN 29/03/2012 2012 Indianapolis Grand Prix Indianapolis USA OQT
4:32.91 Li, Xuanxu CHN 28/07/2012 2012 Olympic Games London GBR OQT
4:33.45 Rice, Stephanie AUS 15/03/2012 2012 EnergyAustralia Swimming Adelaide AUS OQT
4:33.91 Belmonte Garcia, Mireia ESP 29/03/2012 Spanish Open Spring Swimming Championships Malaga ESP OQT
4:34.48 Leverenz, Caitlin USA 25/06/2012 USA Olympic Team Trials Omaha USA OQT
4:35.68 Jakabos, Zsuzsanna HUN 21/05/2012 European Swimming Championships Debrecen HUN OQT
4:36.21 Evans, Blair AUS 27/01/2012 South Australian State Open Championships Adelaide AUS OQT
4:36.64 Otsuka, Miyu JPN 02/04/2012 2012 Japan National Championships Tokyo JPN OQT
4:37.48 Willmott, Aimee GBR 03/03/2012 British Gas Swimming Champs 2012 London GBR OQT

Direct data download

(I'll zip up the cleaned data and host it on Google Drive soon.)

Variables

We define the following variables to simplify our discussion of the analysis:

  • t_{2011}: swimmer's best 400m IM time in 2011
  • t_{2012}: swimmer's best 400m IM time in 2012
  • \tau_{2011}: date when t_{2011} is achieved
  • \tau_{2012}: date when t_{2012} is achieved

and compute several derived quantities that can be used as swimmer's performance improvement indicators:

  • dt = t_{2011} - t_{2012}: absolute improvement (unit: second); it should be positive if 2012 performance is faster than that of 2011;

  • \delta t = \left(t_{2011}-t_{2012}\right)/t_{2011}: relative improvement (unit: %)

  • \delta t' = \left(t_{2011} - t_{2012} \right)/\left( t_{2011} \left( \tau_{2012} - \tau_{2011} \right) \right): time rate of relative improvement (unit: %/day)

Ye's performance improvement in 400m IM during 2011-2012 is

  • dt = 5.23~\mathrm{sec}

  • \delta t = 1.91\%

  • \delta t' = 0.0067\%/\mathrm{day}

Analysis

Distribution of performance improvement indicators

We examine the distributions of three performance improvement indicators dt, \delta t, and \delta t' in histograms and quantile plots:

dt.png deltat.png deltatprime.png

The distribution of \delta t is closest to a normal distribution, which has standard deviation 0.379 sec and mean 3.45 sec. Ye Shiwen's \delta t = 5.23 sec is at 1.41 sigma. She is in the top 8% highest relative performance improvement.

One can compare Ye to all 400m IM swimmers in the \left(t_{2011}, t_{2012}\right) space:

t2011-t2012.png

A few comments:

  • The sample points are approximately distributed along the diagonal, which likely suggests that for the majority top swimmers, there is no systematic improvement within a short time window < 2 years. So dividing the performance improvment (\delta t or dt) by time (d\tau) is not terribly relevant as data doesn't suggest such trend.

  • The sample also obviously seperates into two categories: male and female. Although, the distribution of the two categories seem similar up to a shift of their center. (More quantitative study is due on this.) So it is intriguing to shift and combine the two categories and study the shape characteristics of the distribution for the combined sample.

  • Interestingly but not surprisingly, Ye is at the relatively unique place that her 2011 and 2012 best performance t_{2011} = 4:33.66 sec and t_{2012} = 4:28.43 sec are both in between majority male and female swimmers. Therefore it is non-trivial to compare her with either the majority of male swimmers or the female ones. But this might not be exactly surprising, given that she's the world's No. 1 female in this event.

  • The SC times enjoy a greater performance gain and lies below the diagonal. A short course pool might mean improvement on the pool-end technique can significantly contribute to the overall time improvement. (Just a guess though!)

  • It seems the more of the top female and male swimmers tend to have a performance increase as compared to others within same sex category, as the lower left corner of each sex category slightly bends below the diagonal.

  • Similarly, the swimmers with worst 2011 best performance t_{2011} tend to have performance improvement. This is probably simply because they have more room/potential for improvement compared to the best of the best.

  • There seem to be a higher fraction of male swimmers who gain a better best performance in 2012 than that of female swimmers. (Visually, there are more squares under the diagnol than dots.)

One can also plot the performance improvement indicators against 2011 best performance t_{2011} and the period of time d\tau in between 2011 and 2012 best performances to see some of these trends:

improvment-t2011-dtau.png

Sub-sample of great performance improvers

To select a subsample of performance improvers to compare with Ye's significant performance improvement in London 2012 Olympics, one can select out swimmers who has at least one of the three performance improvement indicator better than 85% of that of Ye's. We also restrict to "LC" which is the pool size same as or closer to the Olympics swimming pool size. It turns out there are as many as 68 swimmers satisfying this condition. (See table in Section 4). Furthermore, there are actually 21 of them who beat Ye Shiwen in all the three improvement indicators. (See table in Section 5).

Performance improvement v.s. age

It is also noticable that younger swimmers are more likely to gain performance improvement. Most great performance improvement are done by swimmers under 22. And Ye doesn't look terribly anomalous in gaining a high performance improvement among many other top teenage swimmers:

improvment-age-height-mass.png

Swimmers who achieved good performance improvement in 400m IM over the 2011-2012 period

name sex country d\tau t_{2011} d t \delta t \delta t' age height weight t_{2011} 2011 best performance t_{2012} 2012 best performance
Trombetti, Luisa F ITA 81 293.7 5.9 0.0248 19.6 4:53.70 Italian Open Winter Nationals 2011 4:47.80 Italian National Spring Championships
Suggitt, Chris M GBR 78 269.81 4.71 1.74 0.0223 4:29.81 British Gas Swim Wales Winter 4:25.10 British Gas Swimming Champs 2012
Rousseau, Sebastien M RSA 157 266.95 9.12 3.41 0.0217 21.9 1.9 80 4:26.95 Minneapolis Grand Prix 4:17.83 Sa National Aquatic Championships
Meyer, Michael M RSA 136 263.87 7.45 2.82 0.0207 24.66 4:23.87 Open Dutch Championships 4:16.42 Sa National Aquatic Championships
Caldwell, Katy F CAN 49 291.09 2.83 0.972 0.0198 18.6 4:51.09 2011 Canada Cup 4:48.26 2012 Austin Grand Prix
Chen, Xinyi F CHN 167 289.95 8.94 3.08 0.0184 14.6 4:49.95 7th National City Games 2011 4:41.01 National Swimming Championships
Cuoghi, Alessandro M ITA 81 262.94 3.58 1.36 0.0168 21.6 4:22.94 Italian Open Winter Nationals 2011 4:19.36 Italian National Spring Championships
Maestri, Riccardo M ITA 81 270.16 2.92 1.08 0.0133 18.3 1.77 74 4:30.16 Italian Open Winter Nationals 2011 4:27.24 Italian National Spring Championships
Mann, Becca F USA 227 290.17 8.56 2.94 0.0129 14.6 4:50.17 Minneapolis Grand Prix 4:41.61 USA Olympic Team Trials
Ventrone, Stefano M ITA 81 271.73 2.8 1.03 0.0127 21.6 4:31.73 Italian Open Winter Nationals 2011 4:28.93 Italian National Spring Championships
McMaster, Keryn F AUS 121 290.8 4.43 1.52 0.0125 4:50.80 2011 McDonald's Queenslands Championships 4:46.37 2012 Australian Age Champs
Mckeown, Taylor F AUS 121 289.32 4.29 1.48 0.0122 4:49.32 2011 McDonald's Queenslands Championships 4:45.03 2012 Australian Age Champs
Seltenreich-Hodgson, Erika F CAN 311 294.3 10.5 3.56 0.0114 17.6 4:54.30 2011 Canadian Age Group Championships 4:43.80 Mare Nostrum
Berrada, Morad M MAR 92 268.27 2.69 0.0108 21.12 4:28.27 Arab Games 2011 4:25.58 Elite French Championships
Coton, Quentin M FRA 241 268.85 6.63 2.46 0.0102 21.04 4:28.85 Summer Nationals 4:22.22 Elite French Championships
Beraud, Romain M FRA 241 270.91 6.53 2.41 0.01 23.98 4:30.91 Youth Senior Open Championships 4:24.38 Elite French Championships
Tutumi, Takahiro M JPN 213 265.35 5.47 2.06 0.00967 19.9 4:25.35 Japan Inter-College Swimming Competition 4:19.88 2012 Japan National Championships
Siwicki, Breanne F CAN 250 293.79 7.01 2.38 0.00954 17.6 4:53.79 Summer Nationals 4:46.78 2012 Canadian Olympic and Paralympic Trials
Geni, Simone M ITA 81 269.98 2.04 0.755 0.00932 4:29.98 Italian Open Winter Nationals 2011 4:27.94 Italian National Spring Championships
Gilmour, Tianni F AUS 121 295.65 3.31 1.11 0.00925 4:55.65 2011 McDonald's Queenslands Championships 4:52.34 2012 Australian Age Champs
Wedel, Kevin M GER 309 268.84 7.64 2.84 0.00919 18.6 4:28.84 38th European Junior Championships 2011 4:21.20 124th German Championships
Hosszu, Katinka F HUN 116 275.76 2.93 1.06 0.00915 4:35.76 UT Invite Long Course Time Tri 4:32.83 2012 Indianapolis Grand Prix
Soerensen, Katrine F DEN 245 293.96 6.58 2.23 0.00913 4:53.96 Summer Nationals 4:47.38 Danish Open
Donaldson, Mitchell M NZL 107 270.86 2.62 0.967 0.00904 4:30.86 2011 Auckland Age Groups Invit 4:28.24 State 2012 NZ Open Championships
Mann, Karley F GBR 356 294.94 9.3 3.15 0.00885 18.6 4:54.94 British Gas ASA Youth Champs 2011 4:45.64 British Gas Nat Youth MC Chmps 2012
Glavnyk, Iryna F UKR 238 294.7 6.21 2.1 0.00885 16.24 1.74 58 4:54.70 38th European Junior Championships 2011 4:48.49 Open Ukrainian National Championships
Pinto, Andreina F VEN 181 292.6 4.58 1.56 0.00864 4:52.60 XVIII National Games 4:48.02 2012 US Santa Clara International
Lowe, Danielle F GBR 356 295.9 9.1 3.07 0.00863 17.6 4:55.90 British Gas ASA Youth Champs 2011 4:46.80 British Gas Nat Youth MC Chmps 2012
McKee, Anton Sveinn M ISL 281 270.15 6.51 2.4 0.00857 4:30.15 38th European Junior Championships 2011 4:23.64 Icelandic National Championships
Persson, Erik M SWE 260 271.82 5.86 2.15 0.00829 18.6 4:31.82 38th European Junior Championships 2011 4:25.96 Danish Open
Quah, Zheng Wen M SIN 122 264.33 2.63 0.994 0.00815 15.85 1.75 57 4:24.33 XXVI Sea Games 2011 4:21.70 Singapore National Age Group Championships
Proud, Stephanie F GBR 223 288.31 5.21 1.8 0.0081 23.99 1.68 65 4:48.31 2011 FINA World Championships 4:43.10 British Gas Swimming Champs 2012
Kochetkova, Kristina F RUS 261 294.48 6.08 2.06 0.00791 19.52 4:54.48 Russian National Swimming Cup 4:48.40 International Meeting
Kuhn, Sierra F USA 231 293.88 5.17 1.75 0.00761 4:53.88 2011 Conoco Phillips National Championships 4:48.71 2012 NCSA Junior National Swim
Smiddy, Sam M USA 234 268.74 4.58 1.7 0.00728 18.6 4:28.74 2011 Speedo Junior National Championships 4:24.16 2012 Indianapolis Grand Prix
Gyurta, Gergely M HUN 281 261.9 5.34 2.03 0.00725 20.903 1.74 68 4:21.90 CXIII Hungarian Swimming Championship 4:16.56 Open National Championships
Aoki, Takehiro M JPN 213 268.36 4.02 1.49 0.00703 4:28.36 Japan Inter-College Swimming Competition 4:24.34 2012 Japan National Championships
Schepers, Jan David M GER 282 264.71 5.24 1.97 0.00701 4:24.71 German Championships 4:19.47 Qualification for European Championships
Nguyen, Thi Anh Vien F VIE 214 294.65 4.38 1.48 0.00694 15.74 1.72 53 4:54.65 XXVI Sea Games 2011 4:50.27 1st SEA Swim Championships
Tezuka, Yuki M JPN 114 261.93 2.04 0.778 0.00683 17.6 4:21.93 2011 JPN Open 4:19.89 2012 Victorian Championships
Mori, Yousuke M JPN 213 261.22 3.79 1.45 0.00681 4:21.22 Japan Inter-College Swimming Competition 4:17.43 2012 Japan National Championships
Vanderkaay, Peter M USA 398 263.28 7.06 2.68 0.00673 28.48 1.93 90 4:23.28 2011 Michigan Grand Prix 4:16.22 2012 NC Charlotte UltraSwim
Ye, Shiwen F CHN 285 273.66 5.23 1.91 0.0067 16.27 1.6 45 4:33.66 7th National City Games 2011 4:28.43 2012 Olympic Games
Zhou, Min F CHN 365 284.69 6.86 2.4 0.0066 4:44.69 National Swimming Championships 4:37.83 National Swimming Championships
Hersey, Kathleen F USA 139 286.03 2.61 0.912 0.00656 22.46 1.8 64 4:46.03 Minneapolis Grand Prix 4:43.42 2012 Indianapolis Grand Prix
Kuramatsu, Mako F JPN 213 292.16 4.05 1.38 0.0065 4:52.16 Japan Inter-College Swimming Competition 4:48.11 2012 Japan National Championships
Tanaka, Mizuho F JPN 259 291.18 4.76 1.63 0.00631 18.6 4:51.18 National Games - Swimming Competition 4:46.42 Japan Open 2012
Suvorau, Yury M BLR 390 267.71 6.36 2.37 0.00609 21.36 4:27.71 2011 Open Champ of Belarus 4:21.35 European Swimming Championships
Satou, Gou M JPN 213 271.41 3.46 1.27 0.00598 4:31.41 Japan Inter-College Swimming Competition 4:27.95 2012 Japan National Championships
Weiss, Michael M USA 328 261.35 5.04 1.92 0.00587 4:21.35 2011 Conoco Phillips National Championships 4:16.31 USA Olympic Team Trials
Gilliland, Jared M AUS 298 270.15 4.66 1.72 0.00578 4:30.15 XLIV Santa Clara International 4:25.49 2012 Australian Age Champs
Kron, Kristian M SWE 364 271.52 5.47 2.01 0.00553 4:31.52 Swedish Championships 4:26.05 Swedish Championships 2012
Le Clos, Chad M RSA 327 256.88 4.64 1.8 0.00552 4:16.88 10th All African Games - Maputo 2011 4:12.24 2012 Olympic Games
Fraser-Holmes, Thomas M AUS 349 256.75 4.94 1.92 0.00551 4:16.75 2011 Telstra Australian Swimming Championships 4:11.81 2012 EnergyAustralia Swimming
Evans, Blair F AUS 301 280.86 4.65 1.65 0.0055 4:40.86 2011 Telstra Australian Swimming Championships 4:36.21 South Australian State Open Championships
Adams, Cammile F USA 304 282.99 4.72 1.66 0.00548 20.906 4:42.99 2011 Conoco Phillips National Championships 4:38.27 2012 ST TXLA Elite Invite
Tikhonov, Alexander M RUS 318 259.73 4.49 1.72 0.00543 4:19.73 2011 Barcelona Mare Nostrum 4:15.24 Russian National Swimming Championships
Fujino, Maiko F JPN 359 283.97 5.42 1.9 0.00531 29.2 1.61 57 4:43.97 2011 International Competition Selection Trial 4:38.55 2012 Japan National Championships
Hagino, Kosuke M JPN 435 254.58 5.64 2.21 0.00509 17.98 1.75 70 4:14.58 2011 Japan Open 4:08.94 2012 Olympic Games
Muir, Ross M GBR 399 264.23 5.13 1.94 0.00486 4:24.23 British Gas ASA National Championships 4:19.10 British Gas Nat Youth MC Chmps 2012
Oldershaw, Marni F CAN 363 291.56 5.07 1.73 0.00479 4:51.56 World Trials 4:46.49 2012 Canadian Olympic and Paralympic Trials
Stevens, Leah F USA 405 295.04 5.62 1.9 0.0047 15.6 4:55.04 2011 SE NAC Summer Sizzler 4:49.42 2012 ST TXLA American LC Champ
Stitski, Monika F CAN 323 295.23 4.45 1.5 0.00466 4:55.23 2011 IA Speedo Champions Series - CZ Section 1 4:50.78 2012 Mutual of Omaha Swimvitational
Marin, Luca M ITA 428 257.04 1.94 0.00454 4:17.04 Italian Spring National Championships 4:12.04 49th Sette Colli Trophy
Brandon, Bonnie F USA 347 293.81 4.61 1.56 0.00452 4:53.81 2011 CA Los Angeles Invitational 4:49.20 USA Olympic Team Trials
Wallburger, Tim M GER 388 264.05 4.63 1.75 0.00451 4:24.05 2011 German open 4:19.42 Qualification for European Championships
Martynova, Yana F RUS 365 283.24 4.55 1.6 0.0044 4:43.24 Russian National Championships 4:38.69 Russian National Swimming Championships
Tranter, Daniel M AUS 398 260.84 4.46 1.7 0.00429 20.6 1.93 80 4:20.84 2011 New South Wales Open Champs 4:16.38 2012 EnergyAustralia Swimming

Direct data download

Swimmers who gained better performance improvement than Ye Shiwen over the 2011-2012 period

name sex country d\tau t_{2011} d t \delta t \delta t' age height weight t_{2011} 2011 best performance t_{2012} 2012 best performance
Trombetti, Luisa F ITA 81 293.7 5.9 0.0248 19.6 4:53.70 Italian Open Winter Nationals 2011 4:47.80 Italian National Spring Championships
Rousseau, Sebastien M RSA 157 266.95 9.12 3.41 0.0217 21.9 1.9 80 4:26.95 Minneapolis Grand Prix 4:17.83 Sa National Aquatic Championships
Meyer, Michael M RSA 136 263.87 7.45 2.82 0.0207 24.66 4:23.87 Open Dutch Championships 4:16.42 Sa National Aquatic Championships
Chen, Xinyi F CHN 167 289.95 8.94 3.08 0.0184 14.6 4:49.95 7th National City Games 2011 4:41.01 National Swimming Championships
Mann, Becca F USA 227 290.17 8.56 2.94 0.0129 14.6 4:50.17 Minneapolis Grand Prix 4:41.61 USA Olympic Team Trials
Seltenreich-Hodgson, Erika F CAN 311 294.3 10.5 3.56 0.0114 17.6 4:54.30 2011 Canadian Age Group Championships 4:43.80 Mare Nostrum
Coton, Quentin M FRA 241 268.85 6.63 2.46 0.0102 21.04 4:28.85 Summer Nationals 4:22.22 Elite French Championships
Beraud, Romain M FRA 241 270.91 6.53 2.41 0.01 23.98 4:30.91 Youth Senior Open Championships 4:24.38 Elite French Championships
Tutumi, Takahiro M JPN 213 265.35 5.47 2.06 0.00967 19.9 4:25.35 Japan Inter-College Swimming Competition 4:19.88 2012 Japan National Championships
Siwicki, Breanne F CAN 250 293.79 7.01 2.38 0.00954 17.6 4:53.79 Summer Nationals 4:46.78 2012 Canadian Olympic and Paralympic Trials
Wedel, Kevin M GER 309 268.84 7.64 2.84 0.00919 18.6 4:28.84 38th European Junior Championships 2011 4:21.20 124th German Championships
Soerensen, Katrine F DEN 245 293.96 6.58 2.23 0.00913 4:53.96 Summer Nationals 4:47.38 Danish Open
Mann, Karley F GBR 356 294.94 9.3 3.15 0.00885 18.6 4:54.94 British Gas ASA Youth Champs 2011 4:45.64 British Gas Nat Youth MC Chmps 2012
Glavnyk, Iryna F UKR 238 294.7 6.21 2.1 0.00885 16.24 1.74 58 4:54.70 38th European Junior Championships 2011 4:48.49 Open Ukrainian National Championships
Lowe, Danielle F GBR 356 295.9 9.1 3.07 0.00863 17.6 4:55.90 British Gas ASA Youth Champs 2011 4:46.80 British Gas Nat Youth MC Chmps 2012
McKee, Anton Sveinn M ISL 281 270.15 6.51 2.4 0.00857 4:30.15 38th European Junior Championships 2011 4:23.64 Icelandic National Championships
Persson, Erik M SWE 260 271.82 5.86 2.15 0.00829 18.6 4:31.82 38th European Junior Championships 2011 4:25.96 Danish Open
Kochetkova, Kristina F RUS 261 294.48 6.08 2.06 0.00791 19.52 4:54.48 Russian National Swimming Cup 4:48.40 International Meeting
Gyurta, Gergely M HUN 281 261.9 5.34 2.03 0.00725 20.903 1.74 68 4:21.90 CXIII Hungarian Swimming Championship 4:16.56 Open National Championships
Schepers, Jan David M GER 282 264.71 5.24 1.97 0.00701 4:24.71 German Championships 4:19.47 Qualification for European Championships
Vanderkaay, Peter M USA 398 263.28 7.06 2.68 0.00673 28.48 1.93 90 4:23.28 2011 Michigan Grand Prix 4:16.22 2012 NC Charlotte UltraSwim
Ye, Shiwen F CHN 285 273.66 5.23 1.91 0.0067 16.27 1.6 45 4:33.66 7th National City Games 2011 4:28.43 2012 Olympic Games

Direct data download

References

  • [1] Ewen Callaway, Why great Olympic feats raise suspicions, http://www.nature.com/news/why-great-olympic-feats-raise-suspicions-1.11109

  • [2] FINA, "Swimming World Rankings" data base, http://www.fina.org/H2O/index.php?option=com_wrapper&view=wrapper&Itemid=805

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