Introd u ction to s w imming data C ASE STU D IE S IN STATISTIC AL - - PowerPoint PPT Presentation

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Introd u ction to s w imming data C ASE STU D IE S IN STATISTIC AL - - PowerPoint PPT Presentation

May 15, 2023 155 likes •442 views

Introd u ction to s w imming data C ASE STU D IE S IN STATISTIC AL TH IN K IN G J u stin Bois Lect u rer , Caltech The 2015 FINA World Championships 1 Photo b y Chan - Fan , CC - BY - SA -4.0 CASE STUDIES IN STATISTICAL THINKING Strokes at

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Introduction to swimming data

C ASE STU D IE S IN STATISTIC AL TH IN K IN G

Justin Bois

Lecturer, Caltech

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CASE STUDIES IN STATISTICAL THINKING

The 2015 FINA World Championships

Photo by Chan-Fan, CC-BY-SA-4.0

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CASE STUDIES IN STATISTICAL THINKING

Strokes at the World Championships

Freestyle Breaststroke Buery Backstroke

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CASE STUDIES IN STATISTICAL THINKING

Events at the World Championships

Dened by gender, distance, stroke Example: men's 200 m freestyle

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CASE STUDIES IN STATISTICAL THINKING

Rounds of events

Heats: First round Seminals: Penultimate round in some events Finals: The nal round; the winner is champion

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CASE STUDIES IN STATISTICAL THINKING

Data source

Data are freely available from OMEGA at omegatiming.com

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Domain-specific knowledge is

Imperative An absolute pleasure

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Let's practice!

C ASE STU D IE S IN STATISTIC AL TH IN K IN G

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Do swimmers go faster in the finals?

C ASE STU D IE S IN STATISTIC AL TH IN K IN G

Justin Bois

Lecturer, Caltech

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CASE STUDIES IN STATISTICAL THINKING

Event Time Venue Date Round 100 m free 47.51 Beijing 2008-08-11 Final 200 m free 1:42.96 Beijing 2008-08-12 Final 400 m free 3:47.79 Indianapolis 2005-04-01 Final 100 m back 53.01 Indianapolis 2007-08-03 Final 200 m back 1:54.65 Indianapolis 2007-08-01 Final 100 m breast 1:02.57 Columbia 2008-02-17 Final 200 m breast 2:11.30 San Antonio 2015-08-10 Final 100 m y 49.82 Rome 2009-08-01 Final 200 m y 1:51.51 Rome 2009-29-07 Final

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CASE STUDIES IN STATISTICAL THINKING

Event Time Venue Date Round 50 m free 23.67 Budapest 2017-07-29 Seminal 100 m free 51.71 Budapest 2017-07-23 Final 200 m free 1.54.08 Rio de Janeiro 2016-08-09 Final 400 m free 4.06.04 Amiens 2014-03-16 Final 50 m back 27.80 Borås 2017-06-30 Final 100 m back 59.98 Eindhoven 2015-04-05 Final 50 m y 24.43 Borås 2014-07-05 Final 100 m y 55.48 Rio de Janeiro 2016-08-07 Final

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CASE STUDIES IN STATISTICAL THINKING

Your question

Do swimmers swim faster in the nals than in other rounds? Individual swimmers, or the whole eld? Faster than heats? Faster than seminals? For what strokes? For what distances?

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Your question

Do individual female swimmers swim faster in the nals compared to the seminals? Events: 50, 100, 200 meter freestyle, breaststroke, buery, backstroke

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CASE STUDIES IN STATISTICAL THINKING

Diff'rent strokes

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Fractional improvement

f = semifinals time semifinals time − finals time

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Your question(s)

Original question: Do swimmers swim faster in the nals than in other rounds? Sharpened questions: What is the fractional improvement of individual female swimmers from the seminals to the nals? Is the observed fractional improvement commensurate with there being no dierence in performance in the seminals and nals?

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Let's practice!

C ASE STU D IE S IN STATISTIC AL TH IN K IN G

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How does the performance of swimmers decline

  • ver long events?

C ASE STU D IE S IN STATISTIC AL TH IN K IN G

Justin Bois

Lecturer, Caltech

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CASE STUDIES IN STATISTICAL THINKING

More swimming background

Photo by Chan-Fan, CC-BY-SA-4.0

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More swimming background

Split: The time is takes to swim one length of the pool

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More swimming background

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More swimming background

Image: Miho NL, CC-BY-3.0

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More swimming background

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Slowing down

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Quantifying slowdown

Use women's 800 m freestyle heats Omit rst and last 100 meters Compute mean split time for each split number Perform linear regression to get slowdown per split Perform hypothesis test: can the slowdown be explained by random variation?

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Hypothesis tests for correlation

Posit null hypothesis: split time and split number are completely uncorrelated Simulate data assuming null hypothesis is true

scrambled_split_number = np.random.permutation( split_number )

Use Pearson correlation, denoted rho , as test statistic

rho = dcst.pearson_r(scrambled_split_number, splits)

Compute p-value as the fraction of replicates that have Pearson correlation at least as large as observed

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Let's practice!

C ASE STU D IE S IN STATISTIC AL TH IN K IN G