Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Quantifying the limits of human athletic performance: A Bayesian analysis of elite decathletes

Paul-Hieu V. Nguyen, James M. Smoliga, Benton Lindaman, Sameer K. Deshpande

Abstract

Because the decathlon tests many facets of athleticism, including sprinting, throwing, jumping, and endurance, many consider it to be the ultimate test of athletic ability. On this view, estimating the maximal decathlon score and understanding what it would take to achieve that score provides insight into the upper limits of human athletic potential. To this end, we develop a Bayesian composition model for forecasting how individual athletes perform in each of the 10 decathlon events of time. Besides capturing potential non-linear temporal trends in performance, our model carefully captures the dependence between performance in an event and all preceding events. Using our model, we can simulate and evaluate the distribution of the maximal possible scores and identify profiles of athletes who could realistically attain scores approaching this limit.

Quantifying the limits of human athletic performance: A Bayesian analysis of elite decathletes

Abstract

Because the decathlon tests many facets of athleticism, including sprinting, throwing, jumping, and endurance, many consider it to be the ultimate test of athletic ability. On this view, estimating the maximal decathlon score and understanding what it would take to achieve that score provides insight into the upper limits of human athletic potential. To this end, we develop a Bayesian composition model for forecasting how individual athletes perform in each of the 10 decathlon events of time. Besides capturing potential non-linear temporal trends in performance, our model carefully captures the dependence between performance in an event and all preceding events. Using our model, we can simulate and evaluate the distribution of the maximal possible scores and identify profiles of athletes who could realistically attain scores approaching this limit.
Paper Structure (19 sections, 10 equations, 7 figures, 4 tables)

This paper contains 19 sections, 10 equations, 7 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Motivation: realistic max decathlon score
  3. Related Literature
  4. Our contributions
  5. Data and Model
  6. Data
  7. Modeling decathlon performance over time
  8. Posterior inference and simulated performance
  9. Model comparison and validation
  10. Studying inter-event relationships
  11. Simulating decathlon performance over time
  12. Measuring latent skill
  13. Athlete Profiles - Breaking 9200
  14. Discussion
  15. Additional results
  16. ...and 4 more sections

Figures (7)

  • Figure 1: Top decathlon scores from 2001-2022. We highlight the previous world record holders and scores. All decathlon performances greater than 8500 are included in this graph (n = 126).
  • Figure 2: Boxplots depicting the posterior predictive correlations for the simple and compositional models over 2000 simulated datasets between the 100m and long jump (top) and javelin and long jump (bottom). For each model, the 25th, 50th, and 75th percentile is marked in the boxplot. The empirical correlation from the observed data is marked with a red line.
  • Figure 3: Histogram of posterior draws of $\beta$ associated with 100m for prediction of 1500m.
  • Figure 4: Posterior predictive shotput (left) and 400m (right) intervals for selected athletes. The shaded areas represent the 95% posterior predictive interval for each respective model, and the solid line depicts the posterior mean. Each dot represents an observation for a given athlete. Greater distances for shot put and faster times for the 400m correspond to more points.
  • Figure 5: Boxplots of quantiles for event intercepts for Ashton Eaton and Kevin Mayer across 4000 MCMC samples.
  • ...and 2 more figures