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.
The decathlon is a combined track-and-field event consisting of ten disciplines spread over two days. These events test multiple facets of athletic ability, including sprinting, jumping, throwing, technique, and endurance. The decathlon is widely regarded as the ultimate test of athletic ability due to its diversity of events and demand on both the body and mind. The order of events is consistent for each decathlon. Day one emphasizes explosiveness -athletes compete in the 100m, long jump (LJ), shot put (SP), high jump (HJ), and 400m -while day two focuses on technique and endurance, featuring the 110m hurdles, discus throw (DT), pole vault (PV), javelin throw (JT), and 1500m. Decathletes earn points based on their performance in each discipline based on a scoring table developed by the World Athletics. Their overall decathlon score is the sum of each event's points. The scoring system is intentionally designed to reward versatility: excelling in only a single discipline is insufficient to guarantee a top decathlon score.
More specifically, let Y e measure an decathlete’s performance in event e. For track events (i.e., the 100m, 400m, 110m hurdles, or 1500m), Y e is a time and smaller values of Y e correspond to better performance. For all others (i.e., LJ, SP, HG, DT, PV, and JT), Y e is distance and larger values correspond to better performance. Decathletes earn a e -(b e -Y e ) ce points for track events and a e -(Y e -b e ) ce points for all other events, where a e , b e , and c e are event-specific coefficients (see Table A2). Figure 1 shows the best decathlon scores from 2001 to 2022, with world records by Roman Šerble (2001), Ashton Eaton (2012and 2015), and Kevin Mayer (2019). These athletes differ in their event-specific strengths, with Šerble excelling in jumping events, Eaton excelling in sprinting, and Mayer doing well across all disciplines. Mayer broke the previous world record by roughly eighty points. Given these trends, we ask whether a new performance threshold, say another eighty point increase for a 9200 point total, is realistically attainable, and what combination of event abilities would be required to achieve 9200 points.
Based on World Athletics scoring table, if a decathlete managed to attain world-record performance in each individual event, their score would be 12,676. Of course, it is unrealistic to expect an athlete to perform at a world-record level in all ten disciplines. If, on the other hand, a decathlete managed to attain the highest score in each event that has ever been observed specifically in a decathlon, their score would be 10,669. Even this hypothetical is unrealistic as it requires a decathlete to attain peak performance in all disciplines at exactly the same time. Intuitively, we would expect individual event performance to vary with age (Villaroel et al., 2011), with performance peaking in different events at different times.
Motivated by this, we build age curves for individual decathlete’s performances in each discipline. By applying World Athletics’ scoring table to forecasted individual event performances, we can predict an individual decathlete’s overall score over the course of their career. To capture the inter-event dependencies, we specifically fit compositional age curves in which performance in one discipline depends not only on a non-linear function of age but also on performance in the immediately preceding disciplines. That is, our model for LJ performance depends on the observed 100m. We take a Bayesian approach, which allows us to quantify and propagate uncertainty about forecasted discipline performance through to final decathlon score in a coherent fashion.
The majority of prior research on the decathlon has been descriptive in nature focusing on clustering different disciplines (Cox and Dunn, 2002;Woolf et al., 2007;Walker and Caddigan, 2015) and creating archetypes of decathletes who perform similarly across different discipline clusters (Dziadek et al., 2022;Kenny et al., 2005;Van Damme et al., 2002). Cox and Dunn (2002), for instance, applied hierarchical clustering to group decathlon events, broadly separating the track disciplines and field disciplines, with javelin as an outlier. Woolf et al. (2007) used cluster analysis based on personal best performances of elite decathletes and suggest track athletes may have a scoring advantage. Other authors have performed principle component analysis (PCA) to analyze decathlon performance. Park and Zatsiorsky (2011) used PCA to identify latent structures across events while Dziadek et al. (2022) tracked how the structure of the decathlon shifts over an athlete’s career and found that athletes broadly shift from generalists to specializing in particular events.
Several authors have attempted to identify trade-offs between specializing in different disciplines. Van Damme et al. (2002) found evidence of antagonistic traits, as well as tradeoffs between specialist and generalist phenotypes. Aoki e
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