The purpose of this study was to quantify the impact of morphological characteristics on freestyle swimming performance by event and gender.

Height, mass, body mass index (BMI) and speed data were collected for the top 100 international male and female swimmers from 50 to 1500 m freestyle events for the 2000–2014 seasons.

Several Bayesian hierarchical regressions were performed on race speed with height, mass and BMI as predictors. Posterior probability distributions were computed using Markov chain Monte Carlo algorithms.

Regression results exhibited relationships between morphology and performance for both genders and all race distances. Height was always positively correlated with speed with a 95% probability. Conversely, mass plays a different role according to the context. Heavier profiles seem favourable on sprint distances, whereas mass becomes a handicap as distance increases. Male and female swimmers present several differences on the influence of morphology on speed, particularly about the mass. Best morphological profiles are associated with a gain of speed of 0.7%–3.0% for men and 1%–6% for women, depending on race distance. BMI has been investigated as a predictor of race speed but appears as weakly informative in this context.

Morphological indicators such as height and mass strongly contribute to swimming performance from sprint to distance events, and this contribution is quantified for each race distance. These profiles may help swimming federations to detect athletes and drive them to compete in specific distances according to their morphology.

Taller swimmers have a higher probability to swim faster, and the complete probability distributions are computed for all distances and genders (only freestyle technique was investigated).

For sprinters, a larger mass is an advantage, whereas distance swimmers need to be lighter.

Optimal morphological profiles, depending on distance, gives a 0.7%–3.0% (male) and 1%–6% (female) increase in speed.

Body mass index offers a poor predictor of performance and appears as a low-informative morphological feature in swimming.

This study provides reference values of morphological characteristics as height and body mass for freestyle swimming. These insights should help coaches and swimming federations to detect talents and drive them to compete in specific distances, depending on their morphological profiles.

In swimming, a major challenge of the athlete lies in transformation of metabolic power into mechanical power with a given energetic efficiency,

Until now, no study has quantified relationships between each morphological characteristic and performance for elite swimmers with a Bayesian approach. Such a methodology offers straightforward interpretations of the results in terms of probability. Moreover, a Bayesian model also gives more nuances to the computed parameters by estimating a complete distribution instead of a unique value. The present paper aimed to quantify the impact of morphological characteristics on freestyle swimming performance by event and gender.

The results of the top 100 world-ranking swimmers were collected each year from 2000 to 2014 for both genders for all freestyle events. Name, height, mass, BMI, event, date and best time performance (converted into speed, in m/s) was recorded for each swimmer. All data were collected from the website of the international swimming federation (FINA). The database is composed of 8484 observations for male swimmers and 8606 observations for female swimmers.

Several athletes appear multiple times in the database because of their different race results in the time period, and this could lead to biases if not addressed. This particularity was taken into account in the definition of the model. In order to study relationships between morphology and performance, a hierarchical Bayesian regression model was built. The hierarchical approach settles the problem of multiple appearances of athletes in the database. Each swimmer was considered as a random effect in the model, allowing considering their own variability of performance, as well as the variability between different swimmers.

Since the scatterplot of performance according to mass or height shows a linear trend, the model assumes linear relations. However, because of its definition, the BMI was not considered as a predictor variable in the same model. Indeed, BMI does not bring any additional information into a regression model with height and mass covariates. Thus, BMI has been studied within an alternative model as a unique predictor variable. Formally, the first hierarchical Bayesian regression model is defined as

where

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· H is the height.

· M is the mass.

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· ϵ is an error term, a centred Gaussian variable of SD σ.

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In a Bayesian framework, all parameters of the model are assumed to be random variables, and the resulting estimations are made on their probability distributions. The hypothesis on the likelihood and the prior distributions of the models are as follows:

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The model was fitted and estimated using a Markov chain Monte Carlo (MCMC) algorithm from the package of the software. The resulting distributions are sampled from a stable MCMC and stored as a vector of size 50 000. Prior distributions are chosen vague, with high variances. Considering the number of observations, one can consider the influence of the prior on the results as extremely weak.

A similar framework was used to define the regression of speed by BMI through the following model:

where B represents the BMI and other components are the same as previously mentioned. Thanks to the MCMC simulations, a posterior distribution has been estimated for

Several statistics and information were extracted from resulting parameter distributions of these models, such as mean and credible intervals. One should be aware that those numbers are always less informative than an entire probability distribution that a Bayesian analysis provides. However, in this study, the necessity to compare multiple variables and race distances forced us to use such measures to present results in a meaningful way.

The research protocol qualified as non-interventional, in which ‘…all acts are performed in a normal manner, without any supplemental or unusual procedure of diagnosis or monitoring’ (Article L1121–1 of the French Public Health Code). According to the law, its approval therefore did not fall under the responsibility of a committee for the protection of persons, therefore not requiring informed consent from individual athletes.

During the studied period (2000–2014 across all freestyle events), a world top 100 male swimmer was, on average, 1.87 m tall and weighted 80 kg, and thus had a BMI of 22.9 kg/m². Furthermore, a world top 100 female swimmer was, on average, 1.74 m tall and weighed 63.5 kg, leading to a BMI of 21 kg/m².

A summary of the results of the height–mass regression is provided in

Summary of posterior probabilities for regression coefficients

Gender | Event | σ | |||

Men | 50 m | 7.587 | 0.0015 | 0.0015 | 0.0671 |

100 m | 7.020 | 0.0015 | −0.0004 | 0.0593 | |

200 m | 6.031 | 0.0046 | −0.0035 | 0.0281 | |

400 m | 5.963 | 0.0019 | −0.0013 | 0.0257 | |

800 m | 5.638 | 0.0034 | −0.0032 | 0.0315 | |

1500 m | 5.468 | 0.0031 | −0.0022 | 0.0502 | |

Women | 50 m | 6.433 | 0.0038 | −0.0007 | 0.0473 |

100 m | 6.058 | 0.0022 | 0.0009 | 0.0505 | |

200 m | 5.672 | 0.0019 | 0.0001 | 0.0254 | |

400 m | 5.203 | 0.0037 | −0.0020 | 0.0119 | |

800 m | 4.833 | 0.0059 | −0.0049 | 0.0542 | |

1500 m | 4.909 | 0.0046 | −0.0044 | 0.0298 |

First, the coefficient σ is a SD term. It informs us about the uncertainty and the dispersion of the observations around the linear plan defined by the regression model. Posterior distributions of σ appeared rather comparable between different race distances and gender, which seems consistent, knowing that all models are fitted using an equivalent number of observations. Nevertheless, one can note that 200 and 400 m for both genders seem less scattered. This could indicate that results are tighter on those races, possibly as a consequence of more contest on such intermediate distances.

Second, the coefficient

Posterior probability distributions of race speed according to the height–mass Bayesian hierarchical regression model for two different morphological profiles. Distributions are sampled from a Markov chain of length 50 000.

(A) Heat map of mean speed probabilities for multiple possible height–mass profiles for male swimming events from 50 to 1500 m. At each point of coordinates (height and mass), the corresponding probability distribution of speed from the regression model is summarised by its mean and displayed as a colour gradient on the graph. (B) Heat map of mean speed probabilities for multiple possible height–mass profiles for male swimming events from 50 to 1500m. At each point of coordinates (height and mass), the corresponding probability distribution of speed from the regression model is summarised by its mean and displayed as a colour gradient on the graph.

As mentioned earlier,

Throughout the analysis, BMI was considered separately as a unique predictor of another Bayesian regression model. Contrary to previous results, the posterior distribution of coefficients and speed exhibit moderate trends and are much more complicated to analyse. Every 95% credible intervals for the slope

This study shows that elite swimmers have morphological parameters structurally organised, depending on event and gender. Moreover, this is the first study to estimate the probability to swim faster in relation to morphological characteristics for all distances and gender. Results of this study emphasise the relevancy of height and mass as a key determinant (from 0.7% to 6% speed differences) of swimming performance, in relation to physiological and biomechanical factors. The main findings of this study are as follows: (1) taller freestyle swimmers have a higher probability to swim faster, for all distances and genders; (2) for sprinters, a larger mass is an advantage, whereas (3) distance swimmers need to be lighter.

It has been shown that speed increases with height. A taller swimmer will have a better probability to win than a shorter swimmer. Although such a relation was already known,

On short distances, mass is a beneficial feature because of the substantial contribution of anaerobic power, which is enhanced by a significant muscular mass.

BMI was identified as a relevant performance indicator in athletics,

Results of the study reveal similar trends for men and women. However, although mass was found to be a major determinant for male sprinters, its influence seems less clear for female sprinters. First, male swimmers have generally more muscle mass than female swimmers on short distances, whereas maximisation of anaerobic metabolism, mainly involved in the total energy requirements in sprint, increases with muscle mass.

Depending on the race distance, beneficial morphological profiles were highlighted. Through several analyses of biometric parameters such as body mass and height, some authors offered a new understanding on an elite athlete’s body composition to realise optimal performance.

There exist some other models in the literature to study relationships between morphology and performance. For example, the multiplicative allometric model used in several papers

To our knowledge, since no previous Bayesian analysis studying this problem exists, the prior distributions chosen were less informative. A major advantage of the Bayesian framework is its ability to take into account prior knowledge or experts' beliefs, which was not the case here. However, this work can now serve as a starting point for further analysis. Using present posterior probability results as prior distributions to study new data in this context would act as an update and would combine naturally findings of the present study with future outcomes. Future studies including other strokes and age-group swimmers should be investigated in association with other factors contributing to swimming performance. It may provide new insights about relationships between morphology and physiology or biomechanics, for example. Furthermore, it would be interesting to see if the morphological profiles have changed over the past 20 years, while world records were regularly broken and swimsuits rules have changed during our study period.

This study describes impact of morphology on elite swimmers' performances. Indicators such as height and mass can provide physique profiles, influential on speed in swimming events. These results highlight that height is positively associated with speed. For male sprinters, higher mass is also correlated with higher speed. However, an excessive mass is associated with a lower speed from 100 m and more and more as the distance increases. This morphological organisation has to be linked with other factors contributing to performance, such as physiological, technical and psychological determinants. With these insights into the optimal morphological profiles of elite swimmers, coaches can better assess swimmers' physical capacities and offer training programmes tailored to their potential. Sprinters will need more muscular power to improve their start while long-distance swimmers will need to reduce their water resistance to save energy.

This research was aided by the French Ministry of Sport and did not receive any material support.

@RobiinRoad

AL, AS and J-FT conceived the idea. AL developed the theory and performed the computations. FK, MB and RM helped with the data collection and the statistical analysis. AS encouraged RP to investigate the findings of this work. RP took the lead in the manuscript and was helped by PH to supervise in the Introduction and Discussion sections. AL wrote the Methods and Results sections. J-FT and AS supervised the project. RP and AL discussed the research direction. All authors discussed the results and commented on the manuscript.

The authors have not declared a specific grant for this research from any funding agency in the public, commercial or not-for-profit sectors.

None declared.

Not required.

Not commissioned; externally peer reviewed.

Data are available upon reasonable request.