Many data collected in sport science come from time dependent phenomenon. This article focuses on Functional Data Analysis (FDA), which study longitudinal data by modelling them as continuous functions. After a brief review of several FDA methods, some useful practical tools such as Functional Principal Component Analysis (FPCA) or functional clustering algorithms are presented and compared on simulated data. Finally, the problem of the detection of promising young swimmers is addressed through a curve clustering procedure on a real data set of performance progression curves. This study reveals that the fastest improvement of young swimmers generally appears before 16 years old. Moreover, several patterns of improvement are identified and the functional clustering procedure provides a useful detection tool.

Background This study aimed to identify a Relative Age Effect (RAE) among French young swimmers and apply corrective adjustment procedures to rebalance performances according to categories and events. Methods 5,339,351 performances of French swimmers aged 10 to 18 were collected between 2000 and 2019. Birth quarters distribution was examined according to competitiveness level (‘All’, ‘Top50%’, ‘Top25%’ and ‘Top10%’), event and age category. A linear relationship between the distribution of performances and calendar days provides a calibration coefficient allowing to rebalance performances by considering the effect of RAE for each event. Then, adjusted performances are recalculated using this coefficient, the initial performance and the relative age. Results Proportion of swimmers born in the first quarter was higher than the proportion of those born in the last quarter for all events and strokes (p < 0.01). RAE increases with the competitiveness level for all events. Indeed, among ’All’ 12 years old 50m freestyle swimmers, the proportion born in the first quarter is 30.9% vs 19.2% in the fourth quarter, while among the “Top10%”, 47.5% were born in the first quarter vs 10.3% in the last one. (p-value < 0.01). In average, each day represents a gap of 0.008 second, resulting in a difference of almost 3 seconds over a year. This tool is validated by comparing swimmers who have performed at least twice in a season. It provides a day by day rebalancing method for all swimming events and age categories. Conclusions Relative age effect is present among French young male and female swimmers, and is strengthened by competitiveness level. A new corrective adjustment procedure to rebalance performances considering categories and events is proposed and validated. By applying such a tool, we are able to reveal the full potential of swimmers and make it possible to compare them at the same relative age.