Stroke rate-stroke length dynamics in elite freestyle swimming: application of kernel density estimation.

Objectives: To analyse stroke rate (SR) and stroke length (SL) combinations among elite swimmers to better understand stroke strategies across all race distances of freestyle events. Design: We analysed SR and SL data from 324 male and female swimmers competing in all individual freestyle events (50 m to 1,500 m) at the 2019 European Short-Course Championships using video-based kinematic analysis. Methods: Two-dimensional kernel density estimation (2D KDE) was applied to visualise SR-SL combinations. Spearman correlations quantified relationships between stroke parameters and speed by sex and race distance. Results: In the 50 m sprint, SL showed the strongest positive correlation with speed (men: ρ = 0.57; women: ρ = 0.50), while SR correlations were trivial. As race distance increased, SR correlations with speed strengthened, reaching moderate levels in long-distance events (men's 1,500 m: ρ = 0.37; women's 800 m: ρ = 0.45), whereas SL correlations weakened. The 2D KDE heatmaps revealed an inverse SR-SL relationship, with medallists often employing stroke strategies distinct from finalists and the broader field. Gold medallists in sprint events favoured above-average SR without compromising SL, while in middle- and long-distance races, a shift toward higher SR and reduced SL was observed, particularly among women. Conclusions: These findings highlight the complexity and individuality of stroke mechanics at elite levels and suggest that superior conditioning and technique enable medallists to sustain elevated SR without compromising SL. The application of 2D KDE provides a novel, intuitive method to capture nuanced biomechanical strategies, offering valuable insights for coaching and performance optimisation.