Kernel Density Estimation: A Novel Tool for Visualizing Training Intensity Distribution in Biathlon

Craig Staunton^1*Andreas Kårström²Hannes Kock²Marko S Laaksonen²Glenn Björklund²

• ¹Halmstad University, Halmstad, Sweden
• ²Swedish Winter Sports Research Centre, Faculty of Human Sciences, Mid Sweden University, Östersund, Sweden

Purpose: This study introduces two-dimensional (2D) Kernel Density Estimation (KDE) plots as a novel tool for visualizing Training Intensity Distribution (TID) in biathlon. The goal was to assess how KDE plots, alongside traditional training metrics, might provide a more detailed understanding of heart rate (HR) intensity patterns, aiding in the evaluation of training quality and compliance.Methods: Fifteen elite-level youth biathletes from two national academy programmes were monitored over 5–6 weeks using HR monitors. Training sessions were measured via time-in-zone (TIZ) within a five-zone HR model with any time accumulated below the threshold for Zone 1, considered Zone 0. Sessions were dichotomized into those planned as low-intensity training (LIT) or those planned with high-intensity training (HIT). KDE analyses were conducted in MATLAB (Version R2020b) using the ‘ksdensity’ function to create 2D KDE plots that visualize HR intensity accumulation across each programme, session type (e.g., Low-intensity training: LIT; High-intensity training: HIT), and individual athlete responses. Traditional histogram plots and grouped bar charts were also used for comparison.Results: For LIT sessions, athletes performed less time in Zone 1 than planned, while performed time exceeded planned time in Zone 2. For HIT sessions, performed time in Zone 5 was lower than planned. All sessions contained unplanned time in Zone 0. The 2D KDE plots provided a continuous and detailed representation of HR intensity accumulation throughout training sessions, revealing patterns and intensity fluctuations that complement traditional TIZ analyses. Conclusions: 2D KDE plots might serve as a valuable complementary tool for assessing TID in biathlon, offering a more nuanced and continuous view of HR intensity. By identifying discrepancies between planned and performed training intensity, coaches can refine strategies and provide individualised feedback. Incorporating KDE plots into training monitoring could improve training alignment, helping reduce overtraining or undertraining risks and optimizing athlete development.