Exploring models to optimise the prediction of interval times and step counts between hurdles in 400 m hurdles

Abstract

The present study aimed to identify the optimal modelling method for predicting interval times and step counts between hurdles in 400 m hurdles. We obtained 337 data from previous studies and official race reports (mean race time: 49.31 ± 1.09 s, range: 46.29–50.99 s). Due to missing step count data, 337 data were used for the time prediction and 229 data for the step count prediction. We evaluated three models: a hierarchical model, a generalised additive model, and a function-on-scalar model. Leave-one-out cross-validation was applied, and evaluation metrics (the mean squared error; MSE, mean absolute error; MAE, and coefficient of determination; R²) were calculated. The function-on-scalar regression exhibited the highest accuracy for interval time prediction (MSE: 0.006 ± 0.003 s², MAE: 0.060 ± 0.016 s, R²: 0.610 ± 0.140), whereas the hierarchical model exhibited the best accuracy for step count prediction (MSE: 0.134 ± 0.041 step², MAE: 0.292 ± 0.041 step, R²: 0.661 ± 0.107). This discrepancy may be attributed to the fundamental difference between interval times, continuous time-varying variables, and step counts, discrete count variables following a Poisson distribution, exhibiting distinct patterns of variation throughout the race. The present study provided fundamental insights into modelling for more accurate prediction of interval times and step counts between hurdles, based on the nature of the data.