Fig. 11.

Out-of-sample relative predictive error for each piecewise-defined model vs the power-law model for the running dataset from the section  "Large-data study in running". For each athlete, we fitted the models to the same six randomly chosen race results and predicted average velocities of the remaining races. Note that the piecewise-defined models often could not be fitted as they require a certain minimum number of data points above and below $T_{\ast }$. Whenever this happened, we excluded the corresponding athlete to ensure that both models in each panel are applied to exactly the same data. This figure illustrates that the piecewise-defined models discussed in this section suffer from overfitting (at least for the small sample sizes that are typically available)