Assessing the limitations of the Banister model in monitoring training

Abstract

The aim of this study was to carry out a statistical analysis of the Banister model to verify how useful it is in monitoring the training programmes of elite swimmers. The accuracy, the ill-conditioning and the stability of this model were thus investigated. The training loads of nine elite swimmers, measured over one season, were related to performances with the Banister model. First, to assess accuracy, the 95% bootstrap confidence interval (95% CI) of parameter estimates and modelled performances were calculated. Second, to study ill-conditioning, the correlation matrix of parameter estimates was computed. Finally, to analyse stability, iterative computation was performed with the same data but minus one performance, chosen at random. Performances were related to training loads for all participants (R(2) = 0.79 +/- 0.13, P < 0.05) and the estimation procedure seemed to be stable. Nevertheless, the range of 95% CI values of the most useful parameters for monitoring training was wide: t(a) = 38 (17, 59), t(f) = 19 (6, 32), t(n) = 19 (7, 35), t(g) = 43 (25, 61). Furthermore, some parameters were highly correlated, making their interpretation worthless. We suggest possible ways to deal with these problems and review alternative methods to model the training-performance relationships.

Figure 1

Example for subject 3 (Olympic finalist): (a) Modelled (line) and actual performances (dotted line with triangles). 95% CI for modelled performances are also presented. Performances on vertical axis were expressed in percentage of the personal record $\underset{\text{t}}{min}({\text{P}}_{\text{t}})$ and computed as ${\text{p}}_{\text{t}}=\frac{\underset{\text{t}}{min}({\text{P}}_{\text{t}})}{{\text{P}}_{\text{t}}}\ast 100$. (b) Training loads on vertical axis are expressed as a percentage of the maximal training load performed by the subject during the course of the study. Time in horizontal axis is expressed in weeks.