# Power-Cadence Relationships in Cycling: Building Models from a Limited Number of Data Points
## 4 Discussion  
The main finding of this study is that a better fit of the meaningful data points collected during the Force-Velocity test and a more accurate estimate of Pmax can be obtained using models built on five data points selected to reflect participants' maximal power-producing capacity, drawn from strategic regions of the power-cadence relationship known to influence the coefficients of third-order polynomial regressions. The Low-Number of data points (LN) model introduced here was specifically designed to help researchers and practitioners model power-cadence relationships after excluding non-maximal data points that are frequently recorded during force-velocity testing (Figure 2). By relying on only five carefully selected points, the LN model captured participants' maximal power-producing capacity across a wide range of cadences more effectively than a model that included all data points and the model we previously proposed [5]. Our results highlight the need for both the research and applied communities; including strength and conditioning professionals, athletic trainers, and clinicians; to re-evaluate the procedures used to process the data collected from Force-Velocity testing on a stationary cycle ergometer. We argue that future modeling procedures should prioritize distinguishing genuine cadence-specific maximal power levels from the biological noise that often contaminates raw data [5]. The LN modeling method was built around this principle and appears to provide a more valid means of quantifying Pmax in young and physically active male adults [4; 20; 22; 25; 26; 34; 39]. Our results show that the quality of the model fit improved as the number of data points used to characterize the power-cadence curve decreased and the likelihood that those points were truly maximal increased. This was demonstrated by significant and large effects of model type on both R\({}^{2}\) and SEE values (Figure 2, Table 2), with the LN model yielding the highest R\({}^{2}\) (0.995 \(\pm\) 0.008) and lowest SEE (29 \(\pm\) 15 W). These findings build upon our previous methodological recommendations [5], which emphasized the need to capture the complexity of the power-cadence relationship using third-order polynomial models while avoiding the inclusion of submaximal data points that are inevitably recorded during force-velocity tests. It is also important to consider how testing protocol design and participant characteristics influence the quality and usefulness of the data collected. As illustrated in Figure 1, our protocol yielded relatively few data points at low cadences, while considerable variation in power values across similar cadences suggested that participants were unable to produce cadence-specific maximal power consistently during each pedal cycle (see Figure 2). These limitations are consistent with previous observations [5; 6; 7; 8; 21; 22; 28; 34; 38; 39], though they have not been systematically analyzed. Our findings reinforce earlier recommendations [5] that researchers and practitioners focus on the collection of truly maximal data points, with \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & Exp. Data & HN & MN & LN \\ \hline R\({}^{2}\) & & 0.938 \(\pm\) 0.027 & 0.962 \(\pm\) 0.014 & 0.995 \(\pm\) 0.008 \\ \hline SEE (W) & & 72 \(\pm\) 17 & 53 \(\pm\) 14 & 29 \(\pm\) 15 \\ \hline Ppeak/Pmax (W) & 1218 \(\pm\) 178 & 1126 \(\pm\) 163 & 1157 \(\pm\) 162 & 1220 \(\pm\) 168 \\ \hline Cppeak/Copt (RPM) & 127 \(\pm\) 11 & 125 \(\pm\) 8 & 127 \(\pm\) 8 & 126 \(\pm\) 8 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Summary of metrics used to assess model fit and performance. Values are presented as mean \(\pm\) standard deviation. R\({}^{2}\) = coefficient of determination; SEE = standard error of the estimate; Pmax = modeled maximal power output; Copt = optimal cadence (x-coordinate of the apex of the curve). “Exp. Data” refers to the experimentally measured power peak (Ppeak) and its associated cadence (Cppeak). HN = High-Number model; MN = Moderate-Number model; LN = Low-Number model.