## 4 Discussion
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline  & \(\mathbf{v_{1}}\)**vs. \(\mathbf{v_{2}}\)** & \(\mathbf{v_{2}}\)**vs. \(\mathbf{v_{3}}\)** & \(\mathbf{v_{1}}\)**vs. \(\mathbf{v_{3}}\)** & \begin{tabular}{c} **Body Mass** \\ **vs. \(\%RE\)** \\ \end{tabular} & \begin{tabular}{c} **Speed** \\ **vs. \(\%RE\)** \\ \end{tabular} & \begin{tabular}{c} \(\dot{\mathbf{\dot{\dot{\dot{\dot{\dot{\dot{\dot{\dot{\dot{\dot{\dot{\dot{\dot{ \dot{ }}}}}}}}}}}}}}\) \\ **vs. \(\%RE\)** \\ \end{tabular} & \begin{tabular}{c} \(\dot{\mathbf{\dot{\dot{\dot{\dot{\dot{\dot{\dot{\dot{\dot{\dot{\dot{\dot{ \dot{\dot{\dot{ \dot{ }}}}}}}}}}}}}}}\) \\ **\end{tabular} } & \
\begin{tabular}{c} **Speed** \\ **vs. \(\%RE\)** \\ \end{tabular} &
\begin{tabular}{c} \(\dot{\mathbf{\dot{\dot{\dot{\dot{\dot{\dot{\dot{\dot{\dot{\dot{\dot{\dot{ \dot{\dot{\dot{\dot{\dot{ }}}}}}}}}}}}}}}\) \\ **\end{tabular} } \\ \hline \multicolumn{2}{c}{Parameter} & ECT & ECT & ECT & ECT & ECT & ECT & VO2 vs. ECT \\ \hline HOK & \(r\) & 0.441 & 0.575 * & 0.292 & \(-0.262\)* & \(-0.068\) & \(-0.311\)* & 0.967 * \\  & \(p\) & 0.069 & 0.014 & 0.239 & 0.049 & 0.614 & 0.022 & \(<\)0.001 \\ MIZ & \(r\) & 0.418 & 0.631 * & 0.179 & \(-0.185\) & \(-0.058\) & \(-0.136\) & 0.990 * \\  & \(p\) & 0.086 & 0.006 & 0.477 & 0.169 & 0.671 & 0.328 & \(<\)0.001 \\ PUM & \(r\) & 0.368 & 0.472 * & \(-0.150\) & \(-0.103\) & 0.003 & \(-0.049\) & 0.974 * \\  & \(p\) & 0.133 & 0.050 & 0.552 & 0.446 & 0.980 & 0.724 & \(<\)0.001 \\ SAU & \(r\) & 0.558 * & 0.437 & 0.001 & \(-0.124\) & 0.125 & \(-0.094\) & 0.977 * \\  & \(p\) & 0.018 & 0.072 & 1.000 & 0.359 & 0.355 & 0.499 & \(<\)0.001 \\ \hline \multicolumn{2}{c}{Abbreviations: \(r\) = [PERSON]’s correlation coefficient, \(v_{1}\) = running speed 1, \(v_{2}\) = running speed 2, \(v_{3}\) = running speed 3, speed = absolute running speed (km.h-1), VO2 = oxygen consumption, ECT = energy cost of transport, and \(\%RE\) = percentage change in running economy. * Flags significant correlations. HOK = Hoka Rocket X2, MIZ = Mizuno Wave Rebellion Pro, PUM = Puma Fast-R Nitro Elite, and SAU = Saucony Endorphin Pro 3.} \\ \end{tabular}
\end{table} 
Table 4: [PERSON]’s correlation coefficients of percentage RE changes (\(\%RE\)) between running speeds \(v_{1}\), \(v_{2}\), and \(v_{3}\) and between relative RE changes and body mass, running speed, and VO2,peak. that a substantial proportion of the amateur athletes in our cohort exhibited a heel-striking running pattern. In contrast, the MIZ model features a midsole comprising layers of PEBA and EVA foams throughout the entire shoe, with a carbon plate positioned between them. Given the MIZ's top ranking in our study, it is plausible that this specific layer combination may confer an advantage in terms of improved RE compared to midsole structures with a single foam layer. In essence, these results demonstrate the importance of reporting RE effects of CPRSs on an individual rather than group level. While the Hoka Rocket X2 did not perform best at any increment of improvement and led to the greatest RE improvement in only 4 out of 19 subjects, it consistently performed well with most subjects, resulting in only few non-responders and a large percentage of runners gaining substantial benefit. Conversely, the Mizuno Wave Rebellion Pro and the Saucony Endorphin Pro 3 performed well at opposite ends of the spectrum, with the Saucony model showing the lowest rate of non-responders and leading to greatest RE improvement in 7 out of 19 subjects, while the Mizuno model improved RE beyond 4% for the highest percentage of runners and led to greatest RE improvement in 6 out of 19 subjects. The Puma Fast-R Nitro Elite underperformed at each increment of improvement compared to other CPRS models and led to greatest RE improvement in only 2 out of 19 subjects.