## 3 Results
### Acceleration and Deceleration Clusters  
Table 5 presents the results of the non-predefined cluster of accelerations and decelerations. Three ranges of accelerations and two of decelerations are identified. There is a greater number of decelerations than accelerations, meaning that changes in speed under \(-2\)m/s\({}^{2}\) are more frequent. Accelerations occur more progressively, while decelerations happen more abruptly. The number of high-intensity accelerations is scarce. Generally, decelerations progress gradually, with 30% of them being moderate but with high ranges. Decelerations, while braking, are highly intense, so this factor must be considered by trainers to strengthen the muscle groups responsible for braking and thus prevent potential injuries.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Speed (km/h)** & **Very** & **Low/Standing** & **Lower/Walking** & **Moderate/Jogging** & **High/Running** & **Very High/Sprinting** \\ \hline Cluster centers & 0.92 & 4.73 & 9.85 & 14.70 & 19.35 \\ Ranges & \textless{}2.95 & 2.96 to 7.58 & 7.59 to 12.71 & 12.72 to 17.50 & \textgreater{}17.51 \\ \(n\) & 1,730,473 & 1,071,090 & 355,007 & 154,115 & 35,018 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Results of the five-k means cluster of kinematic OEL speed.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**ACCELERATIONS** & **Very High** \\ \hline Centers & 0.19 & 0.82 & 2.16 \\ Ranges & \textless{}0.45 & 0.49 to 1.42 & \textgreater{}1.43 \\ \% & 43.1\% & 51.7\% & 5.2\% \\ \hline \hline \end{tabular}
\end{table}
Table 5: Results of the two-step cluster of OEL kinematics accelerations and decelerations.  
The unconditioned cluster does not provide an accurate discrimination of acceleration and deceleration ranges. Therefore, Table 6 presents the results of a classification of these two variables into five ranges. The K-means cluster analysis identifies five distinct groups of accelerations (F = 10460669.16; df 4; \(p\) < 0.001) and decelerations (F = 28248438.51; df 4; \(p\) < 0.001) with significant differences between each of the five groups.  
With this clustering, it is confirmed that most accelerations occur at very low intensity, meaning that players progressively increase their speed. Speed increments are smaller when the player is already moving at high intensity. These speed changes might be the factors that differentiate one player from another.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{6}{c}{**ACCELERATIONS**} \\ \hline
**Acc (m/s\({}^{2}\))** & **Very Low** & **Low** & **Moderate** & **High** & **Very High** \\ \hline Centers (m/s\({}^{2}\)) & 0.46 & 1.29 & 3.34 & 6.49 & 14.23 \\ Ranges (m/s\({}^{2}\)) & \textless{}0.95 & 0.96 to 2.53 & 2.54 to 5.31 & 5.32 to 12.  
Regarding the decelerations grouped into five categories, it is observed that over 90% of the decelerations are of low intensity, less than 2 m/s\({}^{2}\). Perhaps the most relevant finding in this cluster is the verification that there are reductions in speed, braking, of moderate, high, and very high intensity, necessitating the design of tasks that can replicate these sudden speed reductions.  
It is essential to remember that the sampling frequency is 100 Hz, so speed variations in both positive and negative directions are recorded 100 times per second. Therefore, the magnitudes of accelerations in the Very High range correspond to a positive speed change of 12.26 m/s\({}^{2}\) (equivalent to 44.14 (km/h)/s) for 0.01 s, which means an increase of 0.44 km/h in speed, and a negative speed change of 14.55 m/s\({}^{2}\) (equivalent to a decrease of 0.52 km/h in speed).