## 3 Results

Table 4: The descriptive statistics for the total perceived impacts of more than 8G, grouped by the players’ positions. Min: minimum value recorded, Max: maximum value recorded, STD: standard deviation of the data, IQR: interquartile range. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Variable** & **Position** & **Min** & **Max** & **Median** & **Mean** & **STD** & **IQR** \\ \hline \multirow{8}{*}{Perceived strikes intensity} & Half & 2 & 8 & 6 & 6.25 & 1.98 & 2 \\ \cline{2-7}  & Prop & 3 & 9 & 6 & 6.23 & 1.82 & 1 \\ \cline{2-7}  & Fly Half & 2 & 9 & 6 & 5.71 & 2.16 & 2.75 \\ \cline{2-7}  & Second Row & 1 & 9 & 4 & 5.46 & 2.76 & 4 \\ \cline{2-7}  & Fullback & 1 & 8 & 5.5 & 5.12 & 2.36 & 3.25 \\ \cline{2-7}  & Wing & 1 & 10 & 6 & 5.11 & 2.34 & 3.5 \\ \cline{2-7}  & Hooker & 1 & 10 & 5 & 5 & 2.88 & 2.75 \\ \cline{2-7}  & Flanker & 1 & 9 & 4.5 & 4.89 & 2.41 & 4 \\ \cline{2-7}  & Centre & 1 & 8 & 5 & 4.42 & 2.05 & 3 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The descriptive statistics for the perception of impact intensity, grouped by the players’ positions. Min: minimum value recorded, Max: maximum value recorded, STD: standard deviation of the data, IQR: interquartile range. the perception of impacts perceived above 8G, we created a new variable calculated as the difference between the perception of impacts above 8G and the recorded number of impacts above 8G. In Figure 3, the relationship between the data collected by the MEMS and the results of the questionnaires can be observed. From these results, we can see that 49.7% of the players overestimated the number of impacts of more than 8G that they received, 39.8% underestimated them, and there was exact agreement in only 10.5% of the cases. Studying the mean error, we can see that for the team in general, it was 0.017 impacts. With the objective of studying what the credibility intervals were for the team's mean error, we used Bayesian methods to estimate its posterior distribution. The decision to use a normal distribution to model the error was based on not being able to reject the null hypothesis of the Shapiro-Wilks test (\(p\)-value \(>\) 0.05). Our region of practical equivalence (ROPE) was from \(-\)0.5 to 0.5 impacts, meaning that we are willing to accept a bias in the mean of \(\pm\)0.5 impacts to consider that the error is acceptable for our purposes. The 95% high-density interval of the posterior distribution of the mean error was from [\(-\)0.46-0.45], and 95.8% of the mean distribution was contained within our ROPE, so at the team level, we can say the impact estimation was not biased. One favorable thing about Bayesian models is that we can access the predictive posterior distribution; in this, we can see that the 95% credibility interval of the error was between \(-\)7.3 and 7.3, indicating that it would be expected that players over or under-estimate the number of impacts by \(\pm\)7.3 impacts per match. While with these results we could say that the mean of the error is acceptably close to zero, when studying the results according to the positions, a different pattern can be observed, and this can be seen in Table 5.  
Figure 2: The correlation matrix between variables. Figure 3: Scatterplot showing the relationship between the 8G impacts recorded by the GPS and the impacts of more than 8G perceived by the players. Observations where players underestimated the impacts are shown in green, in red where they overestimated the impacts, and in gray where there was perfect agreement. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Position** & **Mean Error** & **Mean Impact Over 8G** \\ \hline Centre & \(-0.698\) & 4.72 \\ \hline Flanker & 0.893 & 7.39 \\ \hline Fly Half & \(-0.286\) & 5.5 \\ \hline Fullback & \(-1.25\) & 6.62 \\ \hline Half & 2.38 & 10.5 \\ \hline Hooker & 0.125 & 7.12 \\ \hline Prop & 1 & 9.59 \\ \hline Second Row & \(-1.38\) & 7 \\ \hline Wing & \(-0.0741\) & 6.89 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Mean error and impacts over 8G, segmented by positions.