## 4 Discussion  
The main objective of our study was to test the relationship between the player's perception through a questionnaire and the objective measurement through MEMS of the number of impacts generated in a series of matches. Likewise, we tried to verify the reliability of ordering the intensity of the same through the same questionnaire. The findings of our research reveal some important characteristics about the coding of the perception of impacts in rugby. The first aspect that we can highlight is that the questionnaire created and used to record the perception of the players presents a high association with the MEMS records; this is justified by observing that all the variables studied in the questionnaires correlate significantly with the MEMS records. In our research, we demonstrate that the utilization of an impact perception scale is sensitive in efficiently capturing both the quantity and magnitude of impacts. This scale proves to be a feasible, low-cost tool that enables the quantification of a sensitive aspect of the game. In this regard, [PERSON] et al. recommend integrating microtechnology and video-based analysis simultaneously to ensure maximal accuracy of metrics. Given the high incidence of injuries and the burden of collision events, it is crucial that athletes are adequately prepared for collisions during training to meet the demands of matches. Our study thus expands the arsenal of available tools. When addressing the issue of potential biases that players may have regarding the quantity of impacts exceeding 8G they receive, we must differentiate the scale we are discussing and consider the number of impacts received. If we take a general team-wide scale, we can say that the subjective perception of players is not biased. This is supported by the findings that our ROPE contains the 95% HDI of the estimated mean error. However, when we study the team segmented by positions, we can see that in some cases, this no longer holds true. Taking into account our evidence, some positions tend to underestimate or overestimate the quantity of impacts they receive, as can be seen in Table 6.  
One of the most important findings we would like to highlight is the robust relationship between players' perceptions and the quantity of impacts they receive, which responds in a non-linear manner. This begins to be evidenced by the results of our multivariate model, where we attempted to predict the quantity of impacts exceeding 8G received based on questionnaire results. The goodness of fit of this model remains low even after multiple \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & **ELPD WAIC** & **P WAIC** & **SE** \\ \hline Exponential & \(-186.7\) & \(2.9\) & \(9.9\) \\ \hline Linear & \(-439.6\) & \(4.9\) & \(10.1\) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Model comparison. ELPD WAIC: expected log pointwise predictive density of Watanabe-Akaike Information Criterion, P WAIC: penalized Watanabe-Akaike Information Criterion, SE: standard error of WAIC. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Parameters** & **Mean** & **HDI 2.5\%** & **HDI 97.5\%** & **MCSE Mean** & **ESS** & **R Hat** \\ \hline Exponential Model & & & & & & \\ \hline Beta 0 & \(-3.38\) & \(-3.85\) & \(-2.91\) & \(0.0012\) & \(2810.0\) & \(1\) \\ \hline Beta 1 & \(0.15\) & \(0.14\) & \(0.16\) & \(0.0025\) & \(2275.0\) & \(1\) \\ \hline Linear Model & & & & & & \\ \hline Beta 0 & \(-2.88\) & \(-4.06\) & \(-1.73\) & \(0.046\) & \(1810.0\) & \(1\) \\ \hline Beta 1 & \(0.27\) & \(0.141\) & \(0.39\) & \(0.006\) & \(1680.0\) & \(1\) \\ \hline Beta 0 Sigma & \(2.15\) & \(1.33\) & \(3.05\) & \(0.043\) & \(1400.0\) & \(1\) \\ \hline Beta 1 Sigma & \(0.10\) & \(0.01\) & \(0.19\) & \(0.005\) & \(1420.0\) & \(1\) \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Results of the estimation of the parameters of the linear and exponential models. HDI 2.5%/97.5%: high-density interval, 2.5 and 97.5 percentile, respectively. MCSE: average standard error of the estimate. ESS: effective sample size.