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Article

Subjective Assessment of Impact Quantity and Magnitude in Rugby: A Comparative Analysis with >8G Impact Values from MEMS Technology

by
Leandro Carbone
1,
Matías Sampietro
2,
Manuel García-Sillero
3,*,
Bruno Tartaglia-Pulcini
1,
Agustín Cicognini
1 and
Salvador Vargas-Molina
3
1
Department of Physical Education and Sport, Faculty of Medicine, University of Salvador, Buenos Aires C1020ADN, Argentina
2
Physiotherapy Department, Belgrano Football Club, Nacional University of Cordoba, Cordoba X5000HUA, Argentina
3
Physical Education and Sport, Faculty of Medicine, University of Málaga, 29010 Málaga, Spain
*
Author to whom correspondence should be addressed.
Appl. Sci. 2024, 14(14), 6126; https://doi.org/10.3390/app14146126
Submission received: 13 June 2024 / Revised: 2 July 2024 / Accepted: 11 July 2024 / Published: 14 July 2024
(This article belongs to the Special Issue Innovative Approaches in Sports Science and Sports Training)
Browse Figures
Versions Notes

Abstract

Purpose: The main objective of this research was to develop a questionnaire for the subjective evaluation of the quantity and magnitude of impacts experienced by rugby players. Methods: Thirty-six male rugby union players (mean ± SD, age; 23.5 ± 3.6 years, height; 179 ± 10.0 cm, body mass; 89.58 ± 13.6 kg) participated in this study, comprising eighteen forwards and fourteen backs. Participants were tasked with completing self-reported questionnaires assessing their perception of the quantity and magnitude of impacts after thirteen consecutive matches. Objective data were concurrently collected using Micro-Electrical Mechanical Systems (MEMS) integrated with a GPS device (WIMU, Realtrack Systems, Almeria, Spain). Results: The statistical analysis revealed that 49.7% of players overestimated and 39.8% underestimated the number of impacts above 8G, with a mean team error of 0.017 impacts. Bayesian methods indicated a 95% high-density interval for the mean error between −0.46 and 0.45, with 95.8% within the region of practical equivalence, signifying negligible bias at the team level. Positional variations were notable, with Halfbacks overestimating and Fullbacks and Second Row underestimating impacts. The errors and number of impacts displayed a non-linear relationship, better described by an exponential model. Additionally, the study identified significant correlations between the number of impacts players estimated and the actual impacts received, further underlined by position-specific trends, suggesting that players’ estimation abilities are influenced by the actual exposure to impacts and their playing positions. Conclusions: The utilization of a subjective impact questionnaire is a valid tool to assess rugby players level of impacts during a match. This approach proves particularly valuable in situations where technology is unavailable, showcasing its adaptability as a practical tool in diverse sporting contexts.

1. Introduction

Rugby union and sevens are both forms of invasive team sports that feature a high degree of physical exertion, including high-speed running and collisions. In the game environment of rugby union, the types of collisions that occur, such as tackles, scrums, rucks, and mauls, are very diverse [1,2]. Such demands encompass a wide range of activities, including, but not limited to, running; sprinting; accelerating; decelerating; jumping; and player-to-player interactions, such as scrums, mauls, tackles, carries, and rucks. Research conducted by Fuller and colleagues [3] observed that tackles and rucks were the most prevalent collision activities in rugby union. Furthermore, it was reported that tackling or being tackled were the mechanisms associated with the highest proportion of all injuries sustained during match play [3]. Specifically, in senior professional male rugby union players, the injury incidence rate during tackles is 29.0 injuries per 1000 player hours [4,5,6,7,8]. Additionally, the injury incidence rate in the ruck/maul is 17.0 injuries per 1000 player hours. In the sport of sevens, the injury incidence rate during tackling is 40.4 injuries per 1000 player hours [9], with a rate of 1.2 injuries per 1000 player hours in the mauls and scrums [10]. Therefore, the incidence of injuries reflected in the current literature is higher in rugby union than in sevens.
In a recent study conducted by Roe et al., it was determined that the integration of collision activities within field-based training leads to a significant increase in mean heart rate and perceived exertion during the training session, as well as an elevation in creatine kinase levels in the blood [11]. Previous research on the physical demands of rugby union has primarily focused on locomotive activities, neglecting other important aspects of the game such as collision activities. The inclusion of collision load quantification alongside traditional metrics such as running distance and high-intensity efforts would provide a more comprehensive understanding of the physical demands of rugby union. Moreover, it has been established that among the most rigorous aspects of rugby competition are those involving consecutive tackles and impactful encounters with minimal periods of rest in between [12]. At the highest level of the sport, rugby league players are frequently subject to a range of impacts, ranging from 29 to 74 (such as tackles and carries) per match [12,13], or an average of more than three impacts per minute [14]. In addition, it has been established that success in collision situations is closely linked to overall team success and individual player performance [15,16]. Studies such as Ortega et al. have demonstrated that teams who emerge victorious in matches tend to complete a greater number of tackles than teams who lose [16].
Given the significant incidence and impact of injuries, as well as the positive correlation between winning collisions and performance in rugby union and sevens, it is crucial for coaches and practitioners to properly prepare players for competition and also to be able to accurately estimate players’ stress load [3,11,17]. To achieve this, it is important to have knowledge of the frequency and intensity of these collisions in both training and match scenarios. In the realm of sports, microtechnology often encompasses the utilization of Global Positioning Systems (GPS) and Micro-Electrical Mechanical Systems (MEMS) to capture the external physical demands of competition and training [1,18,19]. One of the earliest studies utilizing microtechnology to assess physical demands in rugby union was published in 2009 [2], and since then, research utilizing these devices has seen significant growth. Initially, GPS was only utilized to provide information on distance and speed [20,21], but advancements in technology have led to the integration of MEMS into GPS devices, which now feature triaxial accelerometers, gyroscopes, and magnetometers [20]. Triaxial accelerometers measure acceleration in three different axes, and the sum of the acceleration in these three axes provides a vector magnitude, which can be used to quantify the intensity of the collision with application to the tackles [13,20,22].
Subjective assessments, such as rating of perceived exertion (RPE), can be used to quantify the perceived physical and technical demands in a variety of sports, including contact sports. This method takes into account the intensity and duration of the activity to calculate the training load (TL) or competition load. Session duration is expressed in minutes. Athletes provide a nominal score describing their RPE of “average training intensity” for that session. Subjective measures can also be more sensitive and consistent than objective measures [23], and session RPE (sRPE) has been reported to be the most commonly assessed TL variable in most team and open sports [24]. Compared to objective measures, sRPE may be able to better account for the allostatic stress experienced by the athlete in mixed training sessions (e.g., tactical, skill, strength, fitness) [25]. But in contact sports, a key aspect, such as severity, is not adequately detailed in such tools. Given the growing importance of controlling this aspect, due to its incidence of injury, its control by means of a subjective scale is increasingly necessary.
In this sense, our goal was to create a questionnaire to subjectively assess the quantity and magnitude of impacts.

2. Materials and Methods

2.1. Participants

Thirty-six male rugby union players (mean ± SD, age: 23.5 ± 3.6 years, height: 179 ± 10.0 cm, body mass: 89.58 ± 13.6 kg) were recruited for this study, including twenty forwards and sixteen backs. All participants were selected from a single semiprofessional rugby union club based in Argentina (Club San Patricio Rugby). Data from thirteen consecutive rugby matches were gathered, and only information from players who actively participated for more than 60 min in each match was considered for analysis. The procedures complied with the Declaration of Helsinki (2013).

2.2. Design and Methodology

2.2.1. Impact Measurements through Micro-Electrical Mechanical System (MEMS)

Participants were equipped with a Micro-Electrical Mechanical System (MEMS) (WIMU, Realtrack Systems, Almeria, Spain), which was securely fastened to the upper back of the athletes using a specialized vest to minimize any potential movement of the unit and ensure its accuracy [22]. The micro-technology units contain a 10 Hz Galileo GPS positioning device, a 3D accelerometer 100G recording at 1000 Hz, and a 3D gyroscope recording at 1000 Hz. The devices were calibrated prior to their placement. A self-calibration system that included all devices in the internal configuration of the boot was used. During the self-calibration process, three factors were considered: (i) keeping the device stationary for 30 s, (ii) placing it on a flat surface, and (iii) ensuring no magnetic devices were present nearby. Previous studies have reported good accuracy and reliability for the sensors in these devices [26,27,28].
The raw acceleration data were extracted from each MEMS device and subsequently processed using a vector summation method, referred to as AcelT, along three axes: mediolateral (x), anteroposterior (y), and vertical (z). This calculation methodology was adopted following the approach established by Gómez-Carmona et al. [28]. AcelT exclusively represents acceleration levels measured in g-force units, as captured by the 3D accelerometers embedded within the inertial device, and it was sampled at a frequency of 1000 Hz. Importantly, no data transformation procedures were applied to alter the raw signal. Consequently, the reliability of the AcelT variable ensures the overall dependability of all parameters derived from accelerometer data [28]. The GPS devices were configured to record acceleration data along three axes, with a threshold of 8G established. This threshold has been reported in the literature as acceptable for detecting high-intensity collisions to identify significant impacts [29,30]. The MEMS data were analyzed using specialized software to determine the total number of impacts exceeding 8G that each player experienced during each match.

2.2.2. Self-Reported Questionnaires

In addition to the objective measurements from MEMS devices, we also obtained the subjective perception of the intensity and quantity of impacts received through self-reported questionnaires. Each player completed the questionnaires immediately after every match, aiming to maximize the accuracy of their recollections.
A questionnaire consisting of four questions was utilized. For the first three questions, players were required to quantify, on a scale of 1 to 10, their perception of the intensity of the impacts received. The fourth question sought a direct numerical estimation of the quantity of high-intensity impacts (exceeding 8G) that the player perceived to have experienced. This question necessitated that players rely on their own judgment and perception of the impact intensity.

2.3. Statistical Analysis

To examine the relationship between athletes’ perceptions of impact intensity and actual 8G impacts recorded by MEMS devices, Pearson’s correlation coefficient was used to analyze the correlation between the first three questionnaire responses and the actual impacts. Statistical significance tests were also conducted.
A multivariable linear model assessed how well the questionnaire responses (four questions) predicted the number of 8G impacts. The Breusch–Pagan test identified heteroscedasticity, addressed by logarithmic and Box–Cox transformations, which stabilized variance and improved model reliability. Principal component transformation reduced multicollinearity among independent variables.
Perception bias was evaluated by calculating the error between recorded impacts and perceived impacts reported in the questionnaires. Bayesian methods estimated the posterior distribution of this error for the entire team and for different field positions, assuming normal distribution. A Shapiro–Wilk test checked data normality.
Two models explored the relationship between perception error and the number of 8G impacts: a linear model addressing heteroscedasticity by estimating variance as a dependent variable of magnitude, and a nonlinear exponential model for a more complex relationship.
To determine the appropriate sample size for our study, we initially sampled the target population. We calculated the Pearson correlation coefficient between the questionnaire responses and impacts greater than 8G. Using this correlation value, we calculated the required sample size to achieve a statistical power of 0.8 in a hypothesis test for the correlation coefficient, maintaining a significance level of 0.05. The necessary sample size for these data was found to be 22 participants. The resulting power of our study was 0.896.
The Python library PyMC3 (version 3.11.5) estimated Bayesian models, while R (version 4.3.1) was used for graphics and descriptive statistics. Parameter estimation details, choice of priors, and convergence assessments (Effective Sample Size and Gelman-Rubin coefficients) are included in the Appendix A, Appendix B and Appendix C.

3. Results

The results of the questionnaires and the descriptive statistics for the number of impacts above 8G can be found in Table 1. In Appendix C, the average data of impacts over 8G and the questionnaire responses are shown, dividing the information into forwards and backs. The average number of impacts above 8G per match was 6.87 impacts, with the maximum recorded value for a player being 27 impacts. The average number of total perceived impacts above 8G was 6.82 impacts, and the maximum perceived value was 14 impacts. It can also be noted that the MEMS records show greater dispersion, exhibiting a standard deviation of 5.3, while the total perceived impacts show a deviation of 3.35.
The mean and standard deviation of the other questions were particularly similar, as we see in part because they had a high correlation between them.
In the information collected from the questionnaires, information about the position in which the respondents played was also included. In this way, we can see which positions suffer the most impacts. These data can be consulted in Table 2 and Figure 1. We can see that the position that received the most impacts on average was the Halves, receiving 10.5 impacts of more than 8G per game, but the position that received the most impacts during the period analyzed was a player in the Prop position, receiving 27 impacts greater than 8G, almost three standard deviations above the mean position
By studying the questionnaire data, we can see that this order was maintained in some cases and not in others. Table 3 and Table 4 show the results for perceived impact intensity and number of perceived impacts above 8G, respectively. We observed variations with the MEMS results in both cases.
When studying the correlation between the questionnaire results and the data obtained with the GPS, we can see that there was a moderate level of correlation. In all cases, the correlation between the questions and the MEMS data was significant (p-value < 0.01). The correlations between variables can be observed in Figure 2.
A linear regression was performed to assess how much variance in MEMS data could be explained by questionnaire responses. Principal component analysis was used to address multicollinearity without reducing dimensionality. The model showed that only 50.1% of the variance in MEMS records could be explained by the questionnaires.
The Breusch–Pagan test indicated heteroscedasticity (p-value < 0.01). To address this, two separate techniques were applied: a logarithmic transformation of the dependent variable improved the p-value to 0.08, and a Box–Cox transformation improved it to 0.11. Despite these adjustments, the R2 values remained low at 55% and 57%, suggesting that the independent variables may not contain sufficient information about the dependent variable, or the relationship may not be linear. To study the possible biases of the players concerning 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 ±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 ±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.
In this table, we can see that there were positions where the error was far from zero. The positions that stand out in this case were, for example, the halves, who on average overestimated the number of impacts by 2.38 impacts. Then, we can see that the Fullbacks and the Second Row underestimated the impacts received by 1.25 and 1.38 impacts, respectively. To study this pattern, we estimated the means and the errors independently. The results of these estimates can be seen in Table 6. Thanks to this analysis, we can see that the Centres, Fullback, Half, and the Second Row had biased estimates of the number of impacts they received.
By looking at Table 5 (error segmented by position), we can see that the positions that received the most impacts of more than 8G were the ones that overestimated them the most, while the positions that received fewer impacts tended to underestimate the impacts. To see how the error relates to the magnitude of the impacts, we used a methodological framework proposed by the Bland–Altman method, where the error (the difference between measurement methods, in our case questionnaire versus MEMS) is plotted against the mean of the two methods. The classic plot of Bland–Altman’s agreement analysis can be seen in Figure 4. One feature we can see is that the error correlated with the magnitude of the measurements. To study this relationship, we proposed two Bayesian models; the first one is a linear model that takes the error as the dependent variable and the magnitude of the measurements as the independent variable (this variable understood as the mean between both measurements), and the variance of the model is also estimated based on the independent variable to not depend on the assumption of homoscedasticity of the linear model.
The second model is an exponential model, which assumes constant variance. The results of the model fittings can be seen in Figure 5 (linear and exponential model).
We can graphically check that the exponential model fit our data more naturally; this situation can be verified in Table 7, where the results of both models are compared. To compare the goodness of fit of the models to the data, the metrics of expected log pointwise predictive density (ELPD) of Watanabe–Akaike Information Criterion (WAIC) were used, where higher values indicate models with a better balance between accuracy and complexity. A penalized version of WAIC for the number of parameters (P WAIC) was also computed, which generally allows evaluating the complexity of the model; higher values indicate that the model is more complex. In our case, we can see that the exponential model is superior to the linear model, as it fit the data better (higher ELPD WAIC) and is simpler since it has fewer parameters (lower P WAIC). The results of the estimates for their parameters can be seen in Table 8. This situation gives us indications that the relationship between the players’ perception and the number of impacts they receive is not linear.

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, Paul 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 data corrections. This serves as evidence that the relationship between these variables is not necessarily linear.
The non-linearities become clearer when studying the relationship between the error in players’ perception and the magnitude of impacts. The superior goodness of fit of our non-linear model is evidence of this. This model has nearly half the parameters of the linear model, yet it still demonstrates superiority in describing the data relationship (see Table 7).
The finding of such nonlinearities is probably the most important finding, as it may be providing clues as to how players decode and adapt to shocks. Similar to the RPE, the perception of the number of impacts received can be affected by multiple internal factors. In our case, we could observe that players who received more impacts begin to distort this perception, overestimating the amount of impacts they received; this may be due, for example, to the fact that tolerance to impacts is not linear and that the physical damage they generate, and their accumulation is not simply a sum of them. To study and confirm the possible mechanisms at work behind these observations, it is necessary to include measurements of physiological fatigue markers such as blood lactate, oxygen consumption levels, or heart rate and variability, as well as markers of inflammatory response or muscle damage that can quantify in some way the mechanical stress induced by the impacts. In this regard, Tiernan, Lyons, Comyns, Nevill, & Warrington [31] suggest that a significant increase in salivary cortisol on certain Mondays may indicate that players did not physically recover from the previous week of training or match at the weekend. The week and weekly matches with a higher quantity and intensity of impacts, as perceived by players using this scale, could be correlated with the hormonal response.
Nevertheless, although we observed discrepancies between the questionnaires and the MEMS records, incorporating subjective information from the players may still be very useful, just as the use of sRPE is valuable for measuring players’ internal load throughout a season. In our research, we found a consistent response of the perception of impacts and external load data, which undoubtedly allows incorporating this scale to monitor and quantify the impacts received both in training and in matches, being possible useful information in the planning of recovery after these types of actions, being used as a prevention tool, both for the loss of performance and injuries. Considering this, the tackle event and concussion injuries should continue to be the focus of future preventative efforts [32].

5. Limitations and Future Research

This study offers valuable insights and a reliable tool for monitoring collisions in rugby, although it has some limitations. The findings are based on data from a single professional rugby union club, which may not be fully applicable to all clubs or other forms of rugby like rugby sevens or rugby league or to other collision sports. A limitation of this study is that the proposed questionnaire can only be used at the end of a match. Future research could consider designing a questionnaire that includes the perception of collisions during both training and matches to enhance the external consistency and sensitivity of the tool. Another potential limitation of this study is that the questionnaire was not tested and corrected previously, and an analysis of factors that could affect the impact of the questionnaire’s application on rugby players was not conducted. Future work could be expanding the study to include a larger cohort, diverse playing styles, and various player positions, which would further enhance the tool’s validity and applicability.

6. Conclusions

The implementation of a subjective perception tool for the quantity and intensity of impacts received in rugby can indeed be a valid method for capturing the quantity and magnitude of high-intensity impacts during a rugby match.
In cases where teams do not have access to MEMS technology or video analysis, controlling this risk factor becomes mandatory, or it serves as a complement to technology. Likewise, in lower categories, we believe that these types of tools should be included in the educational process of developing athletes. Further studies in the various forms of rugby (rugby sevens and even rugby league) would be advisable to increase the reliability of this questionnaire.
Therefore, we consider this questionnaire as a useful aid for rugby teams in various modalities around the world.

Author Contributions

L.C. and M.G.-S. served as the study coordinator. L.C. and M.S. conceivedand designed the experiments. M.S. and B.T.-P. assisted in data collection. A.C. analyzed the data. L.C., M.S., S.V.-M., M.G.-S. and A.C. assisted in analysis and manuscript review. L.C., S.V.-M., A.C., M.G.-S. and M.S. wrote the draft. L.C. and A.C. assisted in the statistics advice, discussion analysis, and manuscript prepartion. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Institutional Review Board Statement

Ethical review and approval was waived for this study because the data were collected in training sessions intended for registration for application in training sessions.

Informed Consent Statement

Informed consent was obtained from all subjects involved in the study.

Data Availability Statement

Data is contained within the article.

Conflicts of Interest

The authors declare no conflict of interest.

Appendix A

  • Error Normal Model
    E r r o r ~ N o r m a l μ , σ
    μ ~ N o r m a l 0,10
    σ ~ H a l f N o r m a l 10
  • Linear Model
    E r r o r ~ N o r m a l μ , σ  
    μ = β 0 + β 1 *   m a g n i t u d e
    σ = β 0   S i g m a + β 1   S i g m a * m a g n i t u d e
    β 0 ~ N o r m a l 0,10
    β 1 ~ N o r m a l 0,10
    β 0   S i g m a ~ H a l f N o r m a l 10
    β 1   S i g m a ~ H a l f N o r m a l 10
  • Exponential Model
    E r r o r ~ N o r m a l μ , σ  
    μ = β 0 + e β 0 * m a g n i t u d e
    β 0 ~ N o r m a l 0,10
    β 1 ~ N o r m a l 0,5
    σ ~ H a l f N o r m a l 10
  • Prior Selection
  • In the estimation of all parameters, non-informative priors were used. This type of prior is particularly useful when there is no prior information about the possible characteristics of our data. The use of non-informative priors allows the data to contribute most of the weight for the parameter estimation. In other words, instead of imposing strong assumptions on the parameters a priori, non-informative priors allow the data to largely determine the subsequent parameter estimates. This can be especially helpful in situations where there is no good reason to believe that the parameters should take specific values based on theory or previous studies. In our specific case, the selection of non-informative priors was due to the lack of previous works on the matter.
    Reason for Using Bayesian Methods
    Bayesian methods provide complete probability distributions for parameters, which can be more intuitive and useful than frequentist confidence intervals. For example, by using the posterior predictive distribution of the error, we can have easily interpretable estimates for how much surveys diverge from GPS measurements.
    Bayesian methods can often handle more complex and hierarchical models than frequentist methods, which is useful when there are multiple levels of variability or complex correlation structures. This allowed us to easily deal with the assumption of heteroscedasticity in the linear model between error and magnitude.
    Bayesian methods can more easily work with non-standard probability distributions and do not require as strict assumptions as normality, which can be an advantage in many practical contexts. In our case, the assumption of normality was not violated, but we can easily adapt the models to other distributions if necessary, which generally saves time during the data analysis process.
  • Sampling Algorithm
    PyMC3 uses what is called the No-U-Turn Sampler (NUTS). NUTS is a type of Hamiltonian Monte Carlo (HMC) sampler. The idea behind HMC is that, instead of randomly exploring the parameter space (as the Metropolis–Hastings method would do, for example), information about the gradient of the distribution can be used to inform the exploration. In this way, HMC can move large distances across the distribution while still being efficient.

Appendix B

Document 1
Questionnaire on the perception of impacts during the training session.
This questionnaire was entirely based on the participant’s perception.
  • What is your sensation regarding the intensity of contact during the training session?
  • What is your perception of the quantity of impacts you experienced during the training session?
  • What is your perception specifically of the quantity of tackles made during the training?
  • What is your perception specifically of the quantity of tackles over 8G received during the training?
Responses one to three were provided on a numerical scale of 1–10, and response four could be any positive integer allowing the participant to analyze and score their response.

Appendix C

Average impact and questionnaire statistics for forwards and backs.
PositionImpact over 8GPerceived Strikes IntensityTotal Perceived StrikesPerceived Produced TacklesPerceived Received Tackles
Forwards7.925.477.696.506.80
Backs5.585.616.724.505.00
Appendix C presents the average statistics of impact and perception for forwards and backs in rugby. The table includes data on the average number of impacts over 8G, perceived strike intensity, total perceived strikes, perceived produced tackles, and perceived received tackles. Forwards tend to experience a higher number of high-intensity impacts and perceive more strikes and tackles, both produced and received, compared to backs.

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Figure 1. Impact distribution over 8G for each position.
Figure 1. Impact distribution over 8G for each position.
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Figure 2. The correlation matrix between variables.
Figure 2. The correlation matrix between variables.
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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.
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.
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Figure 4. Adapted Bland–Altman plot. The red dashed line shows the mean of the error; the black dashed lines indicate the limits of the 95% high-density interval of the predictive posterior distribution.
Figure 4. Adapted Bland–Altman plot. The red dashed line shows the mean of the error; the black dashed lines indicate the limits of the 95% high-density interval of the predictive posterior distribution.
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Figure 5. The fitting of the models for error data as a function of the magnitude of the measurements is shown. The light gray shows the 95% high-density interval of the predictive posterior distribution, and the dark gray shows the 95% high-density interval of the posterior distribution of the mean. Left: the fitting of the linear model is shown. Right: the fitting of the exponential model is displayed.
Figure 5. The fitting of the models for error data as a function of the magnitude of the measurements is shown. The light gray shows the 95% high-density interval of the predictive posterior distribution, and the dark gray shows the 95% high-density interval of the posterior distribution of the mean. Left: the fitting of the linear model is shown. Right: the fitting of the exponential model is displayed.
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Table 1. The descriptive statistics for the questionnaire and GPS data. N: total data count, Min: minimum value recorded, Max: maximum value recorded, STD: standard deviation of the data, IQR: interquartile range.
Table 1. The descriptive statistics for the questionnaire and GPS data. N: total data count, Min: minimum value recorded, Max: maximum value recorded, STD: standard deviation of the data, IQR: interquartile range.
VariableNMinMaxMedianMeanSTDIQR
Total perceived strikes17111476.823.356
Perceived strikes intensity17111055.172.294
Perceived produced tackles17111044.242.454
Perceived received tackles17111044.022.234
Impact over 8G17112756.845.306
Table 2. The descriptive statistics of the impacts of more than 8G recorded by the GPS, grouped by the players’ positions. Min: minimum value recorded. Max: maximum value recorded. STD: standard deviation of the data. IQR: interquartile range.
Table 2. The descriptive statistics of the impacts of more than 8G recorded by the GPS, grouped by the players’ positions. Min: minimum value recorded. Max: maximum value recorded. STD: standard deviation of the data. IQR: interquartile range.
VariablePositionMinMaxMedianMeanSTDIQR
Impact over 8GCentre12044.723.553.5
Flanker11867.395.099
Fly Half11355.53.352
Fullback1195.56.626.127
Half124710.59.6414.8
Hooker1166.57.125.386.75
Prop3276.59.596.348.75
Second Row221476.288
Wing11866.894.215
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.
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.
VariablePositionMinMaxMedianMeanSTDIQR
Perceived strikes intensityHalf2866.251.982
Prop3966.231.821
Fly Half2965.712.162.75
Second Row1945.462.764
Fullback185.55.122.363.25
Wing11065.112.343.5
Hooker110552.882.75
Flanker194.54.892.414
Centre1854.422.053
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.
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.
VariablePositionMinMaxMedianMeanSTDIQR
Total perceived strikesProp21388.592.653
Second Row11488.384.178
Half2147.58.123.804.5
Fullback21387.883.604
Hooker111773.595.5
Wing11186.963.185
Flanker1136.56.52.923.25
Fly Half11155.793.023.75
Centre11155.423.226
Table 5. Mean error and impacts over 8G, segmented by positions.
Table 5. Mean error and impacts over 8G, segmented by positions.
PositionMean ErrorMean Impact Over 8G
Centre−0.6984.72
Flanker0.8937.39
Fly Half−0.2865.5
Fullback−1.256.62
Half2.3810.5
Hooker0.1257.12
Prop19.59
Second Row−1.387
Wing−0.07416.89
Table 6. The results of the estimated error means for the positions. 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. R Hat: Gelman–Rubin scale factor.
Table 6. The results of the estimated error means for the positions. 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. R Hat: Gelman–Rubin scale factor.
PositionMeanHDI 2.5%HDI 97.5%MCSE MeanESSR Hat
Centre−0.698−1.473−0.0080.0048000.01
Flanker0.897−0.2392.0070.0068705.01
Fly Half−0.285−1.2780.6430.0076289.01
Fullback−1.217−3.231−0.9650.0137372.01
Half2.3440.2244.7550.0157715.01
Hooker0.130−1.3641.5540.0096758.01
Prop0.983−0.6192.6430.0098408.01
Second Row−1.380−2.800−0.0120.0097536.01
Wing−0.074−1.2161.0910.0077931.01
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.
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.
ModelELPD WAICP WAICSE
Exponential−186.72.99.9
Linear−439.64.910.1
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. R Hat: Gelman–Rubin scale factor.
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. R Hat: Gelman–Rubin scale factor.
ParametersMeanHDI 2.5%HDI 97.5%MCSE MeanESSR Hat
Exponential Model
Beta 0−3.38−3.85−2.910.00122810.01
Beta 10.150.140.160.00252275.01
Linear Model
Beta 0−2.88−4.06−1.730.0461810.01
Beta 10.270.1410.390.0061680.01
Beta 0 Sigma2.151.333.050.0431400.01
Beta 1 Sigma0.100.010.190.0051420.01
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MDPI and ACS Style

Carbone, L.; Sampietro, M.; García-Sillero, M.; Tartaglia-Pulcini, B.; Cicognini, A.; Vargas-Molina, S. Subjective Assessment of Impact Quantity and Magnitude in Rugby: A Comparative Analysis with >8G Impact Values from MEMS Technology. Appl. Sci. 2024, 14, 6126. https://doi.org/10.3390/app14146126

AMA Style

Carbone L, Sampietro M, García-Sillero M, Tartaglia-Pulcini B, Cicognini A, Vargas-Molina S. Subjective Assessment of Impact Quantity and Magnitude in Rugby: A Comparative Analysis with >8G Impact Values from MEMS Technology. Applied Sciences. 2024; 14(14):6126. https://doi.org/10.3390/app14146126

Chicago/Turabian Style

Carbone, Leandro, Matías Sampietro, Manuel García-Sillero, Bruno Tartaglia-Pulcini, Agustín Cicognini, and Salvador Vargas-Molina. 2024. "Subjective Assessment of Impact Quantity and Magnitude in Rugby: A Comparative Analysis with >8G Impact Values from MEMS Technology" Applied Sciences 14, no. 14: 6126. https://doi.org/10.3390/app14146126

APA Style

Carbone, L., Sampietro, M., García-Sillero, M., Tartaglia-Pulcini, B., Cicognini, A., & Vargas-Molina, S. (2024). Subjective Assessment of Impact Quantity and Magnitude in Rugby: A Comparative Analysis with >8G Impact Values from MEMS Technology. Applied Sciences, 14(14), 6126. https://doi.org/10.3390/app14146126

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