# The Relationship between Training Load Measures and Next-Day Well-Being in Rugby Union Players
## 2 Materials and Methods
### Statistical Analysis  
To avoid recent concerns about misinterpretation of p-values [23] Bayesian analysis was used. Bayesian analysis allows the use of domain specific knowledge, permits direct probability statements to be made around each parameter and estimates of uncertainty around the parameter values [24]. To maximize the amount of data collected for training and match loads the participants volunteered from the first 15 squad, we recruited the maximum number of participants available from the first 15 squad. Updating knowledge using Bayesian analysis is legitimate even with very few data points, for this study the average number of data points per player was 35.2 \(\pm\) 10.9. Precision rather than power is the usual goal of Bayesian analysis; where priori sample size calculations are used instead of sample size calculations. To address this 95% CI's have been included in the table. The probabilities and percentages reported can be interpreted as the probability or percentage of a difference between the control condition (TL) and the questionnaire responses. Due to the day-to-day data producing multiple observations for the same participant, traditional multiple regression techniques were not suitable as they assume each observation is independent [24]. Therefore, to assess the relationship between each external and internal training load measure and the next day's subjective well-being, a Bayesian random intercept model was used, where individual y intercepts could vary. These multiple \begin{table}
\begin{tabular}{l c c c c c} \hline \hline  & **1** & **2** & **3** & **4** & **5** \\ \hline \multirow{2}{*}{FATIGUE} & \multirow{2}{*}{Always tired} & More tired than & \multirow{2}{*}{Normal} & \multirow{2}{*}{Fresh} & \multirow{2}{*}{Very fresh} \\  & & normal & & & \\ \hline \multirow{2}{*}{SLEEP QUALITY} & \multirow{2}{*}{Insomnia} & Restless sleep & Difficulty falling & \multirow{2}{*}{Good} & \multirow{2}{*}{Very restful} \\  & & & asleep & & \\ \hline \multirow{2}{*}{GENERAL MUSCLE} & \multirow{2}{*}{Very sore} & Increase in & \multirow{2}{*}{Normal} & \multirow{2}{*}{Feeling good} & \multirow{2}{*}{Feeling great} \\  & & soreness/tightness & & & \\ \hline \multirow{2}{*}{STRESS LEVELS} & Highly stressed & Feeling stressed & Normal & Relaxed & Very relaxed \\ \hline \multirow{2}{*}{MOOD} & \multirow{2}{*}{Highly annoyed: irritable: down} & Snappiness at & Less interested in & \multirow{2}{*}{A generally} & \multirow{2}{*}{Very positive} \\  & & team-mates, family, & objects \& or activities & good mood & mood \\ \cline{1-1}  & & and co-workers & than usual & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The well-being questionnaire that was completed during the study [7]. regression models were applied using the _brms_ package in R statistics program [25; 26]. For each player the internal and external load measures for each training session, on each day of the study were set as the independent or predictor variable. The next-day subjective well-being score for each player was set as the dependent variable. Weakly informative priors were used in the models. The prior used for the intercept was Student t- distribution with 3 degrees of freedom (\(\
u\)), the location parameter (\(\mu\)) the median of the response variable, and the scale parameter (\(\sigma\)) the median absolute deviation of the response variable. Improper flat priors were used for all b coefficients in the model. The priors for standard deviation and sigma were restricted to be non-negative, using a half Student t- distribution prior with 3 degrees of freedom, a zero location and a scale parameter that is 2.5 or the median absolute deviation of the response variable of greater than 2.5. No groupings where included in the models, just intercepts for individual players could vary. The analysis produces coefficients for the fixed effects and random effects.