# Predicting Soccer Player Salaries with Both Traditional and Automated Machine Learning Approaches
## 4 Workflow and Machine Learning Algorithms
### Traditional Machine Learning Models  
This study applies supervised regression models to predict the continuous target variable, _salaryAdjusted_, using player performance features. Both linear and non-linear models are employed to capture diverse data relationships. Linear Regression (LR) is introduced as a baseline owing to its simplicity and interpretability [40]. To address non-linearity and interactions, we include tree-based and boosting methods. The models include:  
* **Linear Regression (LR)--**Establishes a linear relationship between input features and target values [40].
* **Decision Tree (DT)--**Splits data into hierarchical branches based on feature values [41].  
\begin{table}
\begin{tabular}{l l l l l l} \hline \hline
**Feature** & **Description** & **Category** & **Feature** & **Description** & **Category** \\ \hline _goals_ & Total goals scored & Raw Data & _yellowcards_ & Number of yellow cards & Raw Data \\ xG & Expected goals & Raw Data & _red\_cards_ & Number of red cards & Raw Data \\ _assists_ & Total assists & Raw Data & _yps_ & Yellow cards per game & Engineered \\ _xA_ & Expected assists & Raw Data & _ypm_ & Yellow cards per minute & Engineered \\ _shots_ & Total shots taken & Raw Data & _rpg_ & Red cards per game & Engineered \\ _kay\_passes_ & Total key passes & Raw Data & _rpm_ & Red cards per minute & Engineered \\ _urpg_ & Non-penalty goals & Raw Data & _games_ & Total games played & Raw Data \\ _nrgG_ & Non-penalty expected Ggoals & Raw Data & _time_ & Total minutes played & Raw Data \\ xG_Chain_ & xG contribution in possession chains & Raw Data & _gpm_ & Goals per minute played & Engineered \\ xG_Building_ & xG excluding shots and assists & Raw Data & _apg_ & Assists per game & Engineered \\ _xGdiff_ & Difference between xG and goals & Engineered & _slupg_ & Shots per game & Engineered \\ _xGg_ & Expected goals per game & Engineered & _slpm_ & Shots per minute played & Engineered \\ _aGg_ & Actual goals per game & Engineered & _kprg_ & Key passes per game & Engineered \\ _pestation_ & Encoded positional category & Engineered & _kprg_ & Key passes per minute & Engineered \\ _lague\_weight_ & League-specific weight factor & New Feature & _goalsPerPosArg_ & Goals normalized to position average & Engineered \\ _xGPerPosArg_ & xG normalized to position average & Engineered & _assistedPerPosArg_ & Assists normalized to position average & Engineered \\ _xGPerPosArg_ & xGg normalized to position average & Engineered & _aGgPerPosArg_ & aGg normalized to position average & Engineered \\ _xGPerPosArg_ & Shots normalized to position average & Engineered & _goalsSzore_ & Z-score of goals & Engineered \\ _xGZScore_ & Z-score of xG & Engineered & _assisSzore_ & Z-score of assists & Engineered \\ _xGgZScore_ & Z-score of xGg & Engineered & _aGgZScore_ & Z-score of aGg & Engineered \\ _shotsSzore_ & Z-score of shots & Engineered & _keyPlasses_ & Z-score of key passes & Engineered \\ _xGRatio_ & xG to actual goals ratio & Engineered & _xGgRatio_ & xGg to aGg ratio & Engineered \\ _aGgRatio_ & aGg to xGg ratio & Engineered & _teamEnclosed_ & Team-specific encoding & Engineered \\ _positionEncoded_ & Encoded-position category & Engineered & _age_ & Player’s age & Raw Data \\ \hline \hline \end{tabular}
\end{table}
Table 6: Specification of features used for training and prediction.  
Figure 1: Study workflow from data collection to prediction.  
* **Gradient Boosting (GB)**--Iteratively improves performance by correcting previous errors [42].
* **XGBoost (XGB)**--An efficient and scalable gradient boosting method optimized for structured data [43].  
Model performance is evaluated using multiple metrics: mean squared error (MSE), root mean squared error (RMSE), mean absolute error (MAE), and coefficient of determination (\(R^{2}\)), providing a comprehensive overview of accuracy and model fit.