Key Takeaways
• G+ & VAEP models are both efficient models with a certain overlap of rating players- Player Rating Model
• xT is easy interpretable and allows for greater buy in from experts, PV model is based on Liverpool’s Talent ID model
• G+ model allows for a bigger sample (Shots) but relatively less accurate (ML experts)
• A moderation of the G+ model (solved as a multi-class classification problem) or the model itself can be used for Talent ID
Rating System Approaches- In Depth Review
Frequency-based rating approaches:
(Pappalardo et al, 2019) use a frequentist approach to determine a player rating defined as a scalar product of the frequency of set of features representing a player’s performance across matches and weights given to each feature based on a two-phase learning process. The first step is based on the correlation between a team’s performance and the match outcome. The team performance is aggregated over the set of features and averaged over the number of players in that match. The second step is then solved as a classification problem keeping the match outcome as the output variable using a Support Vector Machine (SVM) model for which the weights are then extracted. (Pappalardo et al, 2019) also used cluster centres for automatic role detection amongst players using their average positions through a soft clustering which allows for hybrid roles amongst players (for eg: Attacking Midfielder and Right Wing Forward as positions of the same player).
A similar frequentist-based weighted approach was used by (McHale et al,2012) where a set of six indices were used to evaluate the final rating of a player. The first of the indices was evaluating contributions of players in relation to match outcomes. A set of features (actions) were modelled by an OLS method showing positive and negative coefficient relationships towards match outcome to identify their value. The final match contribution index was defined as a product of the number of actions/contributions a player makes to the value of the contribution identified through the model.
To evaluate effectiveness of all roles amongst players, three other indices were created specifically for strikers (goal scorers), goal keepers and assist makers (key passes leading to a goal). An inclusion of an index to evaluate number of caps (appearances) made by a player was also used in addition to another index that divides points amongst players based on the number of minutes they spent on the pitch.
Expected Possession Value (EPV) based approaches:
The first of many Expected Possession Value (EPV) framework studies during Open-Play was (Rudd,2011)’s study on player ratings using Markov Chain Decision (MDP) Process. (Rudd, 2011) used 39 states which were subdivided into set pieces, location through zones and the defensive state of the team. It also included “2 absorbing states” defined as a goal or an end of possession.
The probability of scoring from set pieces were calculated by bootstrapping samples and using a k-fold validation (5 folds) across two previous seasons. For the absorption states, the probability of staying in the same state was 1 and transitioning to another state was 0. Transitioning can take place across zones until the probability converges to either of the absorbing states.
(Cervone et al, 2014) notably created an EPV framework using optical tracking data in basketball which is also based on a Markovian model. The model helped understand a players’ decision-making ability by breaking down any action a player makes into two types called micro and macro transitions. The model used the spatial organization of teammates in each moment as potential options. Like (Rudd, 2011)’s study, the so-called transitions were used to define actions (pass or shoot: micro) and (movement in either direction: macro).
In another study using MDP processes, (Singh, 2019), split the field into 192 equally sized zones and evaluated the probability of either moving or shooting from any of these zones. (Singh, 2019) assigned credit to individual actions known as Expected threat (xT) in possession sequences to identify which players in a team are highly like to influence a sequence of play during a possession sequence. Using a transition matrix to identify probabilistic movement of the ball to any of the zones, Expected Threat (xT) iteratively assigns credit to each action based on previous xT values in the chain. xT values start at zero for all zones and reach convergence iteratively typically after 4 iterations or actions (Singh, 2019). The benefit of using xT as an evaluation metric for player ratings is in its interpretability and relatability. It encapsulates the widely accepted Expected Goals (xG) model and the idea of transitioning between zones replicating real life possession sequence of teams.
(Mackay, 2019) introduced a possession-value (PV) framework that evaluates and assigns positive/negative credit based on various actions on the ball. The PV framework considers the likelihood of a sequence containing a set of actions that may end up as a goal based on actions within the sequence. The model awards positive values of possession for progressive actions on the pitch based on bespoke metrics. These bespoke metrics are based on set thresholds defined by average distance of actions like passes and carries (for eg: 5 metres for carries, 30 metres for passes). The model awards negative values in possession sequences to actions that regress the ball further away from goal, lead to a Loss of Possession (LOP) due to an action (unsuccessful: dribble, pass) and LOP that leads to direct attacking threat for the opposition.
(Decroos et al, 2017) used a Dynamic time warping (DTW) algorithm to measure similarities between different possession sequences and combined it with a K-nearest neighbour (KNN) search to identify closest resembling possession sequences within a game. Possession sequences were then rated as a ratio or a proportion of possession sequences that ended up as a goal to the total number of similar possession sequences (KNN algorithm). The possession sequence (PS) rating was then weighted across players who performed actions during the sequence based on exponential decay approach. More importance or weight was provided to actions towards the end of possession sequence rather than initial actions.
Actions based approach
The VAEP framework introduced by (Decroos et al, 2019), evaluates player actions and evaluates ratings broadly based on two outcomes i.e. Scoring a goal and Conceding a goal. The framework defines sequence of actions as a “fixed length feature vector” as part of modelling a sequence of actions using a machine learning algorithm. The game state is defined by three preceding sequence of actions and contextual features such as speed of play, body part, location and action type describing them that constitute the feature set. The probability of scoring and conceding for a given game state were calculated using event-stream data across 5 seasons using xG boost classifier as the optimal algorithm for binary classification of outcomes. The difference in probabilities of scoring prior and post the action is calculated to the identify the first equation known as Score Increase. Simultaneously, the second equation is the difference in probabilities of conceding is calculated for pre-action and post-action game states. The aggregated score provides the likelihood of scoring or conceding for every game state and player. Player ratings are normalised over 90 minutes for purposes of comparison and especially for scouting players across different European leagues.
(Kullowatz et al, 2020) proposed a relatively similar action-based approach called the Goals added G+ model which considers a set of features defined as a feature vector representing the game state. The model predicts the probability of scoring and conceding given the game state within a possession sequence. The model is primarily solved as a regression problem. It is used to predict the Expected Goals (xG) as the target variable from which the value or credit is split and is assigned to players within a possession sequence. The model also considers pass completion percentage due to its design considerations where a passer and receiver are treated as independent agents within a possession sequence.
(Ben Torvaney, 2018) used player actions defined by specific text and vectorized these actions using a word2vec model that is popularly used in the field of Natural-Language-Processing (NLP). The study used a list of role specific actions that defined players contribution to a game by converting these text defined actions to numbers. Ideally the vectorized actions could be fit through any model to determine outcomes but (Ben Torvaney, 2018) brought actions contained in a higher-dimension feature vector and used eigen-vector distances to identify similarity in players. (Perdomo & Gardiner, 2018) used a dimensionality reduction technique called Linear-Discriminant-Analysis (LDA) to identify frequency of actions to contextually categorize players based on their actions.
References
Aalbers, B., & Van Haaren, J. (2018, 9 13). Distinguishing Between Roles of Football Players in Play-by-play Match Event Data.
Kharrat, T., López Peña, J., & Mchale, I. (n.d.). Plus-Minus Player Ratings for Soccer.
Bransen, L., Robberechts, P., Van, J., & Davis, H.-J. (n.d.). Choke or Shine? Quantifying Soccer Players' Abilities to Perform Under Mental Pressure.
Meza, D., Girela, D., Thompson, M., & Goldring, J. (2019). How To Break Down a Set Defence Twenty3 Sport.
Davies, B. (2016). Unsupervised Playing Style Detection PLAYER EFFECTS ON TEAM PERSONA.
Decroos, T., Van Haaren, J., Bransen, L., & Davis, J. (2019). Actions speak louder than goals: Valuing player actions in soccer. Proceedings of the ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (pp. 1851-1861). Association for Computing Machinery.
Decroos, T., Van Haaren, J., Dzyuba, V., & Davis, J. (n.d.). STARSS: A Spatio-Temporal Action Rating System for Soccer
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