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Valuing Actions by Establishing Probabilities (VAEP) Analysis

Updated: Mar 9

Authors: Prasad Mistary, Anusree KJ, Rohan Prabhakar


This blog contains detailed information on Why and How VAEP analysis is done to get VAEP ratings. It also contains information on the algorithms used for the VAEP analysis.

  1. VAEP analysis

  2. How to determine the best TEAM or a WINNING TEAM in Football?

  3. Why do we need the VAEP analysis?

  4. Assigning values to actions…

  5. By assigning values to game states

  6. XT

  7. Implications of XT’s and VAEP’s Design Choices

  8. Actions Speak Louder Than Goals: Valuing Player Actions in Football

VAEP Analysis

A soccer player’s actions impact his team’s performance in games. The task of objectively quantifying the impact of the individual actions performed by football players during games remains largely unexplored to date. While most actions do not have an impact on the scoreline directly, they often have important longer-term effects. For example, a long pass from one flank to the other might not straightaway cause a goal; however it will open up some space to line up a goal probability chance several actions down the line.

To help fill the gap in objectively quantifying player performances, FOT (Friends of tracking), VAEP proposes a novel data-driven framework for valuing actions in a soccer game. Unlike most existing work, it considers every type of action (e.g., passes, crosses, dribbles, take-ons, and shots) and accounts for the circumstances below that each of those actions happened, as well as their possible longer-term effects. That is, an action valued at +0.05 is expected to contribute 0.05 goals in favor of the team performing the action, whereas an action valued at -0.05 is expected to yield 0.05 goals for their opponent. In the field of data science research for analyzing sports data, our approach fits better than most recommendation systems. (e.g., [9, 19, 24, 27]).

We propose SPADL (Soccer Player Action Description Language) as an attempt to unify the current event stream formats into a standard vocabulary that permits succeeding data analysis.

How to determine the best TEAM or a WINNING TEAM in Football?

Why do we need the VAEP analysis?

Assessing the impact of the individual actions performed by football players could be a crucial task in football analytics. But both the traditional metrics (shots and assists) and their context-dependent successors (xG and xA) fall short when addressing the task because they mostly focus on rare actions like shots and goals only. For most players, these constitute less than 1% of all the actions they undertake. Ideally, we wish to assign a worth to every action performed by a player that captures how useful that action was for winning the sport.

Assigning values to actions…

The contributions that we want to measure are restricted by the info we have. This post focuses on approaches for event stream or play-by-play data that suggest that the information solely contains the placement of the player possessing the play, While the location of other players is not considered for valuation. Here’s what the laporte’s stream of the event for passes looks like:

By assigning values to game states

The existing approaches all start by assigning values to game states rather than directly assigning values to actions. Considering the two photos below will give an intuition of the underlying events.

The above images are from the same game, and the image on the right shows Laporte’s passes to Sane and the image on the right shows that Sane, successfully receives and controls the ball. The game was changed with the effect of passing. Intuitively, the sport state entails everything that is going on in a game up until now, therefore the current score, time left, the present location of the ball, all prior actions, etc.

Consequently, a way to assess the quality of an action is by assigning a value to every game state. Then an action’s usefulness is simply the difference between the post-action game state Si and pre-action game state Si−1. This can be expressed as:

U(a_i) = V(S_i) - V(S_{i-1})

where, V is termed to be the value of a particular state of a game.

The variations among the assorted approaches arise in terms of (1) however they represent a game state, that is, outline qualities like the ball’s location or score difference that capture relevant aspects of the game at any specific point in time; and (2) assign a value to that specific game state.


The expected threat(xT) model is a model derived on the basis of possession. That is, it divides matches into possessions, which are periods of the game where the same team has the management of the ball. The key insights underlying xT are that (1) players perform actions with the intention of increasing their team’s chances of scoring, and (2) the prospect of scoring may be adequately captured by considering the placement of the ball.

Point (2) means xT represents a game state only by mistreating the present location of the ball. Therefore, xT overlays an M \times NM×N grid on the pitch in order to divide it into M \cdot NM⋅N zones. Each zone zz is then assigned a value \textrm{xT}(z)xT(z) that reflects how threatening teams are at that location in terms of scoring:

The Markov decision process can provide the value of each zone. For an intuitive explanation of how this works, we refer to Karun’s blog post.VAEP relies on a rather totally different insight than xT, that is that players tend to perform actions with two attainable intentions: (1) to increase their team’s chances of goal evaluation in the future, and (2) to decrease their team’s chances of getting a goal conceded in the near future. The value of game stated by VAEP is as:

Where P{score}(Si, t) and P{concede}(Si, t) are the probabilities that the team which possesses the ball in state Si will respectively score or concede in the next 10 actions.

A more complex representation of the game state is also used by VAEP: Considering the last three actions made with the ball by players : Si = {a{i-2}, a{i-1}, a{i}}. Below are the laporte’s pre and post-action of the event passing:

However, in reality, these game states are converted to a feature-vector representation such that the P{score}(Si, t) and P{concede}(Si, t) values can be “learned." That is, a gradient-boosted binary classifier is trained on historical information to predict; however, a game state can end up supporting what happened in similar game states that arose in past games.

Implications of xT’s and VAEP’s Design Choices

xT and VAEP are similar approaches in the sense that they each value players’ individual on-the-ball actions by computing the variations between the sport state values before and after the action. However, they approach the matter in numerous ways, which end up in 3 vital sensible variations.

Types of actions valued

xT is a “ball-progression model” which only values the events made with the ball and doesn’t focus on the other events (i.e., passes, dribbles, and crosses). Hence, it ignores defensive actions like tackles and interceptions and also ignores valuable offensive actions like take-ons inside an equivalent zone of the pitch. In contrast, VAEP’s continuous game state illustration permits it to think about defensive actions like tackles, interceptions, and recoveries that don't progress the ball.

Risk of actions

The xT model only values the associate action’s offensive contribution, i.e., how it changes the team’s scoring probability. In contrast, VAEP both(1) values a game state by considering the likelihood of concession and (2) reasons regarding what happens after turnovers. Hence, it should capture the risks related to taking certain actions by reasoning how an action alters a team’s likelihood of concession in addition to the action’s offensive contribution.


The xT framework assigns values to game states that only support the situation of the ball. Hence, one will make a case for why a state receives a precise value: it's the expected future xG of a possession beginning in this location. In distinction, VAEP uses an oversized set of options to explain a game state, which needs employing a learned model (e.g., a gradient-boosted tree ensemble) to evaluate game states. As such, game state values are derived from complicated interactions among a large set of options. Explaining why a selected value is allotted to a particular game state is no longer simple during this framework.

Player ratings

These differences have an important impact on the players who are identified as stand-out performers. To illustrate these variations, the table below lists the twenty-five players recording the best output in terms of goals, assists, disturbance, and VAEP within the Premier League 2018/19 season. The more time on the pitch spent by the players helps in its VAEP analysis as players are valued per 90min of the playtime.

The top-25 players United Nations agency contend a minimum of 900 minutes within the 2018/19 Premier League season in terms of goals scored, assists, xT ratings, and VAEP ratings.

Both xT and VAEP are successful at identifying top players. Yet, there are some major variations between each ranking. The main distinction is that the xT-based rankings are biased toward inventive players that complete several key passes and dribbles, whereas VAEP is biased toward strikers. This result of VAEP typically assigns goals high action values such that players will boost their rankings by scoring several goals. The correlation between the different metrics can also provide an intuition of rankings between players. For VAEP (ρ{goals/90} =0.25), we obtain a stronger correlation with goals per 90 minutes than xT (ρ{goals/90} =0.11), while assists per 90 minutes are correlated stronger with xT (ρ{assists/90}=0.40) than with VAEP (ρ{assists/90}=0.37). Most significantly, these correlations prove that each metric turns out rankings that deviate from those created by considering ancient goal-and assist-based metrics. Hence, there are valuable metrics that may give further insights into player performance.

The top of the list contains attacking players, whereas defensive players are ranked lower. In each model, offensive actions have access to higher rewards. It is much easier for offensive players to get higher ratings than defensive players.

Actions Speak Louder Than Goals: Valuing Player Actions in Football

Action ratings

Below four images are the different actions to get an insight into how VAEP and xT assess the difference in context.

A (risky) backward pass within the own half

Backward passes have a stimulating risk-reward trade-off as they typically open up area (reward), however moving the ball nearer to the team’s goal (risk).

Setting up the counter-attack by recovering the ball

Recovering the ball in their own half while the opponent continues to remain in an offensive position provides a team the chance to build a quick counter-attack that exploits the opponents’ unorganized defensive positioning and therefore increases the chances of scoring a goal. The fact that the ball was very recently recovered (and how this differs from traditional open play) may be a contextual clue that can only be leveraged by VAEP’s additional strong reasoning on game states. Hence, VAEP rates these actions considerably higher than xT.

The ball was into the opponent’s penalty box with a forward dribble

xT assigns a value of 0 to the majority of forward dribbles inside the penalty box. Since xT discretizes the pitch into comparatively larger zones, several short dribbles don't move the ball into a different zone and hence do not increase the xT worth. Yet, these short dribbles could be enough to take on a defender and — once the ball is extremely close to the goal — little variations in location will significantly increase the odds of scoring.

A through ball near the opponent’s penalty box

A forward pass to the border of the bench will significantly raise the percentages of evaluation of a goal for two reasons: (1) it moves the ball nearer to the goal, and (2) it usually bypasses a minimum of one player from the opposing team. On average, xT values the advantage of position gained by a through ball more than VAEP. Due to the elaborated game state illustration utilized by VAEP, it's difficult to know why VAEP assigns lower values to these types of actions than xT. One possible explanation for this can be that xT is superior to VAEP at capturing the positional advantage.


VAEP analysis covers about 1600 actions that cannot be covered by traditional matrix methods to analyze the potential of a player. The traditional matrix takes only 1% of actions into consideration, making it difficult to calculate the probability of goals scored and conceded. VAEP is an in-depth research of years on the soccer player's individual actions, which makes it capable of predicting the probability as well as suggesting the recommendation for a soccer player.

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