A soccer match can be seen as a sequence of on-the-ball actions. These include passes, shots, dribbles,...
Only 1% counts
The traditional metrics focus only on shots. For most players, these constitute
less than 1% of all the actions they undertake. Ideally, we want to assign a
value to each action performed by a soccer player that captures how helpful
that action was for winning the game.
An example
As an illustrative example, consider this through ball by Laporte in the
game against Wolverhampton on January 12, 2019.
It is pretty clear that Laporte’s pass plays a crucial role in enabling Jesus’
goal. However, in traditional football statistics, only Sané (assist) and Jesus
(goal) receive credit for their actions. This illustrates why we need more advanced
metrics for valuing the contributions of soccer players.
Actions change the game state
The effect of the pass was to change the game state from one state
to another. Intuitively, the game state entails everything that has
happened in a game up until now, so the current score, time left,
the current location of the ball, all prior actions, etc.
Good actions increase the probability of scoring and decrease the probability of conceding
Notice that the probability of scoring in the near future is much higher in
the post-action state, compared to the pre-action state. At the same time, Manchester City's
probability of conceding (slightly) decreases. Consequently,
a natural way to assess the usefulness of an action is to assign
a value to each game state. Then an action’s usefulness is simply
the difference between the scoring probabilities in the
post-action game state and pre-action game state.
The VAEP formula
This formula expresses this insight in a mathematical form.
Intuitively, the player actions that increase a
team’s chance of scoring receive positive values while those actions
that decrease a team’s chance of scoring receive negative values.
This is a machine learning task!
To compute the VAEP value, we have to estimate the scoring
(Pscores) and conceding (Pconcedes) probabilities for the
team in possession. This is a standard machine learning problem that can be solved
with two probalistic models: one that estimates the probability that the team in possession
will score in the next few actions after game state Si, and a second one that the team in possession will
concede a goal in the next few actions.
VAEP represents a gamestate by the 3 last actions
Instead of defining features based on the entire
current game state, VAEP only considers the previous
three actions.
Transform to feature vectors
From these three actions, VAEP extracts features that impact the
probability of a goal being scored in the near future.
We can now rate every action
We can now assign a value to each individual action, even those that do not impact the scoreline directly.
...and every player
By aggregating soccer players’ action values, their total
contribution can be quantified.