Valuing actions in soccer is one of the hardest and most crucial parts for both game analysis and recruiting.
Frameworks like xG, xT, and VAEP excel at modeling offensive contributions but struggle with defensive
actions that prevent events rather than cause them. This work takes a counterfactual approach: measuring
how a defender's action shifts danger relative to what was expected given the duel's context.
Concretely, for an observed outcome \(c^\star\) at location \((x, y)\) with speed-of-play context \(\text{SoP}\),
the duel's value is
\[
\mathrm{DDV} \;=\; \underbrace{\sum_{c}\; P(c\mid x,y,\text{SoP})\,P(\text{goal}\mid c,x,y,\text{SoP})}_{\text{expected danger}}
\;-\; \underbrace{P(\text{goal}\mid c^\star,x,y,\text{SoP})}_{\text{realized danger}}.
\]
Positive DDV means the defender averted more danger than the average duel in that situation would have.
Where defensive duels happen
Smoothed marginal density of defensive-duel start locations across the dataset. Bright bands show where contests
cluster — wide channels in our own half and along the defensive third — and motivate why DDV is most informative
where duels actually occur.
Methods
Data from 800k+ defensive duels across 7k+ Wyscout matches were analyzed. For each duel, outcome and
spatial features were extracted, and a binary danger label was assigned based on whether a goal was conceded within
20 seconds of the duel. Three speed-of-play features captured pre-duel ball tempo:
net x-displacement of the ball in the prior 30 s — \(\Delta x_{30}\)
total ball distance in the prior 30 s — \(d_{30}\)
ratio of ball distance over 30 vs. 60 s — \(d_{30}/d_{60}\)
Two LightGBM models were trained on the spatial and speed-of-play features:
\[
\text{outcome model:}\quad P(c\mid x,y,\text{SoP}),\;\; c\in\{\text{beat, stopped, recovered}\}
\]
\[
\text{danger model:}\quad P(\text{goal in next 20s}\mid c, x, y,\text{SoP})
\]
Combining the two yields the per-duel value via the formula above. The interactive panels below let you query both
surfaces at any \((x, y, \text{SoP})\) the models support.
Interactive duel breakdown
Click anywhere on the defensive half to place a duel, pick the outcome, and adjust the three speed-of-play context
sliders to see how the location prior \(P(\text{outcome}\mid x, y, \text{SoP})\) and the conditional goal risk
\(P(\text{goal}\mid x, y, \text{outcome}, \text{SoP})\) respond. The Duel Value is the gap between expected
and realized danger, both evaluated at the same location and speed-of-play context.
Step 1 · click to place the duel
Step 2 · pick the observed outcome
Step 3 · Speed of play context
x—
y—
outcome—
Click on the pitch and pick an outcome to see the DDV breakdown.
\(P(\text{outcome}\mid x, y, \text{SoP})\)
Bars shift when you move the speed-of-play sliders — how often each outcome occurs at this location given this
context.
\(P(\text{goal}\mid x, y, \text{outcome}, \text{SoP})\)
Chance a goal is conceded in the next 20 s given the location, outcome, and speed-of-play context.
Combining the two
Duel value—
Where does this duel rank?
Histogram of duel values across all defensive duels in the dataset. The red line marks
this duel's value; percentile is the share of duels with a smaller value.
duel value—
percentile—
population mean—
population std—
—
How the probabilities vary across the pitch
The speed-of-play sliders below control the context used by all four surface tabs. Each tab shows one
panel per outcome (beat / recovered / stopped). Toggle tabs to see where the models place each quantity across the
defensive half.
Speed of play context for surfaces
\(P(\text{outcome}\mid x, y, \text{SoP})\)
\(P(\text{goal}\mid x, y, \text{outcome}, \text{SoP})\)
\(\mathrm{DDV}\mid x, y, \text{outcome}, \text{SoP}\)
\(\mathrm{DDV}\,\cdot\,P(\text{duel}\mid x, y)\)
How speed of play impacts the probabilities
How much does shifting a speed-of-play feature alone change the model's output at each location? Each panel is a
difference heatmap: the probability evaluated with the SoP feature pinned at its 90th percentile
minus the probability evaluated with that feature pinned at its 10th percentile, with the other two SoP
features held at their population medians. Hot cells = the location is markedly more likely to produce that
outcome (or concede a goal) under high-tempo play; cold cells = high tempo suppresses it. Panels are arranged as
SoP feature (rows) × outcome class (columns); use the tabs to switch between the duel outcome and
conditional goal models.
\(\Delta P(\text{outcome}\mid x, y, \text{SoP})\)
\(\Delta P(\text{goal}\mid x, y, \text{outcome}, \text{SoP})\)
Formula derivation
Expected danger is the marginal goal probability at this location given the speed-of-play context:
\[
\mathbb{E}[\text{danger}\mid x, y, \text{SoP}]
\;=\; \sum_{c}\; P(c\mid x, y, \text{SoP})\,P(\text{goal}\mid c, x, y, \text{SoP})
\]
Realized danger is the goal probability under the actual observed outcome \(c^\star\):
\[
\text{realized} \;=\; P(\text{goal}\mid c^\star, x, y, \text{SoP})
\]
Defender value is positive when the observed outcome beat expectations: