Dynamic Threat Under Risk: a structural view of player value in possession

Most football analytics frameworks are built around a single implicit assumption: that value in possession can be meaningfully reduced to how much danger an action creates. Whether expressed as expected goals, expected threat, possession value or packing-based measures, the dominant paradigm evaluates actions primarily by their offensive upside.

This paradigm is powerful, but incomplete.

Football possessions do not fail because they fail to create danger; they fail because they collapse. And collapse is not symmetric to creation. It has its own dynamics, its own contributors, and its own specialists. By collapsing creation and exposure into a single scalar, most existing metrics erase this distinction.

This article introduces a framework designed to explicitly separate these dimensions. We refer to it as Dynamic Threat Under Risk (DTUR) — not as an established standard, but as a working conceptual model that makes its assumptions explicit and falsifiable.

DTUR does not ask how valuable an action is. It asks what structural role a player performs inside possession dynamics.

For the analysis, we will use the Al-Wehda vs Al-Nassr match (2-0) from matchday 5 of the 2024/25 Saudi Pro League.

Threat is dynamic, and so is risk

At the core of DTUR are two quantities measured over short possession windows.

The first is ΔxShot: the change in shot probability between the beginning and the end of a possession window. Importantly, this is not a territorial or geometric measure. It captures how much an action sequence transforms the conditional likelihood of a shot occurring later in the possession.

The second is xLoss (peak): the maximum probability of losing the ball reached during the same window. This is not a turnover label, nor a binary event. It is a measure of exposure: how close the possession comes to structural failure.

These two quantities are not opposites. A possession can simultaneously increase its future shot probability and increase its probability of collapse. Treating one as the negative of the other is a modeling shortcut, not a football truth.

The role space: creation and exposure as orthogonal dimensions

When players are projected into a two-dimensional space defined by mean ΔxShot and mean peak xLoss, several patterns emerge immediately.

First, creation and risk do not form a continuum. Players populate all quadrants of the space, including profiles that generate threat with minimal exposure, and profiles that absorb large amounts of risk without producing direct danger.

Second, the absence of creation does not imply safety. Some of the highest-risk profiles correspond to players whose direct offensive contribution is negligible, yet whose involvement is structurally necessary for the possession to exist at all.

This already challenges one of the most persistent evaluative shortcuts in football analysis: that low attacking output implies low responsibility.

Context is not role: normalizing within possession

Raw values are inseparable from context. A player operating in a dominant positional structure inherits a different baseline of risk and opportunity than one playing in a transitional environment.

To disentangle role from context, DTUR normalizes ΔxShot and xLoss within each possession, using z-scores. This operation does not claim statistical purity; it enforces a conceptual constraint: players are compared to the conditions they actually experience.

The result is revealing. Some profiles shift dramatically after normalization, indicating that their apparent role was largely contextual. Others remain remarkably stable, suggesting that their function persists regardless of possession state.

This distinction is essential for any attempt at role-based evaluation rather than output-based ranking.

Inherited risk: receiving chaos versus creating it

One of the most consequential blind spots in event-based models is the assumption that the player in possession creates the situation they operate in. Tracking data shows that this is frequently false.

DTUR introduces inherited xLoss: the risk level at the moment the player receives the ball. This separates players who actively push possessions into unstable states from those who are tasked with operating inside pre-existing chaos.

The resulting picture reframes several common interpretations. Players with low creation but high inherited risk are often labeled as passive or conservative. In reality, they may be structural stabilizers, absorbing instability generated elsewhere and preventing possession collapse.

Temporal asymmetry: builders and exploiters

Risk inside a possession is not static. It rises, peaks, and resolves. DTUR exploits this temporal structure by splitting each possession at its maximum xLoss and measuring player contribution before and after that point.

This reveals a fundamental asymmetry in player behavior. Some profiles consistently generate threat before the possession becomes unstable. Others specialize in extracting value after instability already exists.

These are not stylistic differences; they are structural roles. Confusing them leads to systematic misinterpretation of forwards, attacking midfielders and wide players whose value depends on chaos created by others.

Efficiency, elasticity and saturation: how risk converts into threat

DTUR introduces several derived diagnostics to explore how players interact with risk.

Efficiency measures creation per unit of exposure. It highlights profiles that extract value cheaply versus those that require large structural risk to produce marginal gains.

Risk elasticity estimates how sensitive a player’s ΔxShot is to changes in xLoss. High elasticity indicates that increased instability translates into threat; low elasticity suggests that risk dissipates.

Risk saturation explores non-linearity: whether additional risk continues to pay off or reaches diminishing returns. The resulting curves are not rankings, but fingerprints of interaction with chaos.

None of these metrics are meant to be definitive scores. Their purpose is diagnostic: to describe how a player converts instability into attacking potential.

Persistence: separating structure from noise

Any dynamic framework must confront the question of stability. DTUR evaluates persistence by tracking role scores across matches or periods.

Players with narrow, centered distributions exhibit role consistency, suggesting that their position in the role space reflects a stable function rather than match-specific variance. Wide or drifting distributions point to context dependency.

This step is critical. Without persistence, role-based interpretation collapses into anecdote.

The counterexample: when non-creation is structural

DTUR explicitly searches for players who violate common evaluative intuition: low creation, high exposure, high inherited risk.

These profiles are often invisible or penalized in traditional metrics. Yet removing them from the system frequently destroys the possession structure itself.

Any framework that cannot accommodate this counterexample is not measuring football; it is measuring highlights.

From abstraction to pitch reality

Finally, DTUR grounds its abstractions in spatial reality. Selected high-impact possessions are visualized using tracking data, showing how risk accumulation, stabilization and threat generation manifest on the pitch.

These trajectories are not illustrative decorations. They are consistency checks: if the abstract role does not align with observable behavior, the model fails.

What DTUR is — and what it is not

DTUR is not a replacement for xG, xT or possession value models. It does not claim to rank players globally or to predict outcomes.

It is a role-disentangling framework. It separates creation from exposure, initiative from inheritance, and structure from output.

Most importantly, it makes explicit a dimension of football that has always existed but has rarely been measured: who carries the risk that makes danger possible.