Dynamic Off-Ball Value (DOV): A Spatially and Temporally Consistent Framework for Off-Ball Evaluation in Football

Modern football analytics has made enormous progress in valuing on-ball actions. Metrics such as xG, xT, possession value, and action-based VAEP-like models have become standard tools to evaluate decision-making when a player interacts directly with the ball.

However, football is a continuous, spatial game, and the majority of tactical value is generated away from the ball. Players constantly move to create space, occupy threatening zones, stretch defensive structures, and prepare future actions that may or may not occur.

Despite this, most off-ball models still suffer from a fundamental limitation:they try to assign value to players, rather than to space.

This article introduces Dynamic Off-Ball Value (DOV), a framework that reframes off-ball evaluation as a spatial and temporal field problem, grounded in tracking data and governed by explicit mathematical constraints. DOV does not ask “which player is valuable?”, but instead:

“Which areas of the pitch are valuable right now, and why?”

1. Off-Ball Value as a Spatial Problem

Off-ball value in football is fundamentally a spatial phenomenon. Players do not create value simply by existing or by moving in isolation, but by altering the value distribution of space around the ball, their teammates, and the opponent’s defensive structure.

For this reason, Dynamic Off-Ball Value (DOV) is not defined at player level. Instead, it is defined over the pitch itself, as a continuously evolving surface. At any moment, every location on the field has a measurable level of offensive usefulness, depending on three conditions:

• How inherently dangerous that space is

• Whether the attacking team can realistically reach it

• Whether the defending team can effectively deny it

Only when all three conditions are satisfied does off-ball value emerge.

2. The Pitch as a Continuous Field

The pitch is treated as a two-dimensional domain expressed in OPTA coordinates, ensuring full compatibility with professional tracking and event data. Rather than assigning discrete zones or static areas, the pitch is discretized into a fine grid purely for numerical stability and visualization.

Each grid cell represents a small region of space where value is evaluated independently at every frame. Importantly, this discretization does not imply that football is discrete; it is simply a computational approximation of a continuous system.

This design choice allows DOV to behave smoothly across space, avoiding artificial boundaries such as thirds, lanes, or fixed tactical zones.

3. Structural Offensive Value: Where Value Exists

The first component of DOV represents structural offensive value. This component answers a simple but crucial question:

If a player could occupy this space without resistance, how threatening would it be?

Structural value depends exclusively on the geometry of the pitch and the location of the opponent’s goal. Central areas closer to goal are inherently more valuable than wide or deep positions. This value decays smoothly with distance and lateral displacement, and it is aligned with the team’s attacking direction.

Crucially, this component is static. It does not depend on players, possession state, or time. It represents the invariant offensive geometry of football.

This separation is deliberate. Structural value defines potential, not realization.

Focus on the V(x) panel

4. Spatial Control: Who Can Reach the Space

Structural value alone is meaningless if a team cannot access it. The second component of DOV captures spatial control, defined as the likelihood that the attacking team can reach a given location before the defending team.

Control is modeled as a competition between players. For each location on the pitch, the model evaluates how quickly attacking and defending players could realistically arrive there. These arrival times are then compared and transformed into a smooth probability.

Unlike classical Voronoi models, control is not binary. No space is ever fully owned. Instead, control gradually fades as defenders approach, reflecting the continuous and uncertain nature of real football interactions.

This makes the model robust to small positional changes and prevents unrealistic sharp borders in control maps.

Focus on the Cₜ(x) panel

5. Effective Pressure: Whether the Space Is Usable

Even if space is valuable and controllable, it may still be unusable due to defensive pressure. The third component of DOV models effective pressure, which represents the defensive capacity to disrupt actions directed toward a given location.

A key design decision is that pressure is directional. It is not evaluated purely based on distance, but relative to the passing or carrying lane from the ball to the target space. This reflects how defensive pressure actually functions in football.

Defenders who are well positioned along the ball–space line exert more pressure than those who are close but poorly oriented. Multiple defenders combine their influence through a saturating mechanism, ensuring that pressure increases realistically without becoming unstable.

Pressure is bounded between zero and one. When pressure approaches its maximum, space becomes functionally inaccessible regardless of its structural value or control.

Focus on the Pₜ(x) panel.

6. Dynamic Off-Ball Value as an Emergent Field

Dynamic Off-Ball Value emerges from the interaction of structure, control, and pressure. Value exists only where all three conditions align.

This multiplicative interaction enforces strict logical consistency:

• Valuable space that cannot be reached has no value

• Controlled space under heavy pressure has no value

• Pressure alone cannot create value

As a result, DOV highlights real, actionable opportunity, not theoretical danger.

7. Aggregation Without Losing Meaning

Because DOV is defined over space, aggregation becomes a natural operation rather than a forced abstraction.

Value can be summed over specific regions such as the final third, half-spaces, or box-adjacent zones. It can also be accumulated over time to analyze possessions, phases of play, or entire matches.

Crucially, aggregation happens after spatial evaluation, not before. This preserves tactical meaning and avoids collapsing spatial context into premature player ratings.

8. What DOV Is — and Is Not

Dynamic Off-Ball Value is not a replacement for xG, xT, or action-based value models. Instead, it complements them by addressing a different question.

DOV does not evaluate decisions after the fact. It evaluates opportunity before action.

It does not assign credit or blame. It describes the evolving landscape in which players operate.

Most importantly, it does not assume value comes from players. It assumes value comes from space — and players compete to exploit it.

9. Practical Implications

For analysts, DOV provides a rigorous way to quantify off-ball dynamics without heuristic shortcuts.

For coaches, it offers a lens to understand spacing, occupation, and structural dominance beyond event outcomes.

For researchers, it establishes a mathematically consistent foundation for future off-ball modeling, grounded entirely in tracking data.

For a deeper technical explanation, please read:

Mathematical Pathway and Technical Rationale Behind the DOV Model

1. From Player Ratings to a Field-Based Definition

The starting point was a conceptual limitation: traditional off-ball metrics are defined at the player level and evaluated retrospectively. They assign value to players, not to space. This makes them unsuitable for answering a more fundamental question: where does value exist on the pitch at a given moment, independently of who occupies it.

To address this, the model was reformulated as a continuous field over space, evaluated at each instant in time. Instead of asking “how valuable was this player’s movement?”, the question becomes:

If the ball were played to any point on the pitch right now, how valuable would that location be for the attacking team?

This shift forces a mathematical representation where value is a function of spatial coordinates and time, not discrete player actions.

2. Explicit Coordinate System and Domain Definition

A strict spatial domain was defined to avoid ambiguity and hidden assumptions.

The pitch is represented in a normalized football coordinate system, later converted to OPTA coordinates for visualization. All computations are performed in a fixed rectangular domain covering the full pitch. The model evaluates value on a regular grid over this domain, producing a discretized approximation of a continuous field.

This ensures that every output is interpretable as a spatial surface, not an artifact of player sampling or event density.

3. Separation of Structural and Temporal Components

A key design decision was to separate what is structural from what is state-dependent.

Structural components do not depend on the current frame. Temporal components depend explicitly on player and ball positions at time t.

This separation prevents information leakage and avoids circular definitions where value depends on itself.

4. Structural Offensive Value as a Static Prior

The first component introduced was a static offensive value surface.

This surface encodes long-term football knowledge. Proximity to goal increases value. Central lanes are more valuable than wide areas. Lateral positions are penalized relative to central ones. Value decays smoothly with distance, avoiding hard thresholds.

Crucially, this component does not depend on players, does not depend on possession, and does not change frame to frame.

It acts as a prior over space, representing where goals are more likely to be created in abstract football terms.

5. Spatial Control as a Race-to-Space Problem

The second component introduces time and players: who can reach each point first.

Instead of using hard Voronoi regions, the model adopts a probabilistic race formulation. For each grid cell, arrival times from attacking and defending players are estimated. Control is expressed as a soft probability, not a binary assignment. Faster players and closer players exert more influence.

This formulation allows overlapping influence zones, produces smooth transitions instead of sharp borders, and is stable under small positional changes.

Spatial control is defined relative to teams, not individual players, ensuring that the model remains team-centric.

6. Effective Pressure with Directional Awareness

Pressure is not defined as simple proximity to defenders.

Instead, pressure is contextual and directional. It is evaluated along the ball-to-location passing line, not in absolute space. Defenders between the ball and the target location exert more pressure than those behind or lateral. Distance, orientation, and accumulation of defenders are combined with saturation to avoid unbounded effects.

This ensures that pressure represents actual obstruction of play, not generic congestion.

7. Gating Logic and Value Collapse Conditions

A critical property of the model is that value must be accessible to exist.

Two hard constraints are enforced implicitly. If the attacking team cannot realistically reach a location first, value collapses. If pressure is maximal, value collapses even if the location is structurally attractive.

This produces a natural gating behavior. High structural value alone is insufficient. Control without safety is insufficient.

Value emerges only where structure, access, and feasibility align.

8. Multiplicative Composition and Boundedness

Instead of summing components, the model combines them multiplicatively.

This choice enforces several mathematical properties. All components are bounded between 0 and 1. The final value is also bounded. No single component can compensate for the complete absence of another.

The result is a field that is interpretable, stable, and can be compared across frames and matches.

9. Aggregation Over Regions and Time

Because the output is a field, it can be integrated over predefined regions such as the final third, half-spaces, or zones. It can be accumulated over time windows and compared between teams symmetrically.

This makes the model suitable not only for visualization, but also for downstream analysis, benchmarking, and tactical evaluation.

10. Outcome: A Mathematically Coherent Off-Ball Value Surface

The final result is not a heuristic score, but a well-defined spatial object. It is defined everywhere on the pitch, grounded in football constraints, responsive to tactical structure, and independent of subjective labeling.

Dynamic Off-Ball Value is therefore best understood not as a player metric, but as a field that reveals where football advantage exists at any given moment.