Introducing Possession Value Added (PV+)

A framework for valuing on-ball actions in terms of goal probability

What is PV+?

PV+ (Possession Value Added) is an action-value model I developed to measure contribution of every on-ball action in soccer. The model estimates how much each action — every pass, carry, tackle, shot, and reception — increases or decreases a team’s chances of scoring and conceding. By translating actions into units of goals scored and prevented, PV+ measures player performance in the currency that actually decides matches.

Background and Inspiration

PV+ was inspired by the pioneering work of American Soccer Analysis and their Goals Added (G+) metric. ASA’s framework demonstrated that on-ball actions could be systematically valued in goal units by modeling how each action changes the probability of scoring. Their work fundamentally shaped how I think about player evaluation, and PV+ would not exist without their foundation.

I built PV+ because I wanted a deeper, more contextual understanding of how action-value frameworks operate in practice — and to bridge this understanding with visualizations that communicate not just outcomes, but why and how actions matter. My motivation was twofold: to explore the limits of action-value modeling for soccer, and to improve the way these insights are communicated visually and intuitively. The result is a model that shares the core philosophy of action-value measurement while introducing its own architectural and interpretive decisions.

What I Built:

1. A complete data pipeline scraping and processing over 1.3 million MLS match events (this number will continue to grow)

2. A dual-model probability architecture (P+ and P-) for separately estimating attacking and defensive value

3. A nine-component value allocation system spanning passing, receiving, carrying, defending, and shooting

4. A framework that attributes Goals Prevented (GP) across all action types, not just defensive actions.

How PV+ Works

Step 1: Model the Game State

For every action, PV+ builds a representation of the current game state including

• Spatial context: Location on pitch, distance to goal, angle, pitch zone

• Momentum: progression, speed of play, directional movement

• Situational context: Post-turnover, set piece sequences, settled vs. transitional play

• Sequence features: What happened immediately before an action

Step 2: Two Probability Models

Unlike single-model approaches, PV+ uses two separate machine learning models trained on different outcomes

P+ (Attacking Model):

Given any game state, what is the probability the team in possession scores within the next 100 actions

P- (Defensive Model)

Given this game state, what is the probability the team in possession concedes within the next 100 actions.

Training these models separately allows PV+ to learn that the game states which lead to goals are different from the states that prevent them. This is particularly important for properly valuing defensive contributions.

Step 3: Measure the Delta

For every action, PV+ compares the game state before and after:

• If a pass increases scoring probability from 4% to 7% that action adds +0.03 Goals Added

• If a tackle decreases conceding probability from 8% to 2%, that action contributes +0.06 Goals Prevented

Step 4: Allocate Credit

Different actions generate value in different ways. PV+ reflects this through specific allocation rules:

• Passing & Receiving - 50% of the pass delta goes to the passer and 50% goes to the receiver

• Carrying - 100% of the carry delta goes to the ball carrier

• Defending - Full credit for both attacking value created and danger eliminated

• Shooting - Scaled xG-based value, rewarding position quality independent of finishing performance

The Nine Components of PV+

PV+ breaks down into nine distinct value components:

Goals Added (GA)

1. GA from Passing

2. GA from Receiving

3. GA from Carrying

4. GA from Defending

Goals Prevented (GP)

5. GP from Passing

6. GP from Receiving

7. GP from Carrying

8. GP from Defending

Shooting

9. Shooting Value

Total PV+ = Σ(Goals Added) + Σ(Goals Prevented) + Shooting Value

This granular breakdown allows analysis of how players create value, not just how much value they accumulate.

Using Player Rankings as Validation

A critical part of developing PV+ was using player rankings as a reality check. After training the model, I examined league-wide PV+ rankings to assess whether the outputs aligned with on-field performance and soccer intuition. The results were encouraging:

The very top of the leaderboard is dominated by established MLS stars—players widely recognized for consistently creating danger, progressing the ball, and generating high-quality chances. Names like Lionel Messi, Hany Mukhtar, Denis Bouanga, and Anders Dreyer naturally rise to the top, reinforcing that PV+ is capturing the attacking impact fans and analysts already recognize.

Just as importantly, defensive contributors also crack the top tier. Players such as Kai Wagner, Jeppe Tverskov, and Alexander Freeman, who add value on both sides of the ball, appear alongside elite attackers. The resulting rankings are not far off from what one might expect from an MLS All-Star XI.

What Makes PV+ Distinct

While PV+ shares philosophical roots with ASA’s Goals Added, I made several independent modeling decisions:

Dual Probability Architecture: Rather than a single possession value model, PV+ trains separate models for scoring probability (P+) and conceding probability (P-). This allows the defensive model to learn features specifically predictive of conceding, rather than simply the inverse of attack. The totals from these models are totaled in order to compute the final PV+ tally.

Action Horizon Approach: PV+ uses a 100-action forward horizon rather than possession-bounded sequences. This captures value that flows across possession changes — critical for properly crediting the value of attacking and defensive actions occurring throughout dynamic game states.

Universal GP Attribution: Goals Prevented value is allocated to all action types (passing, receiving, carrying, and defending), not just defensive actions. For example, an outside back who carries the ball away from danger contributes positive GP. This reflects the reality that all players participate in defensive structure even when their team is in possession.

Limitations

No metric captures everything. PV+ is strictly on-ball, which means:

• Off-ball movement that creates space is not fully captured

• Pressing contributions aren’t measured

• Positioning that closes passing lanes do not contribute value

• Tactical discipline and defensive shape takeaways are limited

Why PV+ Matters

Soccer is a low-scoring game where the moments that decide matches often don’t appear on the scoresheet. For fans, PV+ provides goal-based context for the actions they intuitively recognize as important. It helps explain why and how a player influenced the game, not just what they produced.

For coaches and analysts, PV+ offers a framework to evaluate performance across possessions and game states, highlighting how value is created and prevented throughout a match. It supports tactical analysis by identifying which actions consistently increase danger or suppress it, and which players reliably drive those outcomes.

For clubs, models like PV+ have the potential to support smarter recruitment, squad building, and player development. By measuring contributions in goal-based units across all phases of play, PV+ can help surface undervalued players, clarify role fit, and reinforce tactical principles grounded in how goals are actually created and prevented.

What’s Next

This methodology post is the foundation. Going forward, PV+ will be applied in a consistent, repeatable way through weekly outputs, including:

• Weekly PV+ player performance visualizations

• League-wide and team-specific leaderboards

• Breakdowns by role and contribution type (creation, carrying, defending, shooting)

• Contextual matchweek summaries highlighted where and how value was generated

These updates will focus much less on explaining the model and more on using it — showing how PV+ performs week to week, how player roles differ, and how value accumulates over a season. The goal is to make action-value concepts intuitive, visual, and useful for understanding MLS matches as they happen

More coming soon.

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Acknowledgments

I want to explicitly acknowledge American Soccer Analysis for their foundational work on Goals Added. The g+ methodology, publicly documented and shared with the soccer analytics community, provided the inspiration for PV+. I encourage anyone interested in action-value models to read their original methodology articles and explore their publicly available g+ data. PV+ is my implementation of these ideas-built from scratch, trained on data I collected, with modeling decisions I made independently.