EDMS State Definition

Overview

EDMS (Expandable Decision-Making State) is an advanced state definition system specialized for sophisticated soccer analysis and complex multi-agent learning scenarios. It provides a three-layer structured state representation containing more detailed information than PVS, numerically expressing the tactical aspects of soccer.

Data Structure

EDMS has a hierarchical structure composed of three main state levels:

class State_EDMS(BaseModel):
    relative_state: RelativeState  # Relative state (OnBall/OffBall)
    absolute_state: AbsoluteState  # Absolute state (formation, etc.)
    raw_state: RawState           # Raw state data (same structure as PVS)

State Level Details

1. Relative State

Numerical representation of relative relationships between players and ball, goal, and other players:

OnBall (Information of ball-possessing player):

  • dist_ball_opponent: List of distances between opponent players and ball

  • dribble_score: List of dribble evaluation scores

  • dribble_score_vel: List of dribble scores considering velocity

  • dist_goal: List of distances to goal

  • angle_goal: List of angles to goal

  • ball_speed: Ball velocity

  • transition: List of transition evaluations

  • shot_score: Shot evaluation score

  • long_ball_score: List of long ball evaluation scores

OffBall (Information of non-ball-possessing players):

  • fast_space: List of space scores

  • fast_space_vel: List of space scores considering velocity

  • dist_ball: List of distances to ball

  • angle_ball: List of angles to ball

  • dist_goal: List of distances to goal

  • angle_goal: List of angles to goal

  • time_to_player: List of time to reach other players

  • time_to_passline: List of time to reach pass line

  • variation_space: List of space scores when moving in 8 directions

  • variation_space_vel: List of space scores considering velocity when moving in 8 directions

  • defense_space: List of space scores for defensive players

  • defense_space_vel: List of space scores for defensive players considering velocity

  • defense_dist_ball: List of ball distances during defense

2. Absolute State

Tactical information for the entire team:

  • dist_offside_line: List of distances to offside line

  • formation: Formation string

  • attack_action: Action list of attacking team

  • defense_action: Action list of defending team

3. Raw State

Basic data with the same structure as PVS:

  • ball: Ball position and velocity information

  • players: List of all players

  • attack_players: List of attacking team players

  • defense_players: List of defending team players

Player Information

EDMS player information uses the same structure as PVS:

  • index: Player index

  • team_name: Team name

  • player_name: Player name

  • player_id: Player ID

  • player_role: Player position

  • position: Player position information (x, y coordinates)

  • velocity: Player velocity information

  • action: Player action

  • action_probs: Probability of action occurrence (optional)

Action Structure

EDMS adopts a two-dimensional action structure:

action: List[List[str]]  # [attacking team action, defending team action]

This structure enables the following:

  • action[0]: Action list of each player in the attacking team (attack_action)

  • action[1]: Action list of each player in the defending team (defense_action)

  • Expression of tactical coordinated behavior for each team

EDMS Distinctive Features

Advanced Analysis by Relative State

The greatest feature of EDMS is detailed analysis through relative state (RelativeState):

Spatial Evaluation System:

  • fast_space: Numerical representation of player’s reachable area

  • variation_space: Management of reachable areas when multiple players move in 8 directions with 2D arrays

  • defense_space: Evaluation of defensive players’ reachable areas with dedicated indicators

Integration of Time Elements:

  • time_to_player: Calculate time to reach other players

  • time_to_passline: Predict time to reach pass line

  • Velocity-considered indicators: Integration of velocity information in many evaluations (indicators with _vel suffix)

Tactical Insights:

  • dribble_score: Numerical representation of space scores when moving in 8 directions during ball possession

  • shot_score: Evaluation of shot success probability

  • transition: Evaluation during offensive/defensive transitions

  • long_ball_score: Evaluation of long ball tactics

Data Processing Flow

EDMS has the following processing flow:

  1. Raw State Generation - Acquire basic position, velocity, and action information same as PVS

  2. Relative State Calculation - Numerical representation of detailed OnBall/OffBall relative relationships - Calculate various scores and evaluation indicators

  3. Absolute State Construction - Extract formation information - Calculate offside line distances - Organize team-level actions

  4. Integrated State Representation - Complete State_EDMS structure integrating three state levels

Usage

Example of using the EDMS system:

SAR_data = SAR_data(
    data_provider="fifawc",
    state_def="EDMS",         # Specify EDMS state definition
    data_path=data_path,
    match_id="3814",
    preprocess_method="SAR"
)

Application Scenarios

EDMS is optimal for the following advanced applications:

Research & Academic Use

  • Soccer AI Research: Cutting-edge multi-agent AI research

  • Tactical Analysis Research: Academic-level tactical and strategic analysis

  • Sports Science: Scientific evidence-based player and team analysis

Commercial Applications

  • Professional Team Analysis: Tactical analysis systems for professional soccer teams

  • Player Evaluation: Advanced player performance evaluation

  • Tactical Planning Support: Decision support for coaching and tactical planning

Advanced Applications

  • Real-time Analysis: Live tactical analysis during matches

  • Prediction Systems: High-precision prediction of match results and play outcomes

Technical Specifications

Computational Complexity

  • Spatial Calculation: O(n²) ~ O(n³) complexity (depending on number of players n)

  • Probability Calculation: Multivariate optimization using statistical models

  • Real-time Constraints: High-performance computing environment recommended

Memory Requirements

  • Approximately 3-5 times the memory usage of PVS

  • Retention of large amounts of intermediate calculation results

  • Learning effects through accumulation of historical data

Technical Comparison with PVS

Feature

PVS

EDMS

Data Structure

Simple

3-layer hierarchy

Computational Complexity

O(n)

O(n²) ~ O(n³)

Memory Usage

Lightweight

Heavy (3-5x PVS)

Processing Speed

Fast

Medium~Slow

Analysis Depth

Basic

Research-level

Tactical Analysis

Not supported

Advanced support

Spatial Analysis

None

Voronoi diagram based

Probability Modeling

None

Multivariate statistical model

Real-time Suitability

Optimal

Depends on computing resources

Learning Curve

Easy

Steep

System Requirements

Dependency Libraries

  • NumPy/SciPy: Scientific computing

  • Pandas: Data processing

  • Scikit-learn: Machine learning algorithms

  • Computational geometry library: Voronoi diagram calculation

  • Statistical library: Probability model calculation

File Structure

Main EDMS-related files:

  • SAR_class.py: Factory class for PVS/EDMS switching

  • dataclass.py: EDMS data class definitions (shared with PVS)

  • preprocess_frame.py: EDMS processing functions

  • soccer_SAR_state.py: Main processing routing for EDMS

Data Class Structure

EDMS consists of the following classes:

Basic Classes: * Position, Velocity: Position and velocity information * Player, Ball: Player and ball information (shared with PVS)

EDMS-specific Classes: * OnBall: Detailed information during ball possession * OffBall: Detailed information during non-ball possession * RelativeState: OnBall + OffBall * AbsoluteState: Formation, offside, etc. * RawState: Basic position information (same structure as PVS State_PVS) * State_EDMS: Integration of three state levels

Event Classes: * Event_EDMS: EDMS state + 2D action + reward * Events_EDMS: Sequence management of multiple events

Summary

EDMS is a three-layer structured state definition system that maintains the basic structure of PVS while having two additional layers: relative state (RelativeState) and absolute state (AbsoluteState).

Key Features:

  • Provides detailed relative relationships and tactical information in addition to PVS basic information

  • Multi-faceted analysis indicators including spatial evaluation, time calculation, and tactical scores

  • Optimal for advanced soccer analysis and complex multi-agent learning

Both systems share the same basic classes such as Player and Ball, enabling efficient soccer data analysis by appropriately selecting according to the intended use.