True Playoff Impact (TPI) Model

Overview

True Playoff Impact (TPI) is an advanced, era-adjusted metric designed to rigorously quantify a player's true individual impact during the NBA Playoffs. Moving beyond traditional box score stats, TPI evaluates performance contextually by incorporating efficiency, opponent strength, team capability, injury context, and a physiologically rigorous biological fatigue simulation.

The fundamental equation is:

Total TPI = (Production Score × Resistance Score × Production Multiplier) × Games Played

Where Production Multiplier is the output of a 6-state biological ODE system that simulates the real cumulative metabolic cost of a playoff run, computed from exact play-by-play data.

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The Three Core Components

1. Production Score (Prod_Score)

Evaluates raw on-court output using BPM as the base, adjusted for shooting efficiency relative to the era's league average.

• Base Metric: Box Plus/Minus (BPM) from Basketball Reference.
• Efficiency Multiplier: A non-linear TS% correction (ts_player / ts_league)^1.5 is applied.

2. Resistance Score (Res_Score)

Quantifies the difficulty of the playoff environment by measuring the gap between opponent quality and teammate support.

• Team Capability (SRS-based): Blends Current Regular Season SRS (44.4%) with Previous Postseason SRS (55.6%).
• "Final Boss" Series Weighting: Series are weighted 50% / 25% / 15% / 10% (hardest to easiest) to prioritize elite opponents.
• Injury Context: Missing-BPM penalties are applied for both teammate and opponent injuries.
• Resistance Formula: gap = adj_opp_srs - adj_help_srs. Resistance is calculated as (gap+1)^0.35 for positive gaps.

3. Bio-Fatigue Engine: 6-State ODE System (Production Multiplier)

The TPI Fatigue Engine is a biologically-grounded differential equation system that models six distinct physiological state variables.

The Six State Variables

Variable	Biological Meaning	Range
PCr	Phosphocreatine (Fast-resynthesis capacity)	0–1
Gly	Glycogen stores (Aerobic fuel reserve)	0–1
Lac	Lactate clearance (Normalized efficiency)	0–1
M	Muscle integrity (Contractile capacity)	0–1
CNS	Central Nervous System readiness	0–1
Phi (Φ)	EPOC debt accumulator	0–∞

The Production Multiplier (P)

The output scalar P combines all metrics:

P = PCr^0.5 × Lac^0.4 × Gly^0.3 × M^0.4 × CNS^0.8

Centralized Model (bio_model.py)

The model is centralized in a shared module to ensure consistency across all simulations and visualizations. It includes:

• Active Play: Intensity is calculated as (Movement * 0.5) + (Contact * 0.5).
• Bench/Timeout Rest: Rapid partial recovery.
• Inter-Game Recovery: Long-term metabolic and neural repair using consistent minute-based integration.

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Data Pipeline

1. PBP Reconstruction (data_reconstruction.py): Downloads and parses raw PBP data to extract usage and intensity components.
2. Fatigue Engine (fatigue_engine.py): Runs the full bio-ODE simulation from Regular Season through Postseason.
3. TPI Main (tpi_main.py): Combines Production, Resistance, and Fatigue into the final TPI scores.
4. Visualization (visualization.py): Generates high-fidelity 5-panel charts of the fatigue dynamics.

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Visualization Suite: The Multi-Scale Fatigue View

The TPI visualization engine produces a 5-panel dashboard analyzing fatigue at every level of resolution:

• Graph 1: Intra-Game Dynamics: Minute-by-minute metabolic shifts within a single game (e.g., 2018 Finals G1).
• Graph 2: Recovery Windows: Hourly recovery curves between sequential games.
• Graph 3: Series Progression: Game-to-game fatigue trends within a specific series.
• Graph 4: Playoff Gauntlet: Series-by-series trends across the entire postseason, emphasizing the cumulative cost of deep runs.
• Graph 5: Seasonal Trends: The full journey from Regular Season quintiles to the Postseason peak.

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Career Results (LeBron James 2006–2025)

Year	Total TPI	TPI per G	Prod_Score	Res_Score	Prod_Multiplier	GP
2016	154.28	7.35	14.85	1.431	0.346	21
2018	116.13	5.28	15.08	1.674	0.209	22
2014	115.15	6.06	15.77	1.112	0.345	19
2017	90.94	5.35	14.70	1.235	0.295	17
2012	85.12	3.70	12.71	0.842	0.346	23
2023	70.73	4.16	6.65	1.540	0.406	17
2013	69.17	3.01	10.90	0.757	0.364	23
2015	68.32	3.42	8.92	1.321	0.290	20
2006	62.11	4.78	9.88	1.357	0.356	13
2020	60.52	2.88	14.09	0.564	0.362	21

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Technical Architecture

true_playoff_impact/
├── code/
│   └── tpi_calculations/
│       ├── bio_model.py                # Centralized bio-ODE logic & constants
│       ├── pbp_data_reconstruction.py  # PBP downloader & parser
│       ├── tpi_career_fatigue.py       # Full-career simulation engine
│       ├── tpi_v2.py                   # Final TPI assembly
│       └── plot_tpi.py                 # Multi-panel visualization suite
├── data/
│   ├── fatigue_metric/                 # Simulation inputs and intermediate outputs
│   ├── prod_score/                     # Player efficiency and BPM data
│   ├── res_score/                      # Team/Opponent SRS and Injury data
│   └── tpi_results/                    # Final CSV results and PNG graphs
└── README.md