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SportyPy: Probabilistic Modeling for Sports Analytics

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# SportyPy: Probabilistic Modeling for Sports Analytics

![SportyPy Logo](https://raw.githubusercontent.com/fonnesbeck/sportypy/main/sportypy_logo_256.png)

## Implementation Plan

### I. Foundational Architecture

SportyPy is a probabilistic programming toolkit for sports analytics, leveraging Python's data science ecosystem. The language and core stack rely on **NumPy** for numerical efficiency and **Polars** for high-performance data manipulation, providing a standard and modern data science toolkit. The statistical backend uses **PyMC** as the probabilistic programming foundation, providing MCMC sampling, variational inference, and GPU acceleration via PyTensor. This enables hierarchical Bayesian models for latent skills, uncertainty quantification, and robust inference with heavy-tailed distributions—including applications like ADVI optimization for projections, Bayesian Hierarchical Regression for player/team effects, and Multivariate t distributions for robustness against outliers. The library itself is modular, with distinct sub-modules for different analytical concerns (e.g., `sportypy.projections`, `sportypy.spatial`), offering **high-level wrappers** built on PyMC model classes for defining complex hierarchical models. Through these wrappers, SportyPy abstracts PyMC model construction into domain-specific APIs, balancing flexibility with ease of use.

### II. Core Modeling Modules

SportyPy features dedicated modules for high-level components: Aging Curves/Projections, Selection Bias Adjustments, and Spatial Models.

#### 1. `sportypy.projections` (Latent Skills and Aging Curves)

SportyPy enables performance forecasting using PyMC's hierarchical modeling capabilities.

*   **Latent Skill Modeling:** Implements "true skill" as a **latent quantity** using PyMC's latent variable framework. Applicable to any sport where observed performance metrics reflect underlying abilities.
    *   *Feature Set:* Define inputs $Y_{ijk}$ (observed metrics) and model latent skills $\gamma_{ij}$ based on performance indicators.
    *   *Emission Matrix:* Incorporates a design matrix **B** mapping latent skills to observable performance metrics, distinguishing between identified and associated skills for interpretability.

*   **Aging Curves (`.aging`):** Tools for applying and estimating age-related drift in latent skills ($\alpha_j$) using PyMC's Gaussian Process and spline components.
    *   Aging curves are parameterized as polynomial or spline functions of age to capture expected improvement or decline over time.
    *   The model supports computing projections over arbitrary lengths for simulation of **full career trajectories**.

*   **Probabilistic Output:** All projections return posterior distributions via `arviz.InferenceData` objects, providing both point estimates and **full uncertainty quantification** for risk assessment in predictions about total future value.

#### 2. `sportypy.causal` (Selection Bias and Level Adjustments)

This module implements causal inference techniques using PyMC for Bayesian propensity modeling.

*   **Level Adjustment (`.level_adjust`):** Implements a causal inference framework to derive **level-independent measures of performance**.
    *   The framework models the **promotion propensity score** ($p_{it}$) using PyMC's flexible regression capabilities, capturing residual talent information not explained by performance at the origin level.
    *   Applies Bayesian causal estimators (inverse probability weighting with posterior uncertainty) to mitigate **selection bias** when comparing performance across different competition levels (e.g., minor leagues to top-tier, college to professional, domestic to international).

*   **Value Neutrality:** Tools to create metrics agnostic to **venue, team, and environmental effects** using hierarchical partial pooling in PyMC.

#### 3. `sportypy.spatial` (Spatial and Trajectory Models)

This module provides methods for predicting outcomes based on spatial coordinates or trajectories using PyMC's Gaussian Process framework.

*   **Trajectory Models:** Wrappers for modeling outcomes given object trajectories (ball flight, player movement, shot paths).
    *   Utilizes PyMC's GLM and GP modules with spatial effects learned as functions of trajectory parameters.
    *   Supports the Hierarchical Gaussian Process (HGP) framework with HSGP (Hilbert Space GP) approximations for computational efficiency.

*   **Spatial Performance Models:** Components to evaluate player performance based on location data.
    *   Models that predict expected outcomes (shot success, defensive actions, positioning quality) using PyMC HGPs, accounting for player-specific spatial and linear effects.

### III. Utility and Infrastructure Modules

#### 4. `sportypy.value_attribution` (Value Metrics and Context)

This module handles quantification of value changes during a game using PyMC for hierarchical attribution.

*   **State Transition Modeling:** Tools for modeling game state transitions to calculate **expected value** from a given state. This forms the foundation for many outcome-based metrics.
*   **Hierarchical Attribution:** PyMC-based framework for attributing value to individual players by comparing actual results to predictions from a league-average player, using **Hierarchical Mixed Effects Models**. Applicable to any sport where multiple players contribute to outcomes.

*   **Availability/Temporal Models:** Functionality for modeling time-dependent latent states, such as player availability (fitness/injury risk), using PyMC's **Hidden Markov Model** implementations to capture state persistence and predict long-term injury expectations based on observed activity states.

#### 5. `sportypy.predict` (Model Wrappers)

This module offers high-level PyMC-based wrappers for Bayesian prediction in sports analytics.

*   **Regression and Classification:** Wrappers for Bayesian versions of common sports prediction models:
    *   **Logistic Regression** for binary outcomes (win/loss, shot make/miss)
    *   **Poisson/Negative Binomial Regression** for count data (goals, points, assists)
    *   **Ordinal Regression** for ranked outcomes
*   **Ensemble Methods:** APIs for Bayesian Model Averaging and stacking using PyMC's model comparison tools (`arviz.compare`, `arviz.loo`).
*   **Head-to-Head Matchups:** Tools to structure inputs for predicting team matchups, incorporating team performance aggregates and rating systems (Elo, Bradley-Terry) with full posterior uncertainty.

#### 6. `sportypy.data` (Data Acquisition and Preprocessing)

This module handles integration with external sports data sources.

*   **Data Connectors:** Utilities for connecting to common public APIs and data sources to collect and parse statistics.
*   **Preprocessing Utilities:** Functions for standard tasks like feature standardization and normalization, as well as sport-agnostic feature engineering patterns.
*   **PyMC Integration:** Data preparation utilities that output PyMC-ready coordinate dictionaries and data containers for hierarchical indexing.

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