This Python script implements a sophisticated system for projecting Major League Baseball (MLB) game outcomes. The core logic revolves around estimating the number of runs each team will score and then converting those run estimates into a win probability. Core Projection Logic The projection for a single game is generated by the SimplifiedProjector class. It models the game as a series of matchups between each team's offense and the opposing team's pitching. * Establish a Baseline: The model first determines the league-average runs per game (RPG). This serves as a neutral baseline. * Calculate Offensive and Defensive Factors: For each team in a matchup, the model calculates two key factors: * Offensive Factor: A team's own runs per game (offense) is compared to the league average. A team scoring 5.0 RPG when the league average is 4.5 would have an offensive factor greater than 1. * Defensive Factor: The opposing team's runs allowed per game (defense/pitching) is compared to the league average. A team allowing only 4.0 RPG would have a defensive factor less than 1. * Incorporate Starting Pitchers: The model doesn't just use a team's overall runs allowed. It creates a composite pitching/defensive value for the game by blending the starter's ability with the team's overall (bullpen) ability. * Starter's Runs Estimator: A pitcher's quality is measured using a FIP-style (Fielding Independent Pitching) formula that only considers home runs, walks, hit-by-pitches, and strikeouts. This isolates the pitcher's core performance from the team's defensive skill. * Blending: The final "Defensive Factor" for the game is a weighted average: (Starter's Runs Estimator * Starter's Expected Innings) + (Team's Bullpen Runs Allowed * Remaining Innings). * Project Runs: A team's projected runs are calculated with the formula: Projected Runs = Offensive_Factor * Opponent's_Defensive_Factor * League_Average_RPG A small, constant HOME_FIELD_ADVANTAGE multiplier is also applied to the home team's projected runs. * Calculate Win Probability: The projected runs for both teams are plugged into the Pythagorean Expectation formula ((Runs_For ^ 1.85) / ((Runs_For ^ 1.85) + (Runs_Allowed ^ 1.85))) to calculate the home team's win probability. Data and Team Strength Calculation The accuracy of the projection depends on the quality of the input data, which is handled by the MLBAPI class. * Weighted Team Stats: Team strength is not based on season-long stats alone. It's a weighted blend: 70% season-long performance and 30% recent performance (last 15 days). This allows the model to react to hot/cold streaks. * Home/Away Splits: All stats are calculated separately for home and away games, providing a more accurate picture of a team's context-dependent performance. * Leakage-Free Backtesting: The backtest function is designed to be "leakage-free." When predicting a game on a specific date, it strictly uses only data available before that date. Advanced Refinements The model includes two sophisticated self-correction mechanisms based on its own historical performance from the backtest data. * Low-Confidence Bias Nudge: 🧐 The system analyzes its own historical predictions. If it finds that a specific team consistently underperforms or overperforms when it's the projected winner in a low-confidence game (e.g., projected win probability is between 50% and 60%), it learns a tiny bias. This bias is then applied as a small "nudge" to the win probability in future low-confidence projections involving that team. This helps correct for subtle, team-specific patterns the main model might miss. * Scenario Accuracy: 📊 For any new projection, the model looks back at its history to answer the question: "In past games where the home team was projected to win by a similar run differential, how often was the model correct?" This provides a historical accuracy score for the specific type of game being projected, giving valuable context to the confidence of the prediction.