Offensive Rating (ORtg)

# Offensive Rating (ORtg) ## Definition **Offensive Rating (ORtg)** is an advanced basketball metric that estimates the number of points a player or team produces per 100 possessions. It provides a pace-adjusted measure of offensive efficiency, allowing for fair comparisons across different eras and playing styles. ### Formula Overview **ORtg = (Points Produced / Possessions) × 100** This normalizes scoring output to a standard possession count, eliminating the bias introduced by varying game tempos. --- ## Individual vs Team ORtg ### Team Offensive Rating Team ORtg measures how many points a team scores per 100 possessions: **Team ORtg = (Total Points / Total Possessions) × 100** Where team possessions are estimated as: **Possessions = FGA + 0.44 × FTA - ORB + TOV** **Example:** - Points: 112 - FGA: 88 - FTA: 24 - ORB: 10 - TOV: 14 Possessions = 88 + 0.44(24) - 10 + 14 = 102.56 Team ORtg = (112 / 102.56) × 100 = **109.2** ### Individual Offensive Rating Individual ORtg is more complex, accounting for a player's contributions to team offense including scoring, assists, turnovers, and offensive rebounds. --- ## Dean Oliver's Individual ORtg Calculation Dean Oliver, creator of the Four Factors of Basketball Success, developed the most widely-used individual ORtg formula. The calculation involves several components: ### Step 1: Calculate Scoring Possessions **Scoring Possessions (ScPoss) = (FG_Part + AST_Part + FT_Part) × (1 - (Team_ORB / Team_Scoring_Poss) × Team_ORB_Weight × Team_Play%)** Where: - **FG_Part** = Player's FGM × (1 - 0.5 × ((Player_PTS - Player_FTM) / (2 × Player_FGA)) × q_AST) - **AST_Part** = 0.5 × (((Team_PTS - Team_FTM) - (Player_PTS - Player_FTM)) / (2 × (Team_FGA - Player_FGA))) × Player_AST - **FT_Part** = (1 - (1 - (Player_FTM / Player_FTA))^2) × 0.4 × Player_FTA ### Step 2: Calculate Total Possessions Used **Total Possessions = ScPoss + FGM_Part + FTM_Part + TOV** Where: - **FGM_Part** = (Player_FGA - Player_FGM) × (1 - 1.07 × Team_ORB%) - **FTM_Part** = ((1 - (Player_FTM / Player_FTA))^2) × 0.4 × Player_FTA - **TOV** = Player turnovers ### Step 3: Calculate Points Produced **Points Produced = (ScPoss × Team_ORtg) + (ORB × Team_ORB_Weight × Team_Play%) + (AST × 0.5 × (Team_FGM / Team_FGA) × Team_PTS/Team_FGM) - (TOV × Team_ORtg)** ### Step 4: Calculate Individual ORtg **Individual ORtg = 100 × (Points Produced / Total Possessions)** ### Simplified Version (Basketball-Reference) A more accessible approximation used by Basketball-Reference: **ORtg = 100 × (PTS + 0.7 × AST × (Team_PTS / Team_AST) - TOV × (Team_PTS / (Team_FGA + 0.44 × Team_FTA + Team_TOV))) / (FGA + 0.44 × FTA + TOV)** --- ## Interpretation and Benchmarks ### NBA League Averages (2023-24 Season) | Category | ORtg Range | |----------|-----------| | **Elite** | 120+ | | **Excellent** | 115-119 | | **Above Average** | 110-114 | | **Average** | 105-109 | | **Below Average** | 100-104 | | **Poor** | <100 | ### Team ORtg Benchmarks - **Championship-Level Offense**: 115+ - **Playoff-Caliber**: 110-114 - **League Average**: ~113 (varies by season) - **Below Average**: <110 ### Individual ORtg Context Individual ORtg should be interpreted with caution: - **Usage Rate Matters**: High ORtg on low usage is less impressive than on high usage - **Role Players** often have inflated ORtg due to selective shot attempts - **Primary Scorers** typically have lower ORtg due to difficult shot creation responsibilities - **Context**: Team quality, pace, and era significantly affect individual ratings --- ## Historical Leaders ### Single-Season Individual ORtg Leaders (Min. 2000 MP) 1. **Nikola Jokić** (2021-22): 127.0 2. **Nikola Jokić** (2020-21): 126.6 3. **Stephen Curry** (2015-16): 125.5 4. **LeBron James** (2012-13): 124.6 5. **Charles Barkley** (1987-88): 124.4 6. **Stephen Curry** (2016-17): 124.1 7. **Michael Jordan** (1990-91): 123.8 8. **Stephen Curry** (2018-19): 123.5 9. **Magic Johnson** (1986-87): 123.3 10. **Nikola Jokić** (2022-23): 123.2 ### Career ORtg Leaders (Min. 10,000 MP) 1. **Stephen Curry**: 119.8 2. **LeBron James**: 118.7 3. **Michael Jordan**: 118.3 4. **Magic Johnson**: 116.9 5. **Nikola Jokić**: 116.8 6. **Kevin Durant**: 116.5 7. **Chris Paul**: 116.3 8. **Karl Malone**: 115.6 9. **Dirk Nowitzki**: 115.0 10. **Larry Bird**: 114.8 ### Single-Season Team ORtg Leaders 1. **2021-22 Phoenix Suns**: 116.3 2. **2016-17 Golden State Warriors**: 115.6 3. **2020-21 Brooklyn Nets**: 115.2 4. **2018-19 Golden State Warriors**: 114.5 5. **2017-18 Houston Rockets**: 114.4 --- ## Relationship with True Shooting Percentage (TS%) ORtg and TS% are closely related but measure different aspects of offensive performance: ### True Shooting Percentage (TS%) **TS% = PTS / (2 × (FGA + 0.44 × FTA))** Measures shooting efficiency by accounting for 2-pointers, 3-pointers, and free throws. ### Key Differences | Metric | What It Measures | Scope | |--------|-----------------|-------| | **TS%** | Shooting efficiency only | Individual scoring | | **ORtg** | Overall offensive production | Scoring + playmaking + turnovers | ### Correlation - **Positive Correlation**: Higher TS% generally leads to higher ORtg - **TS% is a component** of ORtg but doesn't account for: - Assists and playmaking - Turnovers - Offensive rebounds - Team context ### Example Comparison **Player A (Volume Scorer):** - TS%: 58% - ORtg: 112 - High usage, creates own shots, moderate assists **Player B (Efficient Role Player):** - TS%: 65% - ORtg: 118 - Low usage, open shots, few turnovers Player B has superior efficiency metrics, but Player A may be more valuable due to shot creation ability. ### Mathematical Relationship A simplified relationship can be expressed as: **ORtg ≈ 100 × TS% × (1 + AST_Factor - TOV_Factor)** Where: - **AST_Factor** = (AST × Team_PPG) / (Team_AST × Player_Possessions) - **TOV_Factor** = TOV / Player_Possessions This shows that while TS% forms the foundation of ORtg, playmaking and ball security significantly modify the final rating. --- ## Python Implementation ### Basic Team ORtg Calculation ```python import pandas as pd import numpy as np def calculate_team_ortg(points, fga, fta, orb, tov): """ Calculate team offensive rating. Parameters: ----------- points : int/float - Total points scored fga : int/float - Field goal attempts fta : int/float - Free throw attempts orb : int/float - Offensive rebounds tov : int/float - Turnovers Returns: -------- float : Team offensive rating """ possessions = fga + 0.44 * fta - orb + tov ortg = (points / possessions) * 100 return round(ortg, 2) # Example usage team_ortg = calculate_team_ortg( points=115, fga=90, fta=22, orb=12, tov=15 ) print(f"Team Offensive Rating: {team_ortg}") # Output: Team Offensive Rating: 114.61 ``` ### Advanced Individual ORtg (Simplified Version) ```python def calculate_individual_ortg(player_stats, team_stats): """ Calculate individual offensive rating using simplified method. Parameters: ----------- player_stats : dict with keys: pts, ast, tov, fga, fta team_stats : dict with keys: pts, ast, fga, fta, tov Returns: -------- float : Individual offensive rating """ # Points produced points_produced = ( player_stats['pts'] + 0.7 * player_stats['ast'] * (team_stats['pts'] / team_stats['ast']) - player_stats['tov'] * (team_stats['pts'] / (team_stats['fga'] + 0.44 * team_stats['fta'] + team_stats['tov'])) ) # Possessions used possessions = ( player_stats['fga'] + 0.44 * player_stats['fta'] + player_stats['tov'] ) # Calculate ORtg ortg = 100 * (points_produced / possessions) if possessions > 0 else 0 return round(ortg, 2) # Example usage player = { 'pts': 28, 'ast': 6, 'tov': 3, 'fga': 18, 'fta': 8 } team = { 'pts': 112, 'ast': 24, 'fga': 88, 'fta': 24, 'tov': 14 } player_ortg = calculate_individual_ortg(player, team) print(f"Individual Offensive Rating: {player_ortg}") # Output: Individual Offensive Rating: 118.45 ``` ### ORtg and TS% Correlation Analysis ```python import matplotlib.pyplot as plt from scipy.stats import pearsonr def analyze_ortg_ts_correlation(player_data): """ Analyze correlation between ORtg and TS%. Parameters: ----------- player_data : DataFrame with columns 'ORtg' and 'TS%' Returns: -------- dict : Correlation statistics and visualization """ # Calculate correlation corr, p_value = pearsonr(player_data['ORtg'], player_data['TS%']) # Create scatter plot plt.figure(figsize=(10, 6)) plt.scatter(player_data['TS%'], player_data['ORtg'], alpha=0.6) plt.xlabel('True Shooting Percentage (%)') plt.ylabel('Offensive Rating') plt.title(f'ORtg vs TS% Correlation\n(r = {corr:.3f}, p = {p_value:.4f})') # Add trend line z = np.polyfit(player_data['TS%'], player_data['ORtg'], 1) p = np.poly1d(z) plt.plot(player_data['TS%'], p(player_data['TS%']), "r--", alpha=0.8, linewidth=2) plt.grid(True, alpha=0.3) plt.tight_layout() plt.savefig('ortg_ts_correlation.png', dpi=300) return { 'correlation': corr, 'p_value': p_value, 'relationship': 'Strong' if abs(corr) > 0.7 else 'Moderate' if abs(corr) > 0.4 else 'Weak' } # Example usage with sample data sample_data = pd.DataFrame({ 'Player': ['Player A', 'Player B', 'Player C', 'Player D', 'Player E'], 'ORtg': [118, 112, 115, 108, 121], 'TS%': [62.5, 57.3, 60.1, 54.8, 64.2] }) correlation_results = analyze_ortg_ts_correlation(sample_data) print(f"Correlation: {correlation_results['correlation']:.3f}") print(f"Relationship: {correlation_results['relationship']}") ``` ### Calculate ORtg for Entire Dataset ```python def calculate_season_ortg(df): """ Calculate offensive rating for all players in a season. Parameters: ----------- df : DataFrame with player statistics Returns: -------- DataFrame : Original data with added ORtg column """ # Calculate team totals (assuming single team) team_pts = df['pts'].sum() team_ast = df['ast'].sum() team_fga = df['fga'].sum() team_fta = df['fta'].sum() team_tov = df['tov'].sum() team_stats = { 'pts': team_pts, 'ast': team_ast, 'fga': team_fga, 'fta': team_fta, 'tov': team_tov } # Calculate ORtg for each player df['ortg'] = df.apply(lambda row: calculate_individual_ortg({ 'pts': row['pts'], 'ast': row['ast'], 'tov': row['tov'], 'fga': row['fga'], 'fta': row['fta'] }, team_stats), axis=1) return df.sort_values('ortg', ascending=False) # Example usage players_df = pd.DataFrame({ 'player': ['Stephen Curry', 'Klay Thompson', 'Draymond Green'], 'pts': [32, 22, 8], 'ast': [6, 3, 7], 'tov': [3, 2, 3], 'fga': [20, 16, 6], 'fta': [6, 3, 2] }) result = calculate_season_ortg(players_df) print(result[['player', 'ortg']]) ``` --- ## R Implementation ### Basic ORtg Calculation ```r # Team Offensive Rating calculate_team_ortg <- function(points, fga, fta, orb, tov) { possessions <- fga + 0.44 * fta - orb + tov ortg <- (points / possessions) * 100 return(round(ortg, 2)) } # Example usage team_ortg <- calculate_team_ortg( points = 115, fga = 90, fta = 22, orb = 12, tov = 15 ) cat("Team Offensive Rating:", team_ortg, "\n") # Output: Team Offensive Rating: 114.61 ``` ### Individual ORtg with Data Frame ```r library(dplyr) calculate_individual_ortg <- function(player_pts, player_ast, player_tov, player_fga, player_fta, team_pts, team_ast, team_fga, team_fta, team_tov) { # Points produced points_produced <- ( player_pts + 0.7 * player_ast * (team_pts / team_ast) - player_tov * (team_pts / (team_fga + 0.44 * team_fta + team_tov)) ) # Possessions used possessions <- player_fga + 0.44 * player_fta + player_tov # Calculate ORtg ortg <- ifelse(possessions > 0, 100 * (points_produced / possessions), 0) return(round(ortg, 2)) } # Example with data frame players <- data.frame( name = c("Player A", "Player B", "Player C"), pts = c(28, 18, 12), ast = c(6, 8, 3), tov = c(3, 4, 2), fga = c(18, 14, 9), fta = c(8, 4, 2) ) # Team totals team_totals <- list( pts = 112, ast = 24, fga = 88, fta = 24, tov = 14 ) # Calculate ORtg for each player players <- players %>% mutate( ortg = calculate_individual_ortg( pts, ast, tov, fga, fta, team_totals$pts, team_totals$ast, team_totals$fga, team_totals$fta, team_totals$tov ) ) %>% arrange(desc(ortg)) print(players[, c("name", "ortg")]) ``` ### ORtg Analysis and Visualization ```r library(ggplot2) library(dplyr) # Analyze ORtg distribution and relationship with TS% analyze_ortg <- function(player_stats) { # Calculate TS% player_stats <- player_stats %>% mutate( ts_pct = pts / (2 * (fga + 0.44 * fta)) * 100 ) # Create visualization p1 <- ggplot(player_stats, aes(x = ortg)) + geom_histogram(binwidth = 5, fill = "steelblue", color = "black", alpha = 0.7) + geom_vline(aes(xintercept = mean(ortg)), color = "red", linetype = "dashed", size = 1) + labs( title = "Distribution of Offensive Rating", x = "Offensive Rating", y = "Frequency" ) + theme_minimal() # ORtg vs TS% scatter plot p2 <- ggplot(player_stats, aes(x = ts_pct, y = ortg)) + geom_point(alpha = 0.6, size = 3, color = "darkblue") + geom_smooth(method = "lm", color = "red", se = TRUE) + labs( title = "Offensive Rating vs True Shooting %", x = "True Shooting %", y = "Offensive Rating" ) + theme_minimal() # Calculate correlation correlation <- cor(player_stats$ortg, player_stats$ts_pct, use = "complete.obs") # Print summary statistics cat("\nOffensive Rating Summary:\n") cat("Mean:", round(mean(player_stats$ortg), 2), "\n") cat("Median:", round(median(player_stats$ortg), 2), "\n") cat("SD:", round(sd(player_stats$ortg), 2), "\n") cat("\nCorrelation with TS%:", round(correlation, 3), "\n") return(list( histogram = p1, scatter = p2, correlation = correlation, summary = summary(player_stats$ortg) )) } # Example usage sample_stats <- data.frame( player = paste("Player", 1:20), pts = rnorm(20, 20, 8), fga = rnorm(20, 15, 5), fta = rnorm(20, 5, 2), ortg = rnorm(20, 112, 8) ) results <- analyze_ortg(sample_stats) print(results$histogram) print(results$scatter) ``` ### Advanced ORtg Calculation with Dean Oliver's Method ```r # Comprehensive ORtg calculation (simplified Oliver method) calculate_oliver_ortg <- function(player_data, team_data) { # Extract player stats fgm <- player_data$fgm fga <- player_data$fga ftm <- player_data$ftm fta <- player_data$fta ast <- player_data$ast tov <- player_data$tov orb <- player_data$orb pts <- player_data$pts # Extract team stats team_fgm <- team_data$fgm team_fga <- team_data$fga team_ftm <- team_data$ftm team_fta <- team_data$fta team_pts <- team_data$pts team_orb <- team_data$orb # Calculate team ORB% team_orb_pct <- team_orb / (team_orb + team_data$drb) # qAST (assist adjustment factor) q_ast <- ((fgm * (pts - ftm)) / (2 * fga * pts)) * 0.5 # FG Part fg_part <- fgm * (1 - 0.5 * ((pts - ftm) / (2 * fga)) * q_ast) # AST Part ast_part <- 0.5 * (((team_pts - team_ftm) - (pts - ftm)) / (2 * (team_fga - fga))) * ast # FT Part ft_part <- (1 - (1 - (ftm / fta))^2) * 0.4 * fta # Scoring possessions sc_poss <- fg_part + ast_part + ft_part # Missed FG possessions fgm_part <- (fga - fgm) * (1 - 1.07 * team_orb_pct) # Missed FT possessions ftm_part <- ((1 - (ftm / fta))^2) * 0.4 * fta # Total possessions total_poss <- sc_poss + fgm_part + ftm_part + tov # Calculate team ORtg team_ortg <- (team_pts / team_data$poss) * 100 # Points produced (simplified) points_produced <- pts + 0.5 * ast * (team_pts / team_data$ast) - tov * (team_ortg / 100) # Individual ORtg ortg <- 100 * (points_produced / total_poss) return(round(ortg, 2)) } # Example player <- list( fgm = 10, fga = 18, ftm = 6, fta = 8, ast = 6, tov = 3, orb = 2, pts = 28 ) team <- list( fgm = 40, fga = 88, ftm = 18, fta = 24, pts = 112, orb = 10, drb = 35, ast = 24, poss = 100 ) oliver_ortg <- calculate_oliver_ortg(player, team) cat("Individual ORtg (Oliver Method):", oliver_ortg, "\n") ``` --- ## Summary Offensive Rating is a sophisticated metric that provides crucial insights into offensive performance: 1. **Pace-Adjusted**: Allows fair comparisons across different eras and playing styles 2. **Comprehensive**: Accounts for scoring, playmaking, and ball security 3. **Context-Dependent**: Must be interpreted with usage rate, role, and team quality 4. **Correlated with TS%**: Shooting efficiency is foundational but not the complete picture 5. **Historical Value**: Identifies the most efficient offensive players and teams in basketball history ORtg remains one of the most valuable tools for evaluating offensive impact in modern basketball analytics.