Field Goal and Free Throw Percentages

# Shooting Percentages Shooting percentages are fundamental efficiency metrics in basketball that measure a player's accuracy from different areas of the court. The three primary shooting percentages are Field Goal Percentage (FG%), Three-Point Percentage (3P%), and Free Throw Percentage (FT%). ## Field Goal Percentage (FG%) ### Calculation Field Goal Percentage measures the ratio of successful field goal attempts to total field goal attempts: ``` FG% = (Field Goals Made / Field Goals Attempted) × 100 ``` **Example:** - Player makes 450 field goals out of 900 attempts - FG% = (450 / 900) × 100 = 50.0% ### League Averages and Benchmarks **NBA League Averages (2023-24 season):** - League average FG%: ~46-47% - Center position: ~55-58% (highest due to proximity to basket) - Guard positions: ~43-46% **Performance Tiers:** - Elite: 55%+ (typically centers and efficient scorers) - Very Good: 50-55% (high-efficiency players) - Above Average: 47-50% - Average: 44-47% - Below Average: <44% **Notable Context:** - Centers like Rudy Gobert and Jarrett Allen often exceed 65% due to dunks and layups - Guards rarely exceed 50% due to longer-distance shots - Era matters: 1980s-90s averages were lower (~47%) vs modern analytics era (~48%) ## Three-Point Percentage (3P%) ### Calculation Three-Point Percentage measures accuracy from beyond the three-point arc: ``` 3P% = (Three-Pointers Made / Three-Pointers Attempted) × 100 ``` **Example:** - Player makes 180 three-pointers out of 480 attempts - 3P% = (180 / 480) × 100 = 37.5% ### League Averages and Benchmarks **NBA League Averages (2023-24 season):** - League average 3P%: ~36-37% - High-volume shooters (6+ attempts/game): ~37-38% - Low-volume shooters (<3 attempts/game): ~35-36% **Performance Tiers:** - Elite: 40%+ (top-tier shooters) - Very Good: 38-40% - Above Average: 36-38% - Average: 34-36% - Below Average: <34% **Historical Context:** - 1980s: ~28% league average (three-point line introduced 1979-80) - 1990s: ~35% league average - 2000s: ~35-36% - 2010s-present: ~36-37% (with increased volume) **Notable Shooters:** - Steve Kerr: 45.4% career (all-time leader, min. 250 makes) - Stephen Curry: ~43% career on high volume - Seth Curry: ~44% career ## Free Throw Percentage (FT%) ### Calculation Free Throw Percentage measures accuracy from the free throw line: ``` FT% = (Free Throws Made / Free Throws Attempted) × 100 ``` **Example:** - Player makes 340 free throws out of 400 attempts - FT% = (340 / 400) × 100 = 85.0% ### League Averages and Benchmarks **NBA League Averages:** - League average FT%: ~77-78% - Guards: ~80-82% - Forwards: ~75-78% - Centers: ~70-73% **Performance Tiers:** - Elite: 90%+ (elite free throw shooters) - Very Good: 85-90% - Above Average: 80-85% - Average: 75-80% - Below Average: 70-75% - Poor: <70% **Historical Excellence:** - Stephen Curry: ~91% career - Steve Nash: 90.4% career - Mark Price: 90.4% career - Wilt Chamberlain: 51.1% career (historically poor for a star) ## Code Examples ### Python: Calculate Shooting Percentages ```python import pandas as pd import numpy as np def calculate_shooting_percentages(df): """ Calculate FG%, 3P%, and FT% from basketball statistics. Parameters: df (DataFrame): DataFrame with columns FGM, FGA, TPM, TPA, FTM, FTA Returns: DataFrame: Original data with added percentage columns """ # Avoid division by zero df['FG%'] = np.where(df['FGA'] > 0, (df['FGM'] / df['FGA']) * 100, 0) df['3P%'] = np.where(df['TPA'] > 0, (df['TPM'] / df['TPA']) * 100, 0) df['FT%'] = np.where(df['FTA'] > 0, (df['FTM'] / df['FTA']) * 100, 0) return df # Example usage player_stats = pd.DataFrame({ 'Player': ['Player A', 'Player B', 'Player C'], 'FGM': [450, 380, 520], 'FGA': [900, 850, 1000], 'TPM': [180, 95, 45], 'TPA': [480, 280, 125], 'FTM': [340, 280, 420], 'FTA': [400, 350, 580] }) player_stats = calculate_shooting_percentages(player_stats) print(player_stats[['Player', 'FG%', '3P%', 'FT%']].round(1)) ``` ### Python: Analyze Shooting Efficiency ```python import matplotlib.pyplot as plt import seaborn as sns def categorize_shooting(fg_pct, three_pct, ft_pct): """Categorize shooting performance.""" categories = { 'FG%': 'Elite' if fg_pct >= 55 else 'Very Good' if fg_pct >= 50 else 'Above Avg' if fg_pct >= 47 else 'Average' if fg_pct >= 44 else 'Below Avg', '3P%': 'Elite' if three_pct >= 40 else 'Very Good' if three_pct >= 38 else 'Above Avg' if three_pct >= 36 else 'Average' if three_pct >= 34 else 'Below Avg', 'FT%': 'Elite' if ft_pct >= 90 else 'Very Good' if ft_pct >= 85 else 'Above Avg' if ft_pct >= 80 else 'Average' if ft_pct >= 75 else 'Below Avg' } return categories # Example: Visualize shooting percentages def plot_shooting_comparison(df): """Create visualization comparing shooting percentages.""" fig, axes = plt.subplots(1, 3, figsize=(15, 5)) # FG% distribution axes[0].hist(df['FG%'], bins=20, edgecolor='black', alpha=0.7) axes[0].axvline(df['FG%'].mean(), color='red', linestyle='--', label=f'Mean: {df["FG%"].mean():.1f}%') axes[0].set_xlabel('Field Goal %') axes[0].set_ylabel('Frequency') axes[0].set_title('FG% Distribution') axes[0].legend() # 3P% distribution axes[1].hist(df['3P%'], bins=20, edgecolor='black', alpha=0.7, color='orange') axes[1].axvline(df['3P%'].mean(), color='red', linestyle='--', label=f'Mean: {df["3P%"].mean():.1f}%') axes[1].set_xlabel('Three-Point %') axes[1].set_ylabel('Frequency') axes[1].set_title('3P% Distribution') axes[1].legend() # FT% distribution axes[2].hist(df['FT%'], bins=20, edgecolor='black', alpha=0.7, color='green') axes[2].axvline(df['FT%'].mean(), color='red', linestyle='--', label=f'Mean: {df["FT%"].mean():.1f}%') axes[2].set_xlabel('Free Throw %') axes[2].set_ylabel('Frequency') axes[2].set_title('FT% Distribution') axes[2].legend() plt.tight_layout() plt.show() # Example usage # plot_shooting_comparison(player_stats) ``` ### Python: Advanced Analysis with Context ```python def calculate_true_shooting_context(df): """ Calculate shooting percentages with volume context. High volume on good percentages is more valuable. """ # Add volume tiers df['3PA_per_game'] = df['TPA'] / df['Games'] df['Volume_Tier'] = pd.cut(df['3PA_per_game'], bins=[0, 3, 6, 10, 100], labels=['Low', 'Medium', 'High', 'Very High']) # Calculate percentages df = calculate_shooting_percentages(df) # Weighted efficiency score (considers volume) df['Shooting_Score'] = ( df['FG%'] * 0.4 + # FG% weighted 40% df['3P%'] * 0.35 + # 3P% weighted 35% df['FT%'] * 0.25 # FT% weighted 25% ) return df ``` ### R: Calculate and Visualize Shooting Percentages ```r library(dplyr) library(ggplot2) library(tidyr) # Calculate shooting percentages calculate_shooting_pct <- function(df) { df %>% mutate( FG_pct = ifelse(FGA > 0, (FGM / FGA) * 100, 0), TP_pct = ifelse(TPA > 0, (TPM / TPA) * 100, 0), FT_pct = ifelse(FTA > 0, (FTM / FTA) * 100, 0) ) } # Example data player_stats <- data.frame( Player = c("Player A", "Player B", "Player C"), FGM = c(450, 380, 520), FGA = c(900, 850, 1000), TPM = c(180, 95, 45), TPA = c(480, 280, 125), FTM = c(340, 280, 420), FTA = c(400, 350, 580) ) # Calculate percentages player_stats <- calculate_shooting_pct(player_stats) # Print results player_stats %>% select(Player, FG_pct, TP_pct, FT_pct) %>% mutate(across(where(is.numeric), round, 1)) # Visualize shooting percentages shooting_long <- player_stats %>% select(Player, FG_pct, TP_pct, FT_pct) %>% pivot_longer(cols = c(FG_pct, TP_pct, FT_pct), names_to = "Shot_Type", values_to = "Percentage") ggplot(shooting_long, aes(x = Player, y = Percentage, fill = Shot_Type)) + geom_bar(stat = "identity", position = "dodge") + geom_hline(yintercept = c(47, 37, 77), linetype = "dashed", color = c("red", "blue", "green")) + labs(title = "Player Shooting Percentages Comparison", subtitle = "Dashed lines represent league averages", y = "Percentage (%)", fill = "Shot Type") + scale_fill_manual(values = c("FG_pct" = "#E41A1C", "TP_pct" = "#377EB8", "FT_pct" = "#4DAF4A"), labels = c("FG%", "3P%", "FT%")) + theme_minimal() + theme(plot.title = element_text(hjust = 0.5, face = "bold"), plot.subtitle = element_text(hjust = 0.5)) ``` ### R: Statistical Analysis of Shooting Trends ```r library(broom) # Analyze shooting percentage trends over time analyze_shooting_trends <- function(df) { # Linear regression for each shooting type fg_model <- lm(FG_pct ~ Season, data = df) tp_model <- lm(TP_pct ~ Season, data = df) ft_model <- lm(FT_pct ~ Season, data = df) # Get tidy results results <- bind_rows( tidy(fg_model) %>% mutate(Type = "FG%"), tidy(tp_model) %>% mutate(Type = "3P%"), tidy(ft_model) %>% mutate(Type = "FT%") ) return(results) } # Categorize shooting performance categorize_shooter <- function(fg_pct, tp_pct, ft_pct) { tibble( FG_Category = case_when( fg_pct >= 55 ~ "Elite", fg_pct >= 50 ~ "Very Good", fg_pct >= 47 ~ "Above Average", fg_pct >= 44 ~ "Average", TRUE ~ "Below Average" ), TP_Category = case_when( tp_pct >= 40 ~ "Elite", tp_pct >= 38 ~ "Very Good", tp_pct >= 36 ~ "Above Average", tp_pct >= 34 ~ "Average", TRUE ~ "Below Average" ), FT_Category = case_when( ft_pct >= 90 ~ "Elite", ft_pct >= 85 ~ "Very Good", ft_pct >= 80 ~ "Above Average", ft_pct >= 75 ~ "Average", TRUE ~ "Below Average" ) ) } ``` ## Limitations and Considerations ### 1. Volume Context Missing **The Problem:** Shooting percentages don't account for volume. A player shooting 50% on 5 attempts per game is different from 50% on 20 attempts per game. **Example:** - Player A: 2/4 FG per game (50%) - Limited sample, fewer defensive pressures - Player B: 10/20 FG per game (50%) - High volume, faces more defensive attention **Solution:** Always consider attempts alongside percentages. Use metrics like True Shooting Percentage (TS%) for better context. ### 2. Shot Difficulty Not Captured **The Problem:** Not all shots are equal. A center dunking (65% FG%) faces easier shots than a guard taking contested jumpers (45% FG%). **Factors Affecting Difficulty:** - Distance from basket - Defender proximity - Shot clock time remaining - Game situation (late clock, end of game) - Play type (catch-and-shoot vs off-the-dribble) **Example:** - Stephen Curry: 47% FG% on high-difficulty, contested threes - Rudy Gobert: 67% FG% on dunks and layups - Gobert's percentage is higher but Curry's shots create more value ### 3. Position and Role Bias **The Problem:** Different positions have vastly different shooting percentage expectations. **Position Benchmarks:** - Centers: 55-60% FG% (close to basket) - Power Forwards: 48-53% FG% - Small Forwards: 45-50% FG% - Shooting Guards: 44-48% FG% - Point Guards: 43-47% FG% **Solution:** Compare players to positional averages, not league-wide averages. ### 4. Sample Size Issues **The Problem:** Small sample sizes create misleading percentages, especially for three-point shooting. **Example:** - Early season: Player goes 8/15 from three (53.3%) - Full season: Player regresses to 120/320 (37.5%) **Guidelines:** - Minimum 100 attempts for reliable 3P% - Minimum 200 attempts for reliable FG% - Minimum 50 attempts for reliable FT% - Use confidence intervals for small samples ### 5. Era and Pace Adjustments **The Problem:** League-wide shooting percentages have changed over time due to rule changes, defensive schemes, and playing style. **Historical Context:** - 1970s-80s: More physical defense, lower percentages - 1990s-2000s: Hand-checking banned (1994), slightly higher percentages - 2010s-present: Analytics revolution, more efficient shot selection **Solution:** Compare to era-adjusted averages, not all-time averages. ### 6. Game Context Ignored **The Problem:** Percentages don't show when shots are taken (garbage time vs clutch moments). **Clutch Shooting:** - Some players shoot better/worse in high-pressure situations - 4th quarter and overtime percentages often differ from overall - Playoff percentages typically drop 2-3% due to defensive intensity ### 7. Two-Point vs Three-Point Mix **The Problem:** FG% doesn't distinguish between twos and threes. A player shooting 33% from three (0.99 points per attempt) has the same FG% as someone shooting 33% from two (0.66 points per attempt). **Example:** - Player A: 45% FG% (all twos) = 0.90 points per attempt - Player B: 45% FG% (all threes) = 1.35 points per attempt - Player B is far more efficient despite identical FG% **Solution:** Use True Shooting Percentage (TS%) or Effective Field Goal Percentage (eFG%). ### 8. Free Throw Context **The Problem:** FT% doesn't show when free throws are taken or how players are fouled. **Considerations:** - And-one free throws (after made FG) vs shooting fouls - Intentional fouls (hack-a-Shaq strategy) - Technical and flagrant free throws - Fatigue effects (late-game free throws) ### 9. Regression to the Mean **The Problem:** Extreme shooting percentages (very high or low) tend to regress toward career averages over time. **Example:** - Hot streak: 55% from three over 10 games - Expected: Regression toward 37% career average - Don't overreact to short-term shooting fluctuations ### 10. Defensive Impact Not Measured **The Problem:** Shooting percentages are offensive metrics only. A poor shooter who plays elite defense can still be valuable. **Example:** - Ben Simmons: Poor FT% (60%) but elite defender - Trae Young: Excellent shooting but defensive liability - Raw shooting percentages don't capture overall player value ## Best Practices for Using Shooting Percentages 1. **Always Include Volume:** Report attempts alongside percentages 2. **Use Sample Size Thresholds:** Don't overweight small samples 3. **Compare to Position:** Use positional benchmarks, not league-wide 4. **Consider Era:** Adjust for historical context 5. **Combine with Advanced Metrics:** Use TS%, eFG%, and other efficiency stats 6. **Account for Shot Quality:** Factor in shot difficulty when possible 7. **Watch for Trends:** Look at multi-year patterns, not single seasons 8. **Context Matters:** Consider game situations, defensive schemes, and roles ## Summary Shooting percentages are essential basketball metrics, but they require context: - **FG%:** Useful but doesn't distinguish shot value (twos vs threes) - **3P%:** Critical in modern NBA; 37% is average, 40%+ is elite - **FT%:** Most stable metric; 80%+ expected for guards, 70%+ for bigs **Key Takeaways:** - Volume matters as much as percentage - Position and role create different expectations - Combine with advanced metrics (TS%, eFG%) for complete picture - Sample size is crucial for reliability - Shot difficulty varies dramatically by player and role For comprehensive player evaluation, use shooting percentages as one component alongside advanced efficiency metrics, defensive statistics, and contextual factors.