Data Analysis Examples

Python Example: Calculating VORP from BPM Data

"""
Calculate and analyze Value Over Replacement Player (VORP)
Install: pip install pandas numpy matplotlib seaborn
"""

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns

# Set visualization style
sns.set_style("whitegrid")
plt.rcParams['figure.figsize'] = (12, 8)


def calculate_vorp(bpm, minutes_played, team_games=82):
    """
    Calculate Value Over Replacement Player.

    Parameters:
    -----------
    bpm : float or array-like
        Box Plus/Minus value(s)
    minutes_played : float or array-like
        Total minutes played
    team_games : int
        Number of team games in season (default 82)

    Returns:
    --------
    float or array-like
        VORP value(s)
    """
    replacement_level = -2.0
    total_team_minutes = team_games * 48 * 5  # Total minutes available

    # Calculate VORP
    vorp = (bpm - replacement_level) * (minutes_played / total_team_minutes)

    return vorp


def categorize_vorp(vorp):
    """
    Categorize VORP value into performance tiers.

    Parameters:
    -----------
    vorp : float
        VORP value

    Returns:
    --------
    str
        Performance category
    """
    if vorp >= 8.0:
        return "MVP Level"
    elif vorp >= 6.0:
        return "All-NBA"
    elif vorp >= 4.0:
        return "All-Star"
    elif vorp >= 2.0:
        return "Quality Starter"
    elif vorp >= 0.5:
        return "Rotation Player"
    elif vorp >= 0.0:
        return "Barely Above Replacement"
    else:
        return "Below Replacement"


def analyze_vorp_distribution(df):
    """
    Analyze VORP distribution across players.

    Parameters:
    -----------
    df : pandas.DataFrame
        Player statistics with PLAYER, BPM, MINUTES columns

    Returns:
    --------
    pandas.DataFrame
        Enhanced dataframe with VORP and categories
    """
    # Calculate VORP
    df['VORP'] = calculate_vorp(df['BPM'], df['MINUTES'])

    # Add categories
    df['VORP_Category'] = df['VORP'].apply(categorize_vorp)

    # Add percentile ranks
    df['VORP_Percentile'] = df['VORP'].rank(pct=True) * 100

    # Summary statistics
    print("VORP Distribution Summary:")
    print(f"Mean VORP: {df['VORP'].mean():.2f}")
    print(f"Median VORP: {df['VORP'].median():.2f}")
    print(f"Std Dev: {df['VORP'].std():.2f}")
    print(f"Max VORP: {df['VORP'].max():.2f} ({df.loc[df['VORP'].idxmax(), 'PLAYER']})")
    print(f"Min VORP: {df['VORP'].min():.2f} ({df.loc[df['VORP'].idxmin(), 'PLAYER']})")

    # Category distribution
    print("\nPlayers by Category:")
    print(df['VORP_Category'].value_counts().sort_index())

    return df


def visualize_vorp_analysis(df):
    """
    Create comprehensive VORP visualizations.

    Parameters:
    -----------
    df : pandas.DataFrame
        Player statistics with VORP calculated
    """
    fig, axes = plt.subplots(2, 2, figsize=(16, 12))

    # 1. VORP Distribution Histogram
    axes[0, 0].hist(df['VORP'], bins=40, edgecolor='black', alpha=0.7, color='#3498db')
    axes[0, 0].axvline(0, color='red', linestyle='--', linewidth=2, label='Replacement Level')
    axes[0, 0].axvline(df['VORP'].mean(), color='green', linestyle='--',
                       linewidth=2, label=f"Mean: {df['VORP'].mean():.2f}")
    axes[0, 0].axvline(8.0, color='gold', linestyle='--', linewidth=2,
                       alpha=0.5, label='MVP Level (8.0)')
    axes[0, 0].set_xlabel('VORP', fontsize=12)
    axes[0, 0].set_ylabel('Number of Players', fontsize=12)
    axes[0, 0].set_title('Distribution of VORP Values', fontsize=14, fontweight='bold')
    axes[0, 0].legend()
    axes[0, 0].grid(True, alpha=0.3)

    # 2. BPM vs VORP Scatter
    axes[0, 1].scatter(df['BPM'], df['VORP'], s=df['MINUTES']/30,
                       alpha=0.6, c=df['BPM'], cmap='RdYlGn')
    axes[0, 1].axhline(0, color='red', linestyle='--', linewidth=1, alpha=0.5)
    axes[0, 1].axvline(0, color='red', linestyle='--', linewidth=1, alpha=0.5)
    axes[0, 1].set_xlabel('Box Plus/Minus (BPM)', fontsize=12)
    axes[0, 1].set_ylabel('Value Over Replacement Player (VORP)', fontsize=12)
    axes[0, 1].set_title('BPM vs VORP Relationship\n(Size = Minutes Played)',
                         fontsize=14, fontweight='bold')
    axes[0, 1].grid(True, alpha=0.3)

    # 3. VORP by Category
    category_order = ['MVP Level', 'All-NBA', 'All-Star', 'Quality Starter',
                      'Rotation Player', 'Barely Above Replacement', 'Below Replacement']
    category_counts = df['VORP_Category'].value_counts().reindex(category_order, fill_value=0)

    colors = ['#FFD700', '#FF8C00', '#1E90FF', '#32CD32', '#90EE90', '#FFE4B5', '#FF6B6B']
    axes[1, 0].bar(range(len(category_counts)), category_counts.values,
                   color=colors, alpha=0.8, edgecolor='black')
    axes[1, 0].set_xticks(range(len(category_counts)))
    axes[1, 0].set_xticklabels(category_counts.index, rotation=45, ha='right', fontsize=9)
    axes[1, 0].set_ylabel('Number of Players', fontsize=12)
    axes[1, 0].set_title('Player Distribution by VORP Category', fontsize=14, fontweight='bold')
    axes[1, 0].grid(True, axis='y', alpha=0.3)

    # 4. Top 15 Players by VORP
    top_15 = df.nlargest(15, 'VORP')[['PLAYER', 'VORP', 'BPM', 'MINUTES']].copy()

    axes[1, 1].barh(range(len(top_15)), top_15['VORP'], color='#3498db', alpha=0.8)
    axes[1, 1].set_yticks(range(len(top_15)))
    axes[1, 1].set_yticklabels(top_15['PLAYER'], fontsize=10)
    axes[1, 1].set_xlabel('VORP', fontsize=12)
    axes[1, 1].set_title('Top 15 Players by VORP', fontsize=14, fontweight='bold')
    axes[1, 1].invert_yaxis()
    axes[1, 1].grid(True, axis='x', alpha=0.3)

    # Add VORP values as text
    for i, (vorp, bpm) in enumerate(zip(top_15['VORP'], top_15['BPM'])):
        axes[1, 1].text(vorp + 0.2, i, f'{vorp:.1f} (BPM: {bpm:.1f})',
                        va='center', fontsize=8)

    plt.tight_layout()
    plt.savefig('vorp_comprehensive_analysis.png', dpi=300, bbox_inches='tight')
    plt.show()


def compare_vorp_win_shares(df):
    """
    Compare VORP rankings with Win Shares rankings.

    Parameters:
    -----------
    df : pandas.DataFrame
        Must include PLAYER, VORP, WIN_SHARES columns
    """
    # Calculate rankings
    df['VORP_Rank'] = df['VORP'].rank(ascending=False, method='min')
    df['WS_Rank'] = df['WIN_SHARES'].rank(ascending=False, method='min')
    df['Rank_Difference'] = abs(df['VORP_Rank'] - df['WS_Rank'])

    # Find biggest discrepancies
    print("\nBiggest Ranking Differences (VORP vs Win Shares):")
    discrepancies = df.nlargest(10, 'Rank_Difference')[
        ['PLAYER', 'VORP', 'VORP_Rank', 'WIN_SHARES', 'WS_Rank', 'Rank_Difference']
    ]
    print(discrepancies.to_string(index=False))

    # Scatter plot comparison
    plt.figure(figsize=(10, 8))
    plt.scatter(df['WIN_SHARES'], df['VORP'], alpha=0.6, s=80, color='#3498db')

    # Add trend line
    z = np.polyfit(df['WIN_SHARES'], df['VORP'], 1)
    p = np.poly1d(z)
    plt.plot(df['WIN_SHARES'], p(df['WIN_SHARES']),
             "r--", linewidth=2, alpha=0.7, label='Trend Line')

    plt.xlabel('Win Shares', fontsize=12)
    plt.ylabel('VORP', fontsize=12)
    plt.title('VORP vs Win Shares Comparison', fontsize=14, fontweight='bold')
    plt.grid(True, alpha=0.3)
    plt.legend()

    # Calculate correlation
    correlation = df['VORP'].corr(df['WIN_SHARES'])
    plt.text(0.05, 0.95, f'Correlation: {correlation:.3f}',
             transform=plt.gca().transAxes, fontsize=12,
             bbox=dict(boxstyle='round', facecolor='wheat', alpha=0.5))

    plt.tight_layout()
    plt.savefig('vorp_vs_win_shares.png', dpi=300, bbox_inches='tight')
    plt.show()


# Example Usage
if __name__ == "__main__":
    # Sample player data (2023-24 season)
    players_data = {
        'PLAYER': [
            'Nikola Jokić', 'Shai Gilgeous-Alexander', 'Giannis Antetokounmpo',
            'Luka Dončić', 'Domantas Sabonis', 'Jayson Tatum', 'Anthony Edwards',
            'Kawhi Leonard', 'Kevin Durant', 'LeBron James', 'Stephen Curry',
            'Joel Embiid', 'Anthony Davis', 'Tyrese Haliburton', 'Devin Booker',
            'Jalen Brunson', 'Rudy Gobert', 'Bam Adebayo', 'Julius Randle', 'Pascal Siakam'
        ],
        'BPM': [
            9.8, 8.7, 8.1, 7.6, 6.5, 5.8, 5.2, 6.1, 5.9, 5.4, 5.7,
            7.2, 4.8, 6.3, 4.5, 5.9, 3.2, 4.1, 3.8, 3.5
        ],
        'MINUTES': [
            2476, 2568, 2580, 2708, 2703, 2862, 2690, 2091, 2328, 2332, 2296,
            2213, 2567, 2448, 2652, 2716, 2605, 2607, 2656, 2489
        ],
        'WIN_SHARES': [
            14.2, 12.8, 11.5, 11.1, 10.9, 10.5, 9.8, 9.2, 9.8, 8.5, 8.9,
            10.2, 9.1, 9.5, 8.8, 9.2, 7.8, 8.1, 7.5, 7.2
        ]
    }

    df = pd.DataFrame(players_data)

    print("=" * 60)
    print("VORP ANALYSIS - 2023-24 NBA SEASON")
    print("=" * 60)

    # Analyze VORP distribution
    df_analyzed = analyze_vorp_distribution(df)

    # Show top 10 by VORP
    print("\n" + "=" * 60)
    print("TOP 10 PLAYERS BY VORP:")
    print("=" * 60)
    top_10 = df_analyzed.nlargest(10, 'VORP')[
        ['PLAYER', 'BPM', 'MINUTES', 'VORP', 'VORP_Category']
    ]
    print(top_10.to_string(index=False))

    # Create visualizations
    print("\nGenerating visualizations...")
    visualize_vorp_analysis(df_analyzed)

    # Compare with Win Shares
    print("\nComparing VORP with Win Shares...")
    compare_vorp_win_shares(df_analyzed)

    # Example: Calculate VORP for individual player
    print("\n" + "=" * 60)
    print("INDIVIDUAL VORP CALCULATION EXAMPLE:")
    print("=" * 60)
    example_player = "Nikola Jokić"
    example_bpm = 9.8
    example_minutes = 2476
    example_vorp = calculate_vorp(example_bpm, example_minutes)

    print(f"Player: {example_player}")
    print(f"BPM: +{example_bpm}")
    print(f"Minutes: {example_minutes}")
    print(f"Calculated VORP: {example_vorp:.1f}")
    print(f"Category: {categorize_vorp(example_vorp)}")
    print(f"\nInterpretation: {example_player} contributed {example_vorp:.1f} points")
    print(f"per 100 possessions above a replacement-level player over the season.")

    print("\nAnalysis complete!")

R Example: VORP Calculation and Visualization

# Value Over Replacement Player (VORP) Analysis in R
# Install packages: install.packages(c("tidyverse", "ggplot2", "scales", "gridExtra"))

library(tidyverse)
library(ggplot2)
library(scales)
library(gridExtra)

# Set visualization theme
theme_set(theme_minimal())


#' Calculate Value Over Replacement Player
#'
#' @param bpm Box Plus/Minus value
#' @param minutes Minutes played
#' @param team_games Number of team games (default 82)
#' @return VORP value
calculate_vorp <- function(bpm, minutes, team_games = 82) {
  replacement_level <- -2.0
  total_team_minutes <- team_games * 48 * 5

  vorp <- (bpm - replacement_level) * (minutes / total_team_minutes)

  return(vorp)
}


#' Categorize VORP value into performance tier
#'
#' @param vorp VORP value
#' @return Performance category string
categorize_vorp <- function(vorp) {
  case_when(
    vorp >= 8.0 ~ "MVP Level",
    vorp >= 6.0 ~ "All-NBA",
    vorp >= 4.0 ~ "All-Star",
    vorp >= 2.0 ~ "Quality Starter",
    vorp >= 0.5 ~ "Rotation Player",
    vorp >= 0.0 ~ "Barely Above Replacement",
    TRUE ~ "Below Replacement"
  )
}


#' Analyze VORP distribution across players
#'
#' @param df Data frame with PLAYER, BPM, MINUTES columns
#' @return Enhanced data frame with VORP analysis
analyze_vorp_distribution <- function(df) {
  df <- df %>%
    mutate(
      VORP = calculate_vorp(BPM, MINUTES),
      VORP_Category = categorize_vorp(VORP),
      VORP_Category = factor(VORP_Category, levels = c(
        "MVP Level", "All-NBA", "All-Star", "Quality Starter",
        "Rotation Player", "Barely Above Replacement", "Below Replacement"
      )),
      VORP_Percentile = percent_rank(VORP) * 100
    )

  # Print summary statistics
  cat("VORP Distribution Summary:\n")
  cat(sprintf("Mean VORP: %.2f\n", mean(df$VORP)))
  cat(sprintf("Median VORP: %.2f\n", median(df$VORP)))
  cat(sprintf("Std Dev: %.2f\n", sd(df$VORP)))
  cat(sprintf("Max VORP: %.2f (%s)\n",
              max(df$VORP), df$PLAYER[which.max(df$VORP)]))
  cat(sprintf("Min VORP: %.2f (%s)\n",
              min(df$VORP), df$PLAYER[which.min(df$VORP)]))

  # Category distribution
  cat("\nPlayers by Category:\n")
  print(table(df$VORP_Category))

  return(df)
}


#' Create comprehensive VORP visualizations
#'
#' @param df Data frame with VORP calculated
visualize_vorp_analysis <- function(df) {

  # Plot 1: VORP Distribution
  p1 <- ggplot(df, aes(x = VORP)) +
    geom_histogram(bins = 30, fill = "#3498db", color = "black", alpha = 0.7) +
    geom_vline(xintercept = 0, color = "red", linetype = "dashed", size = 1.2) +
    geom_vline(aes(xintercept = mean(VORP)), color = "green",
               linetype = "dashed", size = 1) +
    geom_vline(xintercept = 8.0, color = "gold", linetype = "dashed",
               alpha = 0.6, size = 1) +
    annotate("text", x = 0, y = Inf, label = "Replacement Level",
             vjust = 2, hjust = -0.1, color = "red", size = 3.5) +
    annotate("text", x = 8.0, y = Inf, label = "MVP Level",
             vjust = 2, hjust = -0.1, color = "gold", size = 3.5) +
    labs(
      title = "Distribution of VORP Values",
      x = "Value Over Replacement Player (VORP)",
      y = "Number of Players"
    ) +
    theme(
      plot.title = element_text(size = 14, face = "bold"),
      axis.title = element_text(size = 11)
    )

  # Plot 2: BPM vs VORP Scatter
  p2 <- ggplot(df, aes(x = BPM, y = VORP)) +
    geom_point(aes(size = MINUTES, color = BPM), alpha = 0.6) +
    geom_hline(yintercept = 0, color = "red", linetype = "dashed", alpha = 0.5) +
    geom_vline(xintercept = 0, color = "red", linetype = "dashed", alpha = 0.5) +
    scale_color_gradient2(
      low = "#d73027", mid = "#ffffbf", high = "#1a9850",
      midpoint = 0, name = "BPM"
    ) +
    scale_size_continuous(name = "Minutes", range = c(3, 12)) +
    labs(
      title = "BPM vs VORP Relationship",
      subtitle = "Size represents minutes played",
      x = "Box Plus/Minus (BPM)",
      y = "Value Over Replacement Player (VORP)"
    ) +
    theme(
      plot.title = element_text(size = 14, face = "bold"),
      plot.subtitle = element_text(size = 10)
    )

  # Plot 3: VORP by Category
  category_counts <- df %>%
    count(VORP_Category) %>%
    complete(VORP_Category, fill = list(n = 0))

  p3 <- ggplot(category_counts, aes(x = VORP_Category, y = n, fill = VORP_Category)) +
    geom_bar(stat = "identity", alpha = 0.8, color = "black") +
    geom_text(aes(label = n), vjust = -0.5, size = 4) +
    scale_fill_manual(values = c(
      "MVP Level" = "#FFD700",
      "All-NBA" = "#FF8C00",
      "All-Star" = "#1E90FF",
      "Quality Starter" = "#32CD32",
      "Rotation Player" = "#90EE90",
      "Barely Above Replacement" = "#FFE4B5",
      "Below Replacement" = "#FF6B6B"
    )) +
    labs(
      title = "Player Distribution by VORP Category",
      x = "Category",
      y = "Number of Players"
    ) +
    theme(
      axis.text.x = element_text(angle = 45, hjust = 1, size = 9),
      plot.title = element_text(size = 14, face = "bold"),
      legend.position = "none"
    )

  # Plot 4: Top 15 Players by VORP
  top_15 <- df %>%
    arrange(desc(VORP)) %>%
    head(15) %>%
    mutate(PLAYER = fct_reorder(PLAYER, VORP))

  p4 <- ggplot(top_15, aes(x = PLAYER, y = VORP)) +
    geom_col(fill = "#3498db", alpha = 0.8, color = "black") +
    geom_text(aes(label = sprintf("%.1f", VORP)), hjust = -0.2, size = 3.5) +
    coord_flip() +
    labs(
      title = "Top 15 Players by VORP",
      x = "",
      y = "Value Over Replacement Player"
    ) +
    theme(
      plot.title = element_text(size = 14, face = "bold"),
      axis.text.y = element_text(size = 10)
    )

  # Combine plots
  combined_plot <- grid.arrange(p1, p2, p3, p4, ncol = 2)

  # Save combined plot
  ggsave("vorp_comprehensive_analysis.png", combined_plot,
         width = 16, height = 12, dpi = 300)

  return(list(p1 = p1, p2 = p2, p3 = p3, p4 = p4))
}


#' Compare VORP with Win Shares
#'
#' @param df Data frame with VORP and WIN_SHARES columns
compare_vorp_win_shares <- function(df) {
  df <- df %>%
    mutate(
      VORP_Rank = rank(-VORP, ties.method = "min"),
      WS_Rank = rank(-WIN_SHARES, ties.method = "min"),
      Rank_Difference = abs(VORP_Rank - WS_Rank)
    )

  # Find biggest discrepancies
  cat("\nBiggest Ranking Differences (VORP vs Win Shares):\n")
  discrepancies <- df %>%
    arrange(desc(Rank_Difference)) %>%
    head(10) %>%
    select(PLAYER, VORP, VORP_Rank, WIN_SHARES, WS_Rank, Rank_Difference)

  print(discrepancies, n = 10)

  # Create scatter plot comparison
  p <- ggplot(df, aes(x = WIN_SHARES, y = VORP)) +
    geom_point(alpha = 0.6, size = 4, color = "#3498db") +
    geom_smooth(method = "lm", color = "red", linetype = "dashed",
                se = TRUE, alpha = 0.2) +
    labs(
      title = "VORP vs Win Shares Comparison",
      x = "Win Shares",
      y = "Value Over Replacement Player (VORP)"
    ) +
    theme(
      plot.title = element_text(size = 14, face = "bold")
    )

  # Calculate correlation
  correlation <- cor(df$VORP, df$WIN_SHARES)

  p <- p + annotate("text", x = min(df$WIN_SHARES), y = max(df$VORP),
                    label = sprintf("Correlation: %.3f", correlation),
                    hjust = 0, vjust = 1, size = 5,
                    color = "darkred", fontface = "bold")

  print(p)
  ggsave("vorp_vs_win_shares.png", p, width = 10, height = 8, dpi = 300)

  return(df)
}


# Example Usage
main <- function() {
  cat("=" %s% rep("=", 60) %s% "\n")
  cat("VORP ANALYSIS - 2023-24 NBA SEASON\n")
  cat("=" %s% rep("=", 60) %s% "\n\n")

  # Sample player data
  players_df <- tibble(
    PLAYER = c(
      "Nikola Jokić", "Shai Gilgeous-Alexander", "Giannis Antetokounmpo",
      "Luka Dončić", "Domantas Sabonis", "Jayson Tatum", "Anthony Edwards",
      "Kawhi Leonard", "Kevin Durant", "LeBron James", "Stephen Curry",
      "Joel Embiid", "Anthony Davis", "Tyrese Haliburton", "Devin Booker",
      "Jalen Brunson", "Rudy Gobert", "Bam Adebayo", "Julius Randle", "Pascal Siakam"
    ),
    BPM = c(
      9.8, 8.7, 8.1, 7.6, 6.5, 5.8, 5.2, 6.1, 5.9, 5.4, 5.7,
      7.2, 4.8, 6.3, 4.5, 5.9, 3.2, 4.1, 3.8, 3.5
    ),
    MINUTES = c(
      2476, 2568, 2580, 2708, 2703, 2862, 2690, 2091, 2328, 2332, 2296,
      2213, 2567, 2448, 2652, 2716, 2605, 2607, 2656, 2489
    ),
    WIN_SHARES = c(
      14.2, 12.8, 11.5, 11.1, 10.9, 10.5, 9.8, 9.2, 9.8, 8.5, 8.9,
      10.2, 9.1, 9.5, 8.8, 9.2, 7.8, 8.1, 7.5, 7.2
    )
  )

  # Analyze VORP distribution
  players_analyzed <- analyze_vorp_distribution(players_df)

  # Show top 10 by VORP
  cat("\n" %s% rep("=", 60) %s% "\n")
  cat("TOP 10 PLAYERS BY VORP:\n")
  cat(rep("=", 60) %s% "\n\n")

  top_10 <- players_analyzed %>%
    arrange(desc(VORP)) %>%
    head(10) %>%
    select(PLAYER, BPM, MINUTES, VORP, VORP_Category) %>%
    mutate(
      BPM = sprintf("+%.1f", BPM),
      VORP = sprintf("%.1f", VORP)
    )

  print(top_10, n = 10)

  # Create visualizations
  cat("\nGenerating visualizations...\n")
  plots <- visualize_vorp_analysis(players_analyzed)

  # Compare with Win Shares
  cat("\nComparing VORP with Win Shares...\n")
  comparison <- compare_vorp_win_shares(players_analyzed)

  # Individual calculation example
  cat("\n" %s% rep("=", 60) %s% "\n")
  cat("INDIVIDUAL VORP CALCULATION EXAMPLE:\n")
  cat(rep("=", 60) %s% "\n\n")

  example_player <- "Nikola Jokić"
  example_bpm <- 9.8
  example_minutes <- 2476
  example_vorp <- calculate_vorp(example_bpm, example_minutes)

  cat(sprintf("Player: %s\n", example_player))
  cat(sprintf("BPM: +%.1f\n", example_bpm))
  cat(sprintf("Minutes: %d\n", example_minutes))
  cat(sprintf("Calculated VORP: %.1f\n", example_vorp))
  cat(sprintf("Category: %s\n\n", categorize_vorp(example_vorp)))

  cat(sprintf("Interpretation: %s contributed %.1f points\n",
              example_player, example_vorp))
  cat("per 100 possessions above a replacement-level player over the season.\n")

  cat("\nAnalysis complete!\n")

  return(list(
    data = players_analyzed,
    plots = plots,
    comparison = comparison
  ))
}

# Run the analysis
results <- main()