Learning ObjectivesBy the end of this chapter, you will be able to:

1. Analyze play-calling tendencies and patterns across different situations
2. Identify optimal play-call sequences using data-driven methods
3. Understand how defenses adjust to offensive tendencies
4. Apply game theory principles to play-calling strategy
5. Measure and evaluate play-caller efficiency and effectiveness

Introduction

Play-calling is one of the most scrutinized aspects of football. Every Sunday, millions of fans second-guess offensive coordinators, debating whether they should have run or passed, whether they were too conservative or too aggressive. Yet until recently, these debates were largely based on gut feelings rather than rigorous analysis.

Modern analytics provides unprecedented insight into play-calling patterns. We can now quantify tendencies, measure predictability, assess effectiveness across situations, and even identify optimal strategies using game theory. This chapter explores the data science of play-calling, from basic tendency analysis to sophisticated optimization techniques.

The art and science of play-calling represents one of football's most fascinating strategic challenges. An offensive coordinator must balance competing objectives: maintaining unpredictability to prevent defensive adjustments, optimizing play selection for each specific situation, leveraging personnel matchups, executing the game plan, and managing risk. Each play call occurs within layers of strategic consideration—what worked earlier in the game, what the defense has shown, what the down-and-distance situation demands, and what the score and clock dictate.

What makes play-calling analysis particularly compelling is that we can now measure what was previously invisible. Before the analytics era, evaluating play-calling required subjective judgment: Did it "feel" like the coordinator was too predictable? Were they "aggressive enough"? Today, we can quantify these qualities. We can measure exactly how predictable a coordinator is in specific situations, calculate the cost of that predictability, and even determine optimal play frequencies using game theory principles.

This chapter approaches play-calling through multiple lenses. We'll start with descriptive analysis—measuring tendencies across situations, personnel groupings, and game states. We'll examine how down and distance, field position, score differential, and time remaining influence play selection. We'll analyze personnel groupings and their associated tendencies, revealing how defenses read formation tells. Then we'll move to prescriptive analysis, using game theory to understand the value of unpredictability and building recommendation systems for optimal play-calling. Throughout, we'll connect statistical findings to football strategy, explaining not just what the numbers show but why they matter for winning games.

The Importance of Play-Calling Analytics

Effective play-calling requires balancing several competing objectives:

• Unpredictability: Avoiding patterns that defenses can exploit
• Situation optimization: Calling the right plays for each down and distance
• Personnel matching: Leveraging favorable matchups
• Script execution: Following game plan while adapting to circumstances
• Risk management: Balancing aggression with ball security

Analytics helps coordinators achieve this balance by:

1. Identifying their own tendencies and blind spots
2. Detecting opponent tendencies to exploit
3. Measuring effectiveness across different situations
4. Quantifying the cost of predictability
5. Providing data-driven optimization recommendations

Measuring Play-Calling Tendencies

Basic Tendency Metrics

The foundation of play-calling analysis is measuring frequencies across different contexts. Before we can optimize play-calling or identify exploitable patterns, we need to establish baseline measurements: How often does a team pass versus run? How does this balance vary by team, situation, and context?

Understanding basic tendencies serves multiple purposes. For offensive coordinators, it reveals their own blind spots—situations where they've become too predictable. For defensive coordinators, it identifies patterns to exploit. For analysts, it provides the foundation for more sophisticated analyses of efficiency, predictability, and optimization.

At its simplest level, tendency analysis calculates frequency distributions: In situation X, how often does team Y call play type Z? But even this basic analysis reveals fascinating patterns. Some teams pass on 60-65% of plays, while others stay closer to 50-50. These differences reflect philosophical approaches, personnel strengths, and strategic choices.

The methodology for calculating tendencies is straightforward but requires careful attention to data filtering. We must exclude plays that don't represent true offensive play-calling decisions: penalties before the snap, special teams plays, quarterback kneels, and spikes are all excluded because they don't reflect strategic offensive choices. We focus on plays where the offense genuinely chose between running and passing.

When measuring team tendencies, we calculate several key metrics simultaneously. First, we count the raw frequencies—how many passes versus runs did each team call? Second, we convert these counts into rates (proportions) to make teams comparable regardless of how many total plays they ran. Third, we measure the efficiency of each play type using EPA, allowing us to assess not just what teams did but how well it worked.

Let's start by calculating the most basic tendency metric: overall run-pass balance by team. This gives us a sense of each team's offensive identity and philosophy:

#| label: setup-r
#| message: false
#| warning: false

library(tidyverse)
library(nflfastR)
library(nflplotR)
library(gt)
library(ggridges)

# Load 2023 season data
pbp_2023 <- load_pbp(2023)

#| label: basic-tendencies-r
#| message: false
#| warning: false

# Calculate basic play-calling tendencies by team
# This analysis reveals each team's overall offensive philosophy and approach
# We're measuring both frequency (how often) and efficiency (how well)

team_tendencies <- pbp_2023 %>%
  # Filter to valid offensive plays with known teams
  filter(
    !is.na(down),              # Must have a valid down
    !is.na(posteam),           # Must know which team has the ball
    play_type %in% c("run", "pass")  # Only standard run/pass plays
  ) %>%
  # Group all plays by the offensive team
  group_by(posteam) %>%
  # Calculate summary statistics for each team
  summarise(
    total_plays = n(),                              # Total offensive plays
    pass_plays = sum(play_type == "pass"),          # Count of pass attempts
    run_plays = sum(play_type == "run"),            # Count of run attempts
    pass_rate = pass_plays / total_plays,           # Pass frequency (0-1)
    run_rate = run_plays / total_plays,             # Run frequency (0-1)
    # Calculate average EPA for each play type
    avg_epa_pass = mean(epa[play_type == "pass"], na.rm = TRUE),  # Pass efficiency
    avg_epa_run = mean(epa[play_type == "run"], na.rm = TRUE),    # Run efficiency
    .groups = "drop"
  ) %>%
  # Sort from most pass-heavy to most run-heavy
  arrange(desc(pass_rate))

# Display results
team_tendencies %>%
  head(10) %>%
  gt() %>%
  cols_label(
    posteam = "Team",
    total_plays = "Total Plays",
    pass_plays = "Pass Plays",
    run_plays = "Run Plays",
    pass_rate = "Pass Rate",
    run_rate = "Run Rate",
    avg_epa_pass = "Pass EPA",
    avg_epa_run = "Run EPA"
  ) %>%
  fmt_number(
    columns = c(pass_rate, run_rate),
    decimals = 3
  ) %>%
  fmt_number(
    columns = c(avg_epa_pass, avg_epa_run),
    decimals = 3
  ) %>%
  fmt_number(
    columns = c(total_plays, pass_plays, run_plays),
    decimals = 0,
    use_seps = TRUE
  ) %>%
  data_color(
    columns = pass_rate,
    colors = scales::col_numeric(
      palette = c("#F8766D", "#FFFFFF", "#00BFC4"),
      domain = c(0.4, 0.7)
    )
  ) %>%
  tab_header(
    title = "Team Play-Calling Tendencies",
    subtitle = "2023 NFL Regular Season"
  )

#| label: setup-py
#| message: false
#| warning: false

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

# Load 2023 season data
pbp_2023 = nfl.import_pbp_data([2023])

#| label: basic-tendencies-py
#| message: false
#| warning: false

# Calculate basic play-calling tendencies by team
# This analysis reveals each team's overall offensive philosophy and approach
# We're measuring both frequency (how often) and efficiency (how well)

team_tendencies = (pbp_2023
    # Filter to valid offensive plays only
    .query("down.notna() & posteam.notna() & play_type.isin(['run', 'pass'])")
    # Group by team
    .groupby('posteam')
    # Calculate aggregate statistics
    .agg(
        total_plays=('play_type', 'count'),                                    # Total plays
        pass_plays=('play_type', lambda x: (x == 'pass').sum()),              # Pass count
        run_plays=('play_type', lambda x: (x == 'run').sum()),                # Run count
        # Calculate EPA separately for pass and run plays
        avg_epa_pass=('epa', lambda x: x[pbp_2023.loc[x.index, 'play_type'] == 'pass'].mean()),
        avg_epa_run=('epa', lambda x: x[pbp_2023.loc[x.index, 'play_type'] == 'run'].mean())
    )
    # Add calculated columns for rates
    .assign(
        pass_rate=lambda x: x['pass_plays'] / x['total_plays'],  # Pass frequency
        run_rate=lambda x: x['run_plays'] / x['total_plays']     # Run frequency
    )
    # Sort from most pass-heavy to most run-heavy
    .sort_values('pass_rate', ascending=False)
    .reset_index()
)

# Display top 10 teams
print("Team Play-Calling Tendencies (2023 NFL Regular Season)")
print("=" * 90)
print(team_tendencies.head(10).to_string(index=False))

These results reveal significant variation in offensive philosophy across the NFL. The most pass-heavy teams typically have pass rates around 60-65%, while the most run-heavy teams might be around 45-50%. This 15-20 percentage point spread represents fundamentally different approaches to offense.

Why Teams Vary in Pass Rate: Several factors drive these differences:

• Personnel Strengths: Teams with elite quarterbacks (like the Dolphins with Tua Tagovailoa or the Cowboys with Dak Prescott) tend to pass more frequently. Teams with strong offensive lines and running backs may run more.

• Offensive Philosophy: Some coordinators believe in establishing the run to set up play action and control clock. Others believe in attacking through the air to maximize efficiency.

• Game Script Effects: Teams that frequently play with leads run more to protect those leads and drain clock. Teams that trail frequently are forced to pass more.

• Defensive Opponent Strength: A team facing strong run defenses all season might pass more by necessity.

When we examine the EPA metrics alongside pass rate, we often find an intriguing pattern: passing is more efficient (higher EPA) than running for nearly every team, yet most teams run the ball 40-45% of the time. This apparent paradox—why don't teams always use the more efficient play type?—is central to understanding play-calling strategy and will be explored in depth later in this chapter.

Situational Tendencies

Play-calling tendencies vary dramatically by situation. Let's examine tendencies across down and distance:

While overall team pass rates provide a useful baseline, they mask enormous situational variation. A team might pass 55% of the time overall, but that could mean passing 45% on first down, 50% on second-and-short, and 85% on third-and-long. Understanding these situational tendencies is crucial for both offensive and defensive strategy.

Down and distance create the fundamental strategic structure of football. First down offers maximum flexibility—nearly any play type can work. Second down's optimal strategy depends heavily on first-down results: after a successful first-down play, teams have flexibility; after a failed first-down play, teams face pressure. Third down becomes increasingly pass-heavy as distance increases, with third-and-long situations approaching 90% pass rate.

These tendencies aren't arbitrary—they reflect the constraints and opportunities each situation presents. On third-and-15, running the ball rarely converts the first down, so teams pass despite the predictability. On third-and-1, defenses know teams might run, but stopping a power running play is still difficult. The key question is whether teams deviate from optimal strategy due to excessive predictability. Let's measure these patterns:

#| label: situational-tendencies-r
#| message: false
#| warning: false

# Calculate tendencies by down and distance categories
situational_tendencies <- pbp_2023 %>%
  filter(
    !is.na(down),
    down <= 3,
    play_type %in% c("run", "pass")
  ) %>%
  mutate(
    distance_category = case_when(
      ydstogo <= 3 ~ "Short (1-3)",
      ydstogo <= 7 ~ "Medium (4-7)",
      ydstogo <= 10 ~ "Long (8-10)",
      TRUE ~ "Very Long (11+)"
    ),
    distance_category = factor(
      distance_category,
      levels = c("Short (1-3)", "Medium (4-7)", "Long (8-10)", "Very Long (11+)")
    )
  ) %>%
  group_by(down, distance_category) %>%
  summarise(
    plays = n(),
    pass_rate = mean(play_type == "pass"),
    avg_epa = mean(epa, na.rm = TRUE),
    success_rate = mean(epa > 0, na.rm = TRUE),
    .groups = "drop"
  )

# Display as table
situational_tendencies %>%
  gt() %>%
  cols_label(
    down = "Down",
    distance_category = "Distance",
    plays = "Plays",
    pass_rate = "Pass Rate",
    avg_epa = "Avg EPA",
    success_rate = "Success Rate"
  ) %>%
  fmt_number(
    columns = c(pass_rate, avg_epa, success_rate),
    decimals = 3
  ) %>%
  fmt_number(
    columns = plays,
    decimals = 0,
    use_seps = TRUE
  ) %>%
  data_color(
    columns = pass_rate,
    colors = scales::col_numeric(
      palette = c("#F8766D", "#FFFFFF", "#00BFC4"),
      domain = c(0, 1)
    )
  ) %>%
  tab_header(
    title = "Play-Calling Tendencies by Down and Distance",
    subtitle = "2023 NFL Regular Season"
  )

#| label: situational-tendencies-py
#| message: false
#| warning: false

# Calculate tendencies by down and distance categories
def categorize_distance(yards):
    if yards <= 3:
        return "Short (1-3)"
    elif yards <= 7:
        return "Medium (4-7)"
    elif yards <= 10:
        return "Long (8-10)"
    else:
        return "Very Long (11+)"

situational_tendencies = (pbp_2023
    .query("down.notna() & down <= 3 & play_type.isin(['run', 'pass'])")
    .assign(distance_category=lambda x: x['ydstogo'].apply(categorize_distance))
    .groupby(['down', 'distance_category'])
    .agg(
        plays=('play_type', 'count'),
        pass_rate=('play_type', lambda x: (x == 'pass').mean()),
        avg_epa=('epa', 'mean'),
        success_rate=('epa', lambda x: (x > 0).mean())
    )
    .reset_index()
)

# Sort by down and distance order
distance_order = ["Short (1-3)", "Medium (4-7)", "Long (8-10)", "Very Long (11+)"]
situational_tendencies['distance_category'] = pd.Categorical(
    situational_tendencies['distance_category'],
    categories=distance_order,
    ordered=True
)
situational_tendencies = situational_tendencies.sort_values(['down', 'distance_category'])

print("\nPlay-Calling Tendencies by Down and Distance")
print("=" * 80)
print(situational_tendencies.to_string(index=False))

The heat map visualization makes these patterns immediately clear. On first down, pass rates stay relatively balanced across all distances (45-55%). On second down, we see the bifurcation between second-and-short (more balanced, 50-60% pass) and second-and-long (heavy pass, 70-80%). Third down shows the most dramatic gradient, with third-and-short maintaining some run-pass balance (40-50% pass) while third-and-long becomes almost exclusively pass-oriented (85-95%).

What's particularly interesting is identifying the "inflection points" where tendencies shift dramatically. Around 7 yards to go, pass rate jumps significantly—this represents the threshold where teams lose confidence in their ability to convert with a run. On third down, this inflection occurs around 3-4 yards; on second down, it's closer to 7-8 yards. These inflection points represent strategic boundaries that coordinators and defenses both recognize and exploit.

Visualizing Play-Calling Patterns

Heat maps are excellent for visualizing play-calling tendencies across multiple dimensions:

#| label: fig-tendency-heatmap-r
#| fig-cap: "Play-calling heat map by down and distance"
#| fig-width: 10
#| fig-height: 6
#| message: false
#| warning: false

# Create detailed down/distance grid
heatmap_data <- pbp_2023 %>%
  filter(
    !is.na(down),
    down <= 3,
    ydstogo <= 20,
    play_type %in% c("run", "pass")
  ) %>%
  group_by(down, ydstogo) %>%
  summarise(
    plays = n(),
    pass_rate = mean(play_type == "pass"),
    .groups = "drop"
  ) %>%
  filter(plays >= 100)  # Minimum sample size

# Create heat map
ggplot(heatmap_data, aes(x = ydstogo, y = factor(down), fill = pass_rate)) +
  geom_tile(color = "white", linewidth = 0.5) +
  geom_text(aes(label = sprintf("%.0f%%", pass_rate * 100)),
            color = "white", size = 3, fontface = "bold") +
  scale_fill_gradient2(
    low = "#D55E00",
    mid = "#F0E442",
    high = "#0072B2",
    midpoint = 0.5,
    limits = c(0, 1),
    labels = scales::percent
  ) +
  scale_x_continuous(breaks = seq(0, 20, 2)) +
  scale_y_discrete(labels = c("1st", "2nd", "3rd")) +
  labs(
    title = "NFL Play-Calling Tendencies Heat Map",
    subtitle = "Pass rate by down and yards to go (2023 season)",
    x = "Yards to Go",
    y = "Down",
    fill = "Pass Rate",
    caption = "Data: nflfastR | Minimum 100 plays per cell"
  ) +
  theme_minimal() +
  theme(
    plot.title = element_text(face = "bold", size = 14),
    plot.subtitle = element_text(size = 11),
    legend.position = "right",
    panel.grid = element_blank()
  )

#| label: fig-tendency-heatmap-py
#| fig-cap: "Play-calling heat map by down and distance - Python"
#| fig-width: 10
#| fig-height: 6
#| message: false
#| warning: false

# Create detailed down/distance grid
heatmap_data = (pbp_2023
    .query("down.notna() & down <= 3 & ydstogo <= 20 & play_type.isin(['run', 'pass'])")
    .groupby(['down', 'ydstogo'])
    .agg(
        plays=('play_type', 'count'),
        pass_rate=('play_type', lambda x: (x == 'pass').mean())
    )
    .reset_index()
    .query("plays >= 100")  # Minimum sample size
)

# Pivot for heatmap
heatmap_pivot = heatmap_data.pivot(index='down', columns='ydstogo', values='pass_rate')

# Create heat map
plt.figure(figsize=(12, 6))
sns.heatmap(
    heatmap_pivot,
    cmap='RdYlBu',
    center=0.5,
    vmin=0,
    vmax=1,
    annot=True,
    fmt='.0%',
    cbar_kws={'label': 'Pass Rate'},
    linewidths=0.5,
    linecolor='white'
)

plt.xlabel('Yards to Go', fontsize=12)
plt.ylabel('Down', fontsize=12)
plt.title('NFL Play-Calling Tendencies Heat Map\nPass rate by down and yards to go (2023 season)',
          fontsize=14, fontweight='bold', pad=20)
plt.yticks(ticks=[0.5, 1.5, 2.5], labels=['1st', '2nd', '3rd'], rotation=0)
plt.tight_layout()
plt.show()

Run-Pass Balance Optimization

The Efficiency Paradox

One of the most robust findings in football analytics is that passing is generally more efficient than rushing:

#| label: efficiency-comparison-r
#| message: false
#| warning: false

# Compare efficiency by play type
efficiency_comparison <- pbp_2023 %>%
  filter(
    !is.na(epa),
    play_type %in% c("run", "pass"),
    down <= 3
  ) %>%
  group_by(play_type) %>%
  summarise(
    plays = n(),
    mean_epa = mean(epa),
    median_epa = median(epa),
    success_rate = mean(epa > 0),
    explosive_rate = mean(epa > 1.5),
    .groups = "drop"
  )

efficiency_comparison %>%
  gt() %>%
  cols_label(
    play_type = "Play Type",
    plays = "Plays",
    mean_epa = "Mean EPA",
    median_epa = "Median EPA",
    success_rate = "Success Rate",
    explosive_rate = "Explosive Rate"
  ) %>%
  fmt_number(
    columns = c(mean_epa, median_epa, success_rate, explosive_rate),
    decimals = 3
  ) %>%
  fmt_number(
    columns = plays,
    decimals = 0,
    use_seps = TRUE
  ) %>%
  tab_header(
    title = "Pass vs Run Efficiency",
    subtitle = "Overall EPA comparison (2023 season)"
  )

#| label: efficiency-comparison-py
#| message: false
#| warning: false

# Compare efficiency by play type
efficiency_comparison = (pbp_2023
    .query("epa.notna() & play_type.isin(['run', 'pass']) & down <= 3")
    .groupby('play_type')
    .agg(
        plays=('epa', 'count'),
        mean_epa=('epa', 'mean'),
        median_epa=('epa', 'median'),
        success_rate=('epa', lambda x: (x > 0).mean()),
        explosive_rate=('epa', lambda x: (x > 1.5).mean())
    )
    .reset_index()
)

print("\nPass vs Run Efficiency (2023 season)")
print("=" * 70)
print(efficiency_comparison.to_string(index=False))

Despite passing being more efficient, teams typically run the ball 40-45% of the time. Why? Several factors explain this apparent paradox:

1. Clock Management: Running plays keep the clock moving
2. Ball Security: Interceptions are costly negative plays
3. Defensive Adjustment: Heavy passing invites pass rush and coverage adjustments
4. Personnel Fatigue: Pass protection is physically demanding
5. Game Theory: Some unpredictability in play-calling is valuable

This efficiency paradox also reveals something important about play-calling evaluation: we cannot simply maximize EPA on every individual play. The run game serves strategic purposes beyond immediate efficiency—it creates play-action opportunities, controls tempo, manages clock, and keeps defensive fronts honest. A team that abandons the run might see short-term EPA gains but long-term strategic losses as defenses optimize purely for pass defense.

Optimal Balance by Game Script

The optimal run-pass balance depends on game situation:

#| label: script-analysis-r
#| message: false
#| warning: false

# Analyze efficiency by score differential
script_analysis <- pbp_2023 %>%
  filter(
    !is.na(epa),
    !is.na(score_differential),
    play_type %in% c("run", "pass"),
    down <= 3
  ) %>%
  mutate(
    script = case_when(
      score_differential <= -10 ~ "Losing big (10+)",
      score_differential <= -4 ~ "Losing (4-9)",
      score_differential <= 3 ~ "Close game",
      score_differential <= 9 ~ "Winning (4-9)",
      TRUE ~ "Winning big (10+)"
    ),
    script = factor(
      script,
      levels = c("Losing big (10+)", "Losing (4-9)", "Close game",
                 "Winning (4-9)", "Winning big (10+)")
    )
  ) %>%
  group_by(script, play_type) %>%
  summarise(
    plays = n(),
    mean_epa = mean(epa),
    success_rate = mean(epa > 0),
    .groups = "drop"
  ) %>%
  arrange(script, desc(play_type))

# Display results
script_analysis %>%
  gt() %>%
  cols_label(
    script = "Game Script",
    play_type = "Play Type",
    plays = "Plays",
    mean_epa = "Mean EPA",
    success_rate = "Success Rate"
  ) %>%
  fmt_number(
    columns = c(mean_epa, success_rate),
    decimals = 3
  ) %>%
  fmt_number(
    columns = plays,
    decimals = 0,
    use_seps = TRUE
  ) %>%
  tab_header(
    title = "Play-Calling Efficiency by Game Script",
    subtitle = "EPA analysis by score differential (2023)"
  )

#| label: script-analysis-py
#| message: false
#| warning: false

# Analyze efficiency by score differential
def categorize_script(diff):
    if diff <= -10:
        return "Losing big (10+)"
    elif diff <= -4:
        return "Losing (4-9)"
    elif diff <= 3:
        return "Close game"
    elif diff <= 9:
        return "Winning (4-9)"
    else:
        return "Winning big (10+)"

script_analysis = (pbp_2023
    .query("epa.notna() & score_differential.notna() & play_type.isin(['run', 'pass']) & down <= 3")
    .assign(script=lambda x: x['score_differential'].apply(categorize_script))
    .groupby(['script', 'play_type'])
    .agg(
        plays=('epa', 'count'),
        mean_epa=('epa', 'mean'),
        success_rate=('epa', lambda x: (x > 0).mean())
    )
    .reset_index()
)

# Sort by script order
script_order = ["Losing big (10+)", "Losing (4-9)", "Close game", "Winning (4-9)", "Winning big (10+)"]
script_analysis['script'] = pd.Categorical(
    script_analysis['script'],
    categories=script_order,
    ordered=True
)
script_analysis = script_analysis.sort_values(['script', 'play_type'], ascending=[True, False])

print("\nPlay-Calling Efficiency by Game Script (2023)")
print("=" * 70)
print(script_analysis.to_string(index=False))

Play Action Effectiveness

Play action passes—where the quarterback fakes a handoff before passing—are designed to exploit defensive reactions to run tendencies:

#| label: play-action-analysis-r
#| message: false
#| warning: false

# Analyze play action effectiveness
play_action_analysis <- pbp_2023 %>%
  filter(
    play_type == "pass",
    !is.na(epa),
    !is.na(pass_length),
    down <= 3
  ) %>%
  mutate(
    play_action = if_else(is.na(play_action), 0, play_action)
  ) %>%
  group_by(play_action, pass_length) %>%
  summarise(
    plays = n(),
    mean_epa = mean(epa),
    success_rate = mean(epa > 0),
    completion_pct = mean(complete_pass, na.rm = TRUE),
    yards_per_attempt = mean(yards_gained, na.rm = TRUE),
    .groups = "drop"
  ) %>%
  mutate(
    play_action = if_else(play_action == 1, "Play Action", "Standard")
  )

# Display results
play_action_analysis %>%
  gt() %>%
  cols_label(
    play_action = "Pass Type",
    pass_length = "Depth",
    plays = "Plays",
    mean_epa = "Mean EPA",
    success_rate = "Success Rate",
    completion_pct = "Comp %",
    yards_per_attempt = "YPA"
  ) %>%
  fmt_number(
    columns = c(mean_epa, success_rate, completion_pct),
    decimals = 3
  ) %>%
  fmt_number(
    columns = yards_per_attempt,
    decimals = 1
  ) %>%
  fmt_number(
    columns = plays,
    decimals = 0,
    use_seps = TRUE
  ) %>%
  tab_header(
    title = "Play Action vs Standard Pass Efficiency",
    subtitle = "Comparison by pass depth (2023)"
  )

#| label: play-action-analysis-py
#| message: false
#| warning: false

# Analyze play action effectiveness
play_action_analysis = (pbp_2023
    .query("play_type == 'pass' & epa.notna() & pass_length.notna() & down <= 3")
    .assign(play_action=lambda x: x['play_action'].fillna(0))
    .groupby(['play_action', 'pass_length'])
    .agg(
        plays=('epa', 'count'),
        mean_epa=('epa', 'mean'),
        success_rate=('epa', lambda x: (x > 0).mean()),
        completion_pct=('complete_pass', 'mean'),
        yards_per_attempt=('yards_gained', 'mean')
    )
    .reset_index()
    .assign(play_action=lambda x: x['play_action'].map({1: "Play Action", 0: "Standard"}))
)

print("\nPlay Action vs Standard Pass Efficiency (2023)")
print("=" * 80)
print(play_action_analysis.to_string(index=False))

Visualizing Play Action Impact

#| label: fig-play-action-r
#| fig-cap: "Play action pass effectiveness comparison"
#| fig-width: 10
#| fig-height: 6
#| message: false
#| warning: false

# Prepare data for visualization
pa_viz_data <- pbp_2023 %>%
  filter(
    play_type == "pass",
    !is.na(epa),
    down <= 3
  ) %>%
  mutate(
    play_action = if_else(is.na(play_action), 0, play_action),
    play_action_label = if_else(play_action == 1, "Play Action", "Standard Pass")
  )

# Create comparison plot
ggplot(pa_viz_data, aes(x = epa, fill = play_action_label)) +
  geom_density(alpha = 0.6) +
  geom_vline(xintercept = 0, linetype = "dashed", color = "black") +
  scale_fill_manual(
    values = c("Play Action" = "#00BA38", "Standard Pass" = "#619CFF")
  ) +
  scale_x_continuous(limits = c(-5, 10)) +
  labs(
    title = "Play Action Pass EPA Distribution",
    subtitle = "Comparing play action to standard dropback passes (2023)",
    x = "Expected Points Added",
    y = "Density",
    fill = "Pass Type",
    caption = "Data: nflfastR"
  ) +
  theme_minimal() +
  theme(
    plot.title = element_text(face = "bold", size = 14),
    plot.subtitle = element_text(size = 11),
    legend.position = "top"
  )

#| label: fig-play-action-py
#| fig-cap: "Play action pass effectiveness comparison - Python"
#| fig-width: 10
#| fig-height: 6
#| message: false
#| warning: false

# Prepare data for visualization
pa_viz_data = (pbp_2023
    .query("play_type == 'pass' & epa.notna() & down <= 3")
    .assign(
        play_action=lambda x: x['play_action'].fillna(0),
        play_action_label=lambda x: x['play_action'].map({1: "Play Action", 0: "Standard Pass"})
    )
)

# Create comparison plot
plt.figure(figsize=(10, 6))

for label, color in [('Play Action', '#00BA38'), ('Standard Pass', '#619CFF')]:
    data = pa_viz_data[pa_viz_data['play_action_label'] == label]['epa']
    data = data[(data >= -5) & (data <= 10)]
    plt.hist(data, bins=50, alpha=0.6, label=label, color=color, density=True)

plt.axvline(x=0, color='black', linestyle='--', alpha=0.7)
plt.xlabel('Expected Points Added', fontsize=12)
plt.ylabel('Density', fontsize=12)
plt.title('Play Action Pass EPA Distribution\nComparing play action to standard dropback passes (2023)',
          fontsize=14, fontweight='bold')
plt.legend(title='Pass Type', loc='upper right')
plt.xlim(-5, 10)
plt.text(0.98, 0.02, 'Data: nfl_data_py',
         transform=plt.gca().transAxes,
         ha='right', fontsize=8, style='italic')
plt.tight_layout()
plt.show()

The distribution chart clearly shows play action's advantage—the entire EPA distribution shifts right. Not only is the mean EPA higher for play action, but the tail of explosive plays (EPA > 2.0) is thicker as well. This occurs because play action manipulates defensive flow and creates coverage conflicts. Linebackers step toward the line of scrimmage to stop the fake run, creating space underneath. Safeties hesitate before rotating into coverage, allowing receivers to get behind them.

Interestingly, recent research suggests that play action effectiveness doesn't actually correlate strongly with run game success. Teams with poor rushing attacks still benefit significantly from play action, as long as they use it consistently enough that defenses must respect the fake. This finding challenges conventional wisdom—you don't need to "establish the run" to make play action work; you just need to threaten it credibly.

Personnel Groupings and Play-Calling

Personnel groupings significantly influence play-calling tendencies and effectiveness:

#| label: personnel-analysis-r
#| message: false
#| warning: false

# Analyze play-calling by personnel grouping
personnel_analysis <- pbp_2023 %>%
  filter(
    !is.na(personnel_o),
    !is.na(epa),
    play_type %in% c("run", "pass"),
    down <= 3
  ) %>%
  # Focus on common personnel groupings
  filter(personnel_o %in% c("1 RB, 1 TE, 3 WR", "1 RB, 2 TE, 2 WR",
                             "2 RB, 1 TE, 2 WR", "1 RB, 0 TE, 4 WR")) %>%
  group_by(personnel_o, play_type) %>%
  summarise(
    plays = n(),
    mean_epa = mean(epa),
    success_rate = mean(epa > 0),
    .groups = "drop"
  ) %>%
  arrange(personnel_o, desc(play_type))

# Calculate pass rate by personnel
personnel_pass_rate <- pbp_2023 %>%
  filter(
    !is.na(personnel_o),
    play_type %in% c("run", "pass"),
    down <= 3
  ) %>%
  filter(personnel_o %in% c("1 RB, 1 TE, 3 WR", "1 RB, 2 TE, 2 WR",
                             "2 RB, 1 TE, 2 WR", "1 RB, 0 TE, 4 WR")) %>%
  group_by(personnel_o) %>%
  summarise(
    total_plays = n(),
    pass_rate = mean(play_type == "pass"),
    .groups = "drop"
  )

# Display results
personnel_analysis %>%
  left_join(personnel_pass_rate, by = "personnel_o") %>%
  select(personnel_o, play_type, plays, mean_epa, success_rate, pass_rate) %>%
  gt() %>%
  cols_label(
    personnel_o = "Personnel",
    play_type = "Play Type",
    plays = "Plays",
    mean_epa = "Mean EPA",
    success_rate = "Success Rate",
    pass_rate = "Overall Pass Rate"
  ) %>%
  fmt_number(
    columns = c(mean_epa, success_rate, pass_rate),
    decimals = 3
  ) %>%
  fmt_number(
    columns = plays,
    decimals = 0,
    use_seps = TRUE
  ) %>%
  tab_header(
    title = "Play-Calling by Personnel Grouping",
    subtitle = "Common offensive personnel packages (2023)"
  )

#| label: personnel-analysis-py
#| message: false
#| warning: false

# Analyze play-calling by personnel grouping
common_personnel = ["1 RB, 1 TE, 3 WR", "1 RB, 2 TE, 2 WR",
                    "2 RB, 1 TE, 2 WR", "1 RB, 0 TE, 4 WR"]

personnel_analysis = (pbp_2023
    .query("personnel_o.notna() & epa.notna() & play_type.isin(['run', 'pass']) & down <= 3")
    .query("personnel_o in @common_personnel")
    .groupby(['personnel_o', 'play_type'])
    .agg(
        plays=('epa', 'count'),
        mean_epa=('epa', 'mean'),
        success_rate=('epa', lambda x: (x > 0).mean())
    )
    .reset_index()
)

# Calculate pass rate by personnel
personnel_pass_rate = (pbp_2023
    .query("personnel_o.notna() & play_type.isin(['run', 'pass']) & down <= 3")
    .query("personnel_o in @common_personnel")
    .groupby('personnel_o')
    .agg(
        total_plays=('play_type', 'count'),
        pass_rate=('play_type', lambda x: (x == 'pass').mean())
    )
    .reset_index()
)

# Merge and display
personnel_combined = personnel_analysis.merge(personnel_pass_rate, on='personnel_o')

print("\nPlay-Calling by Personnel Grouping (2023)")
print("=" * 90)
print(personnel_combined.to_string(index=False))

Understanding Personnel Grouping Nomenclature

Personnel groupings in football are described using a two-digit system that indicates the number of running backs and tight ends on the field. The first digit represents running backs, the second represents tight ends, and the remaining players (up to 11 total) are wide receivers. Understanding this system is crucial for analyzing play-calling patterns because personnel groupings create strong signals about offensive intent.

Common Personnel Groupings:

• 11 Personnel (1 RB, 1 TE, 3 WR): The most common grouping in modern NFL offenses, accounting for 60-70% of plays for pass-heavy teams. This "spread" formation prioritizes speed and space, making it easier to pass but still allowing for zone-running schemes. Teams average 65-70% pass rate from this grouping.

• 12 Personnel (1 RB, 2 TE, 2 WR): A more balanced grouping that suggests either run or play-action pass. The second tight end can serve as an extra blocker for runs, a receiver on passes, or a play-action decoy. Teams typically pass 55-60% from this grouping, making it less predictable.

• 21 Personnel (2 RB, 1 TE, 2 WR): Increasingly rare in modern NFL play, this heavier grouping strongly signals run intent. Teams pass only 30-40% from 21 personnel, making it highly predictable. Some teams use it specifically to exploit this expectation with play-action.

• 13 Personnel (1 RB, 3 TE, 1 WR): An extreme "heavy" grouping used primarily in short-yardage and goal-line situations. Pass rate from 13 personnel is typically below 20%, but the passes thrown are often highly effective because defenses load the box expecting run.

• 10 Personnel (1 RB, 0 TE, 4 WR): The ultimate spread formation, used by aggressive passing offenses in obvious passing situations. Teams pass 85-90% from this grouping. Some innovative offenses run successfully from 10 personnel precisely because defenses expect pass.

The strategic challenge for offensive coordinators is balancing the matchup advantages of specific personnel groupings against the predictability they create. Using 11 personnel on every play maximizes flexibility and creates favorable matchups for the passing game, but it also signals to defenses that a pass is likely coming. Conversely, shifting to 12 or 21 personnel telegraphs run intent, allowing defenses to adjust their fronts and add defenders to the box.

Advanced offenses address this problem in several ways. First, they develop robust running games from spread personnel (11 personnel), maintaining enough run threat to keep defenses honest. Second, they use personnel groupings that maintain optionality—12 personnel, for instance, can effectively run or pass. Third, they strategically "go against" tendencies, running from 10 personnel or passing from 13 personnel, to exploit defensive over-adjustment.

Down and Distance Tendencies

Understanding down-and-distance tendencies is crucial for both play-calling and defensive game planning. Down and distance create the fundamental strategic framework for every offensive play call. Each combination of down and yards-to-go presents different constraints, opportunities, and risk-reward trade-offs.

First down offers maximum optionality—with three downs to gain ten yards, offenses can pursue various strategies. They might establish the run, test the defense with a deep shot, or use play action to create big plays. The key strategic question on first down is efficiency versus explosiveness: do you prioritize staying ahead of the chains with a high-probability short gain, or do you attack downfield to maximize EPA?

Second down's strategic landscape depends entirely on first-down results. After a successful first-down play (gaining 4+ yards), second down remains relatively open, with both run and pass viable. After a failed first-down play (gaining 0-3 yards), second down becomes critical—the offense faces pressure to avoid third-and-long, while the defense knows the offense is somewhat predictable. Second-and-long situations (8+ yards) see teams pass 70-80% of the time as they try to get back on track.

Third down represents the most critical play-calling situation in football. The distance required to convert the first down overwhelmingly determines play selection. On third-and-short (1-3 yards), teams maintain balance, running 40-50% of the time. On third-and-medium (4-6 yards), pass rate climbs to 75-80%. On third-and-long (7+ yards), teams pass 85-95% of the time. This predictability creates a strategic dilemma: passing is the correct decision given the distance required, but the predictability allows defenses to optimize their coverage schemes and pass rush.

The following analysis examines these patterns in detail, measuring not just tendency but also efficiency. We'll identify which situations create the largest gaps between run and pass efficiency, revealing where conventional play-calling wisdom might leave expected points on the table:

#| label: down-distance-detail-r
#| message: false
#| warning: false

# Detailed analysis of key down-distance situations
key_situations <- pbp_2023 %>%
  filter(
    !is.na(down),
    play_type %in% c("run", "pass"),
    down <= 3
  ) %>%
  mutate(
    situation = case_when(
      down == 1 & ydstogo == 10 ~ "1st & 10",
      down == 2 & ydstogo >= 8 ~ "2nd & Long (8+)",
      down == 2 & ydstogo >= 4 & ydstogo <= 7 ~ "2nd & Medium (4-7)",
      down == 2 & ydstogo <= 3 ~ "2nd & Short (1-3)",
      down == 3 & ydstogo >= 7 ~ "3rd & Long (7+)",
      down == 3 & ydstogo >= 4 & ydstogo <= 6 ~ "3rd & Medium (4-6)",
      down == 3 & ydstogo <= 3 ~ "3rd & Short (1-3)",
      TRUE ~ "Other"
    )
  ) %>%
  filter(situation != "Other") %>%
  group_by(situation) %>%
  summarise(
    plays = n(),
    pass_rate = mean(play_type == "pass"),
    run_epa = mean(epa[play_type == "run"], na.rm = TRUE),
    pass_epa = mean(epa[play_type == "pass"], na.rm = TRUE),
    run_success = mean(epa[play_type == "run"] > 0, na.rm = TRUE),
    pass_success = mean(epa[play_type == "pass"] > 0, na.rm = TRUE),
    .groups = "drop"
  ) %>%
  mutate(
    epa_advantage = pass_epa - run_epa,
    success_advantage = pass_success - run_success
  )

# Display results
key_situations %>%
  gt() %>%
  cols_label(
    situation = "Situation",
    plays = "Plays",
    pass_rate = "Pass Rate",
    run_epa = "Run EPA",
    pass_epa = "Pass EPA",
    run_success = "Run Success",
    pass_success = "Pass Success",
    epa_advantage = "EPA Adv.",
    success_advantage = "Success Adv."
  ) %>%
  fmt_number(
    columns = c(pass_rate, run_epa, pass_epa, run_success,
                pass_success, epa_advantage, success_advantage),
    decimals = 3
  ) %>%
  fmt_number(
    columns = plays,
    decimals = 0,
    use_seps = TRUE
  ) %>%
  data_color(
    columns = epa_advantage,
    colors = scales::col_numeric(
      palette = c("#D55E00", "#FFFFFF", "#0072B2"),
      domain = c(-0.5, 0.5)
    )
  ) %>%
  tab_header(
    title = "Play-Calling Analysis by Key Situations",
    subtitle = "Pass vs Run efficiency (2023)"
  )

#| label: down-distance-detail-py
#| message: false
#| warning: false

# Detailed analysis of key down-distance situations
def categorize_situation(row):
    down = row['down']
    ydstogo = row['ydstogo']

    if down == 1 and ydstogo == 10:
        return "1st & 10"
    elif down == 2 and ydstogo >= 8:
        return "2nd & Long (8+)"
    elif down == 2 and 4 <= ydstogo <= 7:
        return "2nd & Medium (4-7)"
    elif down == 2 and ydstogo <= 3:
        return "2nd & Short (1-3)"
    elif down == 3 and ydstogo >= 7:
        return "3rd & Long (7+)"
    elif down == 3 and 4 <= ydstogo <= 6:
        return "3rd & Medium (4-6)"
    elif down == 3 and ydstogo <= 3:
        return "3rd & Short (1-3)"
    else:
        return "Other"

key_situations_data = (pbp_2023
    .query("down.notna() & play_type.isin(['run', 'pass']) & down <= 3")
    .assign(situation=lambda x: x.apply(categorize_situation, axis=1))
    .query("situation != 'Other'")
)

# Calculate metrics by situation and play type
run_stats = (key_situations_data
    .query("play_type == 'run'")
    .groupby('situation')
    .agg(
        run_plays=('epa', 'count'),
        run_epa=('epa', 'mean'),
        run_success=('epa', lambda x: (x > 0).mean())
    )
)

pass_stats = (key_situations_data
    .query("play_type == 'pass'")
    .groupby('situation')
    .agg(
        pass_plays=('epa', 'count'),
        pass_epa=('epa', 'mean'),
        pass_success=('epa', lambda x: (x > 0).mean())
    )
)

overall_stats = (key_situations_data
    .groupby('situation')
    .agg(
        plays=('play_type', 'count'),
        pass_rate=('play_type', lambda x: (x == 'pass').mean())
    )
)

# Combine all statistics
key_situations = (overall_stats
    .join(run_stats)
    .join(pass_stats)
    .assign(
        epa_advantage=lambda x: x['pass_epa'] - x['run_epa'],
        success_advantage=lambda x: x['pass_success'] - x['run_success']
    )
    .reset_index()
)

print("\nPlay-Calling Analysis by Key Situations (2023)")
print("=" * 100)
print(key_situations.to_string(index=False))

Formation Analysis and Play-Calling

The Strategic Role of Formations

While personnel groupings determine which players are on the field, formations determine where those players line up. Formation analysis provides another layer of insight into play-calling tendencies and effectiveness. Certain formations strongly correlate with specific play types, creating additional signals that defenses can read and exploit.

Modern offenses use formations strategically in several ways. First, formations can create structural advantages—bunching receivers on one side creates natural pick routes, while spreading them out creates isolation matchups. Second, formations can create information advantages or disadvantages—some formations maintain run-pass balance while others telegraph intent. Third, formations interact with personnel groupings to create the overall offensive picture that defenses must process pre-snap.

The shotgun formation has become dominant in modern NFL play-calling. In shotgun, the quarterback stands 5-7 yards behind the center at the snap, providing better vision of the defense and more time to throw. Historically considered a passing formation, modern zone-running schemes have made the shotgun viable for running as well. Today, teams run from shotgun on 70-80% of all plays, fundamentally changing the strategic landscape of play-calling.

Under center formations, where the quarterback takes the snap directly from the center, now signal specific intentions. Teams go under center primarily for power running plays, particularly in short-yardage situations, or for play-action passes designed to exploit aggressive run defenses. The act of going under center itself creates a tendency—teams run approximately 55-60% of the time when under center, compared to passing 65-70% from shotgun.

Specific shotgun variations create additional strategic dimensions. Empty formations (all five eligible receivers split out, no one in the backfield) almost always indicate pass—95%+ pass rate. Trips formations (three receivers to one side) are used for both run and pass but create specific defensive challenges in coverage. Bunch formations (receivers aligned close together) are primarily used for passing, creating natural pick routes and confusion in man coverage.

Measuring Formation Tendencies

Let's analyze play-calling tendencies and efficiency across different formation types. We'll focus on the key distinction between shotgun and under center, as well as examining specific formations like empty and trips:

#| label: formation-analysis-r
#| message: false
#| warning: false

# Analyze play-calling tendencies by formation type
# This reveals how formations signal offensive intent and effectiveness

formation_analysis <- pbp_2023 %>%
  filter(
    !is.na(shotgun),           # Must have formation data
    !is.na(epa),               # Must have EPA calculated
    play_type %in% c("run", "pass"),  # Only offensive plays
    down <= 3                  # Exclude 4th down (special situations)
  ) %>%
  # Create formation categories based on shotgun status
  mutate(
    formation_type = if_else(shotgun == 1, "Shotgun", "Under Center")
  ) %>%
  # Calculate statistics by formation and play type
  group_by(formation_type, play_type) %>%
  summarise(
    plays = n(),                           # Total plays from this formation-play combo
    mean_epa = mean(epa),                  # Average EPA (efficiency)
    success_rate = mean(epa > 0),          # Success rate (% positive EPA)
    explosive_rate = mean(epa > 1.5),      # Big play rate (explosive plays)
    yards_per_play = mean(yards_gained, na.rm = TRUE),  # Average yards gained
    .groups = "drop"
  )

# Calculate overall pass rate by formation
formation_rates <- pbp_2023 %>%
  filter(
    !is.na(shotgun),
    play_type %in% c("run", "pass"),
    down <= 3
  ) %>%
  mutate(formation_type = if_else(shotgun == 1, "Shotgun", "Under Center")) %>%
  group_by(formation_type) %>%
  summarise(
    total_plays = n(),
    pass_rate = mean(play_type == "pass"),
    .groups = "drop"
  )

# Combine and display
formation_analysis %>%
  left_join(formation_rates, by = "formation_type") %>%
  select(formation_type, play_type, plays, pass_rate,
         mean_epa, success_rate, explosive_rate) %>%
  gt() %>%
  cols_label(
    formation_type = "Formation",
    play_type = "Play Type",
    plays = "Plays",
    pass_rate = "Overall Pass Rate",
    mean_epa = "EPA/Play",
    success_rate = "Success %",
    explosive_rate = "Explosive %"
  ) %>%
  fmt_number(
    columns = c(pass_rate, mean_epa, success_rate, explosive_rate),
    decimals = 3
  ) %>%
  fmt_number(
    columns = plays,
    decimals = 0,
    use_seps = TRUE
  ) %>%
  data_color(
    columns = mean_epa,
    colors = scales::col_numeric(
      palette = c("#D55E00", "#FFFFFF", "#0072B2"),
      domain = c(-0.2, 0.3)
    )
  ) %>%
  tab_header(
    title = "Formation Analysis: Shotgun vs Under Center",
    subtitle = "Play-calling tendencies and efficiency by formation (2023)"
  )

#| label: formation-analysis-py
#| message: false
#| warning: false

# Analyze play-calling tendencies by formation type
formation_data = (pbp_2023
    .query("shotgun.notna() & epa.notna() & play_type.isin(['run', 'pass']) & down <= 3")
    .assign(formation_type=lambda x: x['shotgun'].map({1: "Shotgun", 0: "Under Center"}))
)

# Calculate statistics by formation and play type
formation_analysis = (formation_data
    .groupby(['formation_type', 'play_type'])
    .agg(
        plays=('epa', 'count'),                              # Total plays
        mean_epa=('epa', 'mean'),                            # Average EPA
        success_rate=('epa', lambda x: (x > 0).mean()),      # Success rate
        explosive_rate=('epa', lambda x: (x > 1.5).mean()),  # Big play rate
        yards_per_play=('yards_gained', 'mean')              # Average yards
    )
    .reset_index()
)

# Calculate overall pass rate by formation
formation_rates = (formation_data
    .groupby('formation_type')
    .agg(
        total_plays=('play_type', 'count'),
        pass_rate=('play_type', lambda x: (x == 'pass').mean())
    )
    .reset_index()
)

# Combine results
formation_combined = formation_analysis.merge(formation_rates, on='formation_type')

print("\nFormation Analysis: Shotgun vs Under Center (2023)")
print("=" * 100)
print(formation_combined[['formation_type', 'play_type', 'plays', 'pass_rate',
                          'mean_epa', 'success_rate', 'explosive_rate']].to_string(index=False))