Case Study 1: NFL Team Consistency — Which Teams Are Predictable?

Introduction

Not all NFL teams are created equal when it comes to predictability. Some franchises produce narrow, consistent results week after week: they beat weak opponents by modest margins and lose close games to strong ones. Others swing wildly between 40-point blowouts and embarrassing collapses. For a sports bettor, this distinction is not merely interesting; it is exploitable. Sportsbooks set point spreads based on expected performance, but the uncertainty around that expectation varies enormously from team to team. A team with a mean margin of +5.0 and a standard deviation of 8.0 presents a fundamentally different betting proposition than a team with the same mean margin but a standard deviation of 16.0. This case study uses descriptive statistics to quantify NFL team consistency, identify which franchises are most and least predictable, and extract actionable insights for point spread and totals betting.

Data and Methodology

We analyze 17-game seasons for eight NFL teams, examining points scored, points allowed, and point differential on a game-by-game basis. For each team, we calculate the following descriptive statistics:

• Central tendency: mean, median, and trimmed mean of point differential
• Variability: standard deviation, coefficient of variation, interquartile range, and range of point differential
• Distribution shape: skewness and kurtosis of scoring and point differential distributions
• Temporal patterns: rolling 4-game standard deviation to detect consistency changes within a season

The data used here is representative of real NFL patterns, constructed to reflect the typical variance structures observed in league-wide analysis.

Team Profiles

We select four "consistent" teams and four "volatile" teams based on their season-long coefficient of variation in point differential:

Consistent Teams:

Volatile Teams:

Analysis

Step 1: Central Tendency Comparison

import numpy as np
from scipy import stats

consistent_teams = {
    'Team A': [7, 3, 10, -2, 6, 1, 8, -4, 5, 9, 2, -1, 7, 4, 11, 3, 6],
    'Team B': [3, 6, -1, 5, 8, 2, 4, 7, -3, 6, 1, 5, 3, 8, -2, 4, 7],
    'Team C': [-2, 4, 7, 3, -5, 6, 1, 9, -3, 5, 8, -1, 4, 7, 2, 6, -4],
    'Team D': [5, 1, 8, -3, 6, 4, 7, -1, 3, 9, 2, 6, 5, -2, 8, 3, 4],
}

volatile_teams = {
    'Team E': [21, -10, 14, -17, 28, -3, 19, -14, 24, -7, 16, 3, -20, 25, -8, 12, 17],
    'Team F': [-14, 24, 1, -20, 15, -8, 28, -5, 17, -12, 21, -3, 10, -16, 22, 7, -11],
    'Team G': [3, -18, 25, -7, 30, -12, 16, -21, 8, 22, -15, 19, -24, 14, -9, 27, -5],
    'Team H': [28, -7, 17, -21, 10, -15, 24, 3, -18, 31, -9, 20, -14, 26, -3, 15, -12],
}

all_teams = {**consistent_teams, **volatile_teams}

print(f"{'Team':<10} {'Mean':>8} {'Median':>8} {'Trim Mean':>10}")
print("-" * 40)
for name, data in all_teams.items():
    mean = np.mean(data)
    median = np.median(data)
    trim_mean = stats.trim_mean(data, 0.1)
    print(f"{name:<10} {mean:>8.2f} {median:>8.1f} {trim_mean:>10.2f}")

Running this code produces the following summary:

Notice that Teams A and H have the same mean point differential (+4.41) but drastically different medians. For Team A, the mean and median are close, indicating symmetry. For Team H, the large gap between mean and median signals a skewed distribution with extreme values pulling the mean.

Step 2: Variability Analysis

print(f"{'Team':<10} {'SD':>8} {'CV':>8} {'IQR':>8} {'Range':>8}")
print("-" * 40)
for name, data in all_teams.items():
    sd = np.std(data, ddof=1)
    cv = sd / abs(np.mean(data)) if np.mean(data) != 0 else float('inf')
    q75, q25 = np.percentile(data, [75, 25])
    iqr = q75 - q25
    rng = max(data) - min(data)
    print(f"{name:<10} {sd:>8.2f} {cv:>8.2f} {iqr:>8.1f} {rng:>8}")

The contrast is stark. Consistent teams have standard deviations between 3 and 5 points, while volatile teams range from 15 to 18 points. The coefficient of variation tells the story even more clearly: consistent teams have CVs below 2.0, while volatile teams exceed 2.5 and often surpass 4.0.

The practical implication is immediate. If a sportsbook sets Team B as a 4-point favorite, roughly 68% of their actual margins will fall between +0.7 and +7.1 (one SD from the mean). For Team G at the same spread, the corresponding range is -14.7 to +21.1. The bet on Team B involves dramatically less uncertainty.

Step 3: Distribution Shape

print(f"{'Team':<10} {'Skewness':>10} {'Kurtosis':>10}")
print("-" * 34)
for name, data in all_teams.items():
    skew = stats.skew(data)
    kurt = stats.kurtosis(data)  # excess kurtosis
    print(f"{name:<10} {skew:>10.3f} {kurt:>10.3f}")

Consistent teams show near-zero skewness and mild platykurtosis (negative excess kurtosis), meaning their distributions are roughly symmetric with slightly thinner tails than normal. Volatile teams also show near-zero skewness but more pronounced platykurtosis, indicating a flatter distribution with more mass in the tails. This is the statistical signature of a team that produces extreme outcomes in both directions rather than clustering near the mean.

Step 4: Rolling Volatility

The season-long standard deviation masks temporal patterns. A team might be consistent for 10 games, then become volatile due to injuries, or vice versa.

import pandas as pd
import matplotlib.pyplot as plt

fig, axes = plt.subplots(2, 1, figsize=(14, 10))

# Plot consistent team rolling volatility
for name, data in consistent_teams.items():
    series = pd.Series(data)
    rolling_std = series.rolling(window=4).std()
    axes[0].plot(range(1, 18), rolling_std.values, marker='o',
                 markersize=4, label=name, linewidth=1.5)

axes[0].set_title('Rolling 4-Game Standard Deviation: Consistent Teams',
                   fontsize=14, fontweight='bold')
axes[0].set_xlabel('Game Number')
axes[0].set_ylabel('Rolling Std Dev')
axes[0].legend()
axes[0].set_ylim(0, 25)
axes[0].axhline(y=5, color='gray', linestyle='--', alpha=0.5,
                label='Consistency threshold')
axes[0].grid(True, alpha=0.3)

# Plot volatile team rolling volatility
for name, data in volatile_teams.items():
    series = pd.Series(data)
    rolling_std = series.rolling(window=4).std()
    axes[1].plot(range(1, 18), rolling_std.values, marker='o',
                 markersize=4, label=name, linewidth=1.5)

axes[1].set_title('Rolling 4-Game Standard Deviation: Volatile Teams',
                   fontsize=14, fontweight='bold')
axes[1].set_xlabel('Game Number')
axes[1].set_ylabel('Rolling Std Dev')
axes[1].legend()
axes[1].set_ylim(0, 35)
axes[1].axhline(y=5, color='gray', linestyle='--', alpha=0.5,
                label='Consistency threshold')
axes[1].grid(True, alpha=0.3)

plt.tight_layout()
plt.savefig('rolling_volatility_comparison.png', dpi=150, bbox_inches='tight')
plt.show()

The rolling volatility plot reveals that consistent teams maintain their low-variance behavior throughout the season, with their 4-game rolling standard deviation rarely exceeding 6-7 points. Volatile teams, by contrast, oscillate between periods of moderate and extreme variability, with rolling standard deviations that regularly exceed 20 points.

Step 5: Against-the-Spread (ATS) Implications

The central question for bettors is whether consistency translates to ATS profitability. We simulate spreads for each team based on their season averages and examine the resulting ATS margins.

np.random.seed(42)

def simulate_ats_analysis(team_name: str, differentials: list[int]) -> dict:
    """Analyze ATS performance assuming spreads based on team's
    running average adjusted for opponent strength."""
    n = len(differentials)
    # Simulate spreads as team's running mean with noise
    spreads = []
    for i in range(n):
        if i < 3:
            expected = np.mean(differentials[:max(i, 1)])
        else:
            expected = np.mean(differentials[max(0, i-5):i])
        spread = -(expected + np.random.normal(0, 2))
        spreads.append(round(spread * 2) / 2)  # Round to 0.5

    ats_margins = []
    covers = 0
    for i in range(n):
        ats_margin = differentials[i] + spreads[i]
        ats_margins.append(ats_margin)
        if ats_margin > 0:
            covers += 1

    return {
        'team': team_name,
        'ats_record': f"{covers}-{n - covers}",
        'cover_pct': covers / n,
        'ats_mean': np.mean(ats_margins),
        'ats_std': np.std(ats_margins, ddof=1),
        'ats_margins': ats_margins,
    }

print(f"{'Team':<10} {'ATS Record':>12} {'Cover%':>8} "
      f"{'ATS Mean':>10} {'ATS Std':>10}")
print("-" * 55)

for name, data in all_teams.items():
    result = simulate_ats_analysis(name, data)
    print(f"{result['team']:<10} {result['ats_record']:>12} "
          f"{result['cover_pct']:>8.1%} {result['ats_mean']:>10.2f} "
          f"{result['ats_std']:>10.2f}")

The key finding is that the ATS standard deviation for volatile teams is dramatically higher than for consistent teams. While the ATS mean hovers near zero for both groups (as efficient markets would predict), the journey to that mean is vastly different. Consistent teams' ATS margins cluster tightly around zero, meaning covers and non-covers are decided by small margins. Volatile teams produce ATS blowouts in both directions.

Betting Implications

1. Consistent Teams and Teasers

Consistent teams are ideal teaser candidates. Because their point differentials cluster tightly around the mean, moving the line by 6 or 7 points (as in a standard teaser) captures a large proportion of their distribution. If Team B's distribution has a standard deviation of 3.3, a 6-point teaser moves the line by nearly 2 standard deviations, capturing approximately 47.5% of additional probability mass.

2. Volatile Teams and Live Betting

Volatile teams create live betting opportunities. Their games are more likely to feature large lead changes, creating in-game lines that diverge from pre-game expectations. A bettor who recognizes that a volatile team trailing by 14 points at halftime is well within their normal range (less than one standard deviation for Team E) can find value on live moneylines.

3. Totals Betting

Consistent teams make totals more predictable. With lower variance in both points scored and points allowed, the total points in a consistent team's game clusters more tightly around the expected value. Volatile teams produce totals that are spread across a wider range, making totals bets inherently riskier.

4. Season Win Totals

For season win total bets, volatile teams carry more risk for the sportsbook. A team with high game-to-game variance can easily over- or underperform its expected win total by 2-3 games, while a consistent team's wins will hew closely to the Pythagorean expectation. If the market prices both teams similarly, the volatile team's win total over/under may offer value to contrarian bettors who correctly assess the direction of variance.

5. Spread Accuracy and Closing Line Value

Sportsbooks inherently set more accurate spreads for consistent teams because there is less fundamental uncertainty in the outcome. This means closing line value (CLV) is harder to find when betting on or against consistent teams. The edges, when they exist, are small. For volatile teams, the wider uncertainty bands mean larger potential CLV and more frequent mispricing, but also more variance in results.

Quantifying the Edge

To put numbers on this framework, consider a bettor who bets every game for both a consistent and a volatile team, always taking the side with the best CLV. If the bettor achieves an average edge of 1.5% on each bet:

• Consistent team: With ATS SD of ~5.0, the bettor needs roughly 45 bets to achieve statistical significance (z = 1.96) for their edge. Over a 17-game season, the signal is buried in noise.
• Volatile team: With ATS SD of ~17.0, the bettor would need over 500 bets to achieve significance. A single season reveals almost nothing about whether the bettor has genuine skill.

This is why professional bettors emphasize volume and long-term tracking. Descriptive statistics quantify not just the expected value of a bet but the uncertainty around that expectation, which determines how confident you should be in any observed results.

Conclusion

Descriptive statistics transform vague notions like "consistency" and "predictability" into precise, quantifiable metrics. The standard deviation, coefficient of variation, and rolling volatility of point differentials provide a rigorous framework for classifying NFL teams and tailoring betting strategies accordingly. Consistent teams favor teasers, totals bets, and spread bets with tight margins. Volatile teams favor live betting, contrarian season-long positions, and higher-variance bet types where the market struggles to price uncertainty correctly.

The complete Python code for reproducing this analysis is available in code/case-study-code.py.