Appendix E: NFL Analytics Formula Reference

Quick reference for key formulas used throughout the textbook.

Team Rating Formulas

Elo Rating Update

New_Elo = Old_Elo + K × (Actual - Expected)
Expected = 1 / (1 + 10^((Opponent_Elo - Team_Elo) / 400))

• K = 20 for NFL (typical)
• Actual = 1 (win), 0.5 (tie), 0 (loss)

Power Rating from Margin

Power_Rating = (Σ Margin_i × Weight_i) / (Σ Weight_i) + Opponent_Adjustment

Pythagorean Expectation

Win% = PF^n / (PF^n + PA^n)
Expected_Wins = Win% × Games

• NFL: n ≈ 2.37
• PF = Points For, PA = Points Against

Expected Points

Expected Points by Field Position (Approximate)

EP(x) = 7 × (x/100)^1.5 - 2

Where x = yards from own goal line

EPA (Expected Points Added)

EPA = EP_after - EP_before

Success Rate

Success = 1 if:
  1st down: gain ≥ 40% of yards needed
  2nd down: gain ≥ 50% of yards needed
  3rd/4th down: gain ≥ 100% of yards needed

Quarterback Metrics

Passer Rating (NFL)

a = ((Comp% × 100) - 30) / 20
b = (Yards/Att - 3) / 4
c = (TD% × 100) / 5
d = 2.375 - (INT% × 100 × 0.25)

Rating = ((a + b + c + d) / 6) × 100

Each component capped at 0-2.375

ANY/A (Adjusted Net Yards per Attempt)

ANY/A = (Pass_Yards + 20×TDs - 45×INTs - Sack_Yards) / (Attempts + Sacks)

CPOE (Completion Percentage Over Expected)

CPOE = Actual_Comp% - Expected_Comp%

Home Field Advantage

Dynamic HFA Model

HFA = Base_HFA + Team_Adj + Travel_Adj + Context_Adj

Base_HFA ≈ 2.3 pts (modern NFL)
Travel_Adj = TZ_diff × 0.2 + 0.15 (if W→E)

Bye Week Effect

Bye_Advantage = 1.2 × Timing_Multiplier

Timing_Multiplier:
- Early (Wk 4-5): 0.7
- Standard (Wk 6-9): 1.0
- Late (Wk 10-12): 1.2
- Very late (Wk 13+): 1.4

Schedule Adjustments

Rest Differential

Rest_Adj = (Home_Days - Away_Days) × 0.15

Thursday Night Penalty

TNF_Away_Penalty:
- Sunday to Thursday: 1.5 pts
- Monday to Thursday: 3.0 pts

Strength of Schedule

SOS = Σ(Opponent_Win%) / n - 0.500
Win_Impact ≈ SOS × 10 (rough conversion to wins)

Weather Effects

Temperature Adjustment

Temp_Adj = -0.12 × max(0, 55 - Temperature)

Only applies below 55°F

Wind Adjustment

Wind_Adj = -0.25 × max(0, Wind_Speed - 10)

Only applies above 10 mph

Altitude (Denver)

Altitude_Adj = +0.5 to home team
Visiting_Penalty = -0.5 to -1.0

Injury Impact

Position Value Weights

QB: 1.00
RB: 0.25-0.30
WR1: 0.20, WR2: 0.15, WR3: 0.10
TE: 0.12-0.15
OL: 0.08-0.12 per player

WAR (Wins Above Replacement)

WAR = (Player_EPA - Replacement_EPA) / Points_per_Win

Betting Formulas

Implied Probability

American to Implied:
Favorite (-odds): IP = odds / (odds + 100)
Underdog (+odds): IP = 100 / (odds + 100)

Decimal to Implied

IP = 1 / Decimal_Odds

Edge Calculation

Edge = Model_Probability - Implied_Probability

Kelly Criterion

Kelly_Fraction = (bp - q) / b
b = net odds (decimal - 1)
p = probability of winning
q = 1 - p

Expected Value

EV = (Probability × Payout) - (1 - Probability) × Stake

Break-Even Win Rate

BE = Risk / (Risk + Potential_Win)
At -110: BE = 110 / 210 = 52.4%

Fantasy Football

Fantasy Points (PPR)

FP = Pass_Yards × 0.04 + Pass_TD × 4 + INT × (-2)
   + Rush_Yards × 0.1 + Rush_TD × 6
   + Rec_Yards × 0.1 + Rec_TD × 6 + Receptions × 1

VORP

VORP = Player_Projection - Replacement_Level

DFS Leverage

Leverage = Projection / Ownership%

Draft Analysis

Speed Score

Speed_Score = (Weight × 200) / (40_time)^4

Dominator Rating

Dominator = (Rec_Yards_Share + Rec_TD_Share) / 2 × 100

Height-Adjusted Speed

Adj_40 = Actual_40 - (Height_inches - 72) × 0.03

Draft Pick Value (Approximate)

Value ≈ 3000 × e^(-0.05 × Pick)

Regression

Regression to Mean

Regressed = Mean + (Observed - Mean) × (1 - Regression_Rate)

Regression rates: - TD Rate: 75% - INT Rate: 60% - Catch Rate: 40% - Volume: 20%

Win Probability

Basic Win Probability Components

WP = f(Score_Diff, Time_Remaining, Possession, Field_Position)

Point Spread to Win Probability

WP ≈ Φ(Spread / 13.5)

Where Φ is the standard normal CDF

Variance and Confidence

Confidence Interval

CI = Estimate ± z* × Standard_Error
95% CI: z* = 1.96

Sample Size for Stability

n_needed ≈ (z² × σ²) / E²

Where E = desired margin of error

Quick Reference Table

This formula reference provides quick access to key calculations. Refer to the relevant chapter for full context and derivation.