Point Spread Converter

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Quick Primer

Convert point spreads to fair moneyline odds using statistical models. The logistic model fits an S-curve to historical win rates, while the normal model uses a Gaussian distribution. Both approaches transform the point spread into a win probability, then convert that to American odds. Adjust the hold percentage to simulate bookmaker pricing—typical books add 4-5% overround to both sides.

Want the formulas & model details? Open the deep dive below.

Deep Dive: Statistical Models for Spread Conversion Formulas · Parameters · Model comparison

Logistic Model

The logistic function models win probability as an S-curve based on point spread magnitude:

P(favorite wins) = 1 / (1 + e−k·s)

Where s is the absolute spread value and k is the slope parameter controlling curve steepness. The NFL default k=0.14324 comes from Wizard of Odds empirical fitting to decades of game results.

  • Higher k → faster probability change per point
  • Lower k → more gradual probability curve
  • Sport-specific: NFL uses fitted k, NBA/NCAAF derive k from sigma

Normal (Gaussian) Model

Assumes point differentials follow a normal distribution with sport-specific standard deviation σ:

P(favorite wins) = Φ(s / σ)

Where Φ is the cumulative normal distribution function. Standard deviations represent typical scoring variability:

  • NFL: σ = 13.86 points (lower variance, field goals matter)
  • NBA: σ = 12.0 points (moderate variance)
  • NCAAF: σ = 15.0 points (higher variance, blowouts common)

Example: NFL -3.5 Spread

Using the logistic model with k=0.14324:

  • P(favorite) = 1 / (1 + e−0.14324 × 3.5) ≈ 62.28%
  • Fair favorite moneyline: -165 (implied 62.28%)
  • Fair underdog moneyline: +165 (implied 37.72%)
  • With 4.5% hold: favorite becomes -186, underdog +154

Which Model to Use?

Logistic (default): Best for NFL, empirically fitted to real outcomes. More accurate for key numbers (3, 7, 10) where scoring patterns matter.

Normal: Better for sports with more continuous scoring or when you want to adjust sigma based on specific matchup characteristics (defensive strength, pace, weather).

Both models converge for moderate spreads. Differences emerge at extreme spreads (>14 points) where the logistic model's heavier tail better captures upset probability.