Gaussian random-walk model fitted to 2M+ observations (1997–2025).
P(home wins | diff D, time T) = Φ((D + μ·T) / (σera × √T)) —
μ is a drift (pts/sec) so HCA scales with time remaining; one σ per era captures the pace increase.
σ (sigma) is the model's scoring-volatility parameter. Higher σ = same deficit is worth less (more scoring expected). It directly captures the NBA's pace increase.
Sigma rose from ~0.31 in 1997 to ~0.38 in 2025, a +22% increase. This is real and driven by increased pace. However even at 2025's sigma, a 13-point deficit with 12 minutes left carries only ~11% comeback probability (vs ~7% in 1997-2003). The game is faster, but large leads are not "not daunting."
Predicted probability vs actual win rate (binned across all 2M+ observations). Perfect calibration = dots on the diagonal.
The model is well-calibrated across the full range — predicted vs actual win rates are within ~1pp throughout, and under 0.5pp across most of the mid-range. The largest gaps are at the extremes (<5% and >95%), where large late-game deficits enter discrete territory the Gaussian can’t fully capture.