The model produces P(favorite wins series) in three steps:
Given current posterior mean differential δ (favorite NRtg − underdog NRtg) and homecourt advantage h, the probability the favorite wins one game:
where Φ is the standard normal CDF, σ_n is per-game noise, and σ_g reflects posterior uncertainty about the true differential.
After observing margin y in a game with homecourt term μ_0 = δ + h·HCA, the posterior mean and variance update via the standard normal-normal conjugate:
Each game tightens the posterior — variance shrinks toward zero as more evidence accumulates.
From current state (W_f, W_u) with fixed game-location schedule, sum probability across all paths to W_f = 4:
Path enumeration is exhaustive — at most 35 paths from any starting state. The favorite home/road probability is recomputed at each game using the current posterior.
Backtesting showed the raw model overconfident at the extremes. We apply a small symmetric adjustment:
Pulls confident predictions slightly toward the center. Calibrated empirically, not a free parameter.
| Symbol | Value | Meaning |
|---|---|---|
| HCA | 2.5 | Homecourt advantage in points |
| σ_n | 11.5 | Per-game noise standard deviation |
| σ_θ | 2.0 | Initial posterior std on NRtg differential |
| c | 0.6 | Prior regression toward zero (calibrated) |
| κ | 0.0 | Four Factors weight (currently disabled) |
Constants were derived from a backtest over 2015-2024 NBA playoffs. Prior regression c was selected by sweeping values from 0.3 to 1.0 and choosing the midpoint of best log-loss (0.7) and best ECE (0.5). Single point estimate, no per-round or per-bucket variation.
Known calibration limitation: the model is systematically over-confident in matchups with model-assigned probability between 0.50 and 0.60 (close NRtg matchups). For full details on the calibration analysis and known biases, see the README.
The model uses regular-season net rating only. It does not see:
These are real signals the Kalshi market does see (via news, lineup announcements, in-game reactions). The model's edge over the market — when it has one — comes from regression-to-mean discipline, not from richer information.