build_a_totals_model

Build a totals model — worked example

Follow model_development for the method; this is the totals instantiation.

Recipe (run_python, one script)

1. Data: per-game totals for both teams across as many seasons as the regime allows — count EVENTS against the parameter budget (model_development §2: 10–20 outcomes per parameter; a recent-window-only model must say how little it knows). Weight recency (exponential decay, half-life tuned on train) rather than truncating to a tiny window.
2. Model the scoring process: totals are sums of scoring events — Normal(μ, σ) for high-scoring sports (basketball), Poisson for low-scoring (soccer/NHL goals). μ from pace-adjusted team offense/defense; σ estimated, not assumed (floor it sensibly; print it).
3. Probability: p_over = 1 - CDF(line) — hand-rolled normal CDF (0.5 * (1 + math.erf((x - mu) / (sigma * 2**0.5)))) keeps the sandbox dependency-free.
4. Features beyond pace (ask the user which they value — model_development §3): rest days, altitude/venue, weather for outdoor sports. Each one is a parameter; justify it.
5. Holdout: train on the earlier slice, collect {prob, outcome} on the later slice ONLY, calibration_metrics → save_model (params: μ/σ method, weights, seasons, line convention) → record_predictions with honest predicted_at.

Honesty rules

• A Brier ≥ 0.25 on a balanced set is coin-flip territory — say so plainly.
• The bar is the closing total (query_line_movement), not the base rate (quant_concepts: CLV) — report model vs market side by side.