Quant stack
Operator families for the WDI pre-match engine — how intensities become a joint scoreline, how Sharp and Market enter different equations, and what this stack refuses. Production parameters are calibrated per competition and are not published. This website is explanatory and read-only: it does not run the engine in the browser.
A two-layer pre-match pricing engine whose public surface is a frozen Daily Desk — not a live calculator and not a score predictor.
The question is whether a quoted price is worth taking against a model-fair reference: Fair from the joint matrix, checked on Sharp, then scanned on Market. The match result stays random. Layer contracts exist so expected-goals history cannot silently become 1X2 prices, and so an execution quote cannot silently become the pricing book.
Named operators (Frank Copula, COM-Poisson, Shin / Power de-vig, iterative proportional fitting) are standard actuarial tools. How WDI couples them, and the numeric rails that hold a league together, stay inside the engine.
Three surfaces, one direction of travel. Fundamentals feed pricing; pricing never feeds back into fundamentals; publish only freezes what pricing already computed.
Production intensities start from geo expected goals created and conceded — time-decayed, strength-of-schedule adjusted team history. Residual and ensemble skill blends exist as research modes. They do not replace geo on the live Desk, and L2 never outputs 1X2.
Match physics synthesizes home and away scoring rates (λ, μ). COM-Poisson shapes each side’s tails. A Frank Copula builds the joint scoreline matrix. Iterative proportional fitting pulls that joint toward the de-vigged Sharp tip. Expected-value scans and Layer A research tracks read the tip-aligned joint; fill-now Desk tickets use a more physics-weighted coupling of the same Copula family — they do not invent a second model.
Hub stages are WAITING / PREVIEW / FINAL — Desk lamps, not kickoff or full time. The report clock stamps first Final go-live and is never rewritten by later repair. What a plan unlocks is on Pricing; this page is the engine contract.
One directed graph. Geo history is the intensity prior. Opening Sharp anchors λ / μ when the freeze exists — it does not replace the prior. The Copula owns the joint. The Sharp tip reshapes that joint. Market never inverts λ / μ.
Final joint Cθ(Fν(λ), Gν(μ)) → tip-hug → 1X2 / EV Opening Sharp invert · physics (soft couple) · Copula · tip-hug Fair (display) hugs tip. Desk fill-now scores a more physics-weighted tip coupling. Sharp is the pricing book. Market is the follow quote.
In words: start from geo rates; when an opening Sharp 1X2 and totals snapshot is frozen, invert it under the same marginal family used later (COM-Poisson + Frank) and blend match physics toward that anchor rather than overwriting the prior; build the joint; then proportionally fit the joint toward the official Sharp tip. Display Fair hugs that tip-aligned joint; fill-now Desk tickets score a more physics-weighted coupling of the same Copula family. Research EV margins come from the tip-aligned joint — not a separate classifier.
λ and μ are expected goals, not win probabilities. Everything in this section happens before the Copula. It proves the stack is not a pure quote classifier.
Recent matches weigh more than old ones; opponent quality is netted out so a goal against a strong side is not treated like a goal against a weak one. Thin early-season history is shrunk toward a conservative prior.
Does not: emit 1X2, or let a residual skill model replace geo on the live Desk.
Publish may apply flight and altitude to Elo before L1 sees the match, with a floor so ratings cannot collapse. L1 then taxes timezone, rest, and age. Distance is owned by one channel only — Elo or L1 — never both.
Does not: treat Elo as a 1X2 price, or double-count kilometres.
Attack and defense strengths are paired before rates are synthesized. League-aware home advantage lifts intensity. When an opening Sharp invert exists, physics is soft-coupled to that market base so home advantage is not stacked on top of a snapshot that already prices home.
Does not: hard-overwrite λ / μ with raw book prices.
Injuries, fatigue, recovery, and squad depth modulate tails and rates. Confirmed elevens are shown on the report for honesty; production formation topology is off until league feeds are trusted, so a printed XI does not quietly rewrite λ. Match-context capture is an attempt in a kickoff-relative band — empty still counts as attempted.
Does not: treat a missing lineup as a modelling failure, or let XI print replace the Copula.
Asymptotic squash bounds extreme priors so the scoreline grid cannot explode. Intensity explains the COM-Poisson scoring rates. It does not replace Frank Copula, tip-hug, or selection.
Independent Poissons under-price the draw and scramble low-score cells. WDI prices a bivariate count distribution, then reads 1X2 / totals / Asian lines as functions of that joint.
Each side keeps its own scoring marginal. Frank links those CDFs into one joint mass on the score grid. Dependence strength is a single family: the opening invert and the final matrix must share it. Production default is pure Frank. A mixture (Frank with extra lower/upper tail copulas) is opt-in for mutual-draw or high-volatility cases — not the league default. Near-zero dependence is treated as independence.
Does not: invent 1X2 from gradient boosting, or mix copulas as the default book.
Poisson forces variance equal to the mean. COM-Poisson lets a side be over- or under-dispersed — useful under chaos, fatigue, or cup context — before the Copula couples the sides. Opening invert and the joint matrix share the same marginal helper. When market-anchored, rates are re-fit under the final dispersion so invert and Copula stay in one margin family.
Does not: replace the Copula joint step, or use a second unpublished dependence engine.
Gluing two Poisson PMFs assumes home and away goals ignore each other. That systematically mis-states P(draw) and the 0–0 / 1–0 mass that Asian and totals books live on. Independence remains available as a diagnostic ablation of Frank, not as the production joint.
Does not: sell independence as the live Desk generator.
Dixon–Coles only patches a handful of low-score cells on an independence grid. It is weaker than a copula with COM-Poisson marginals, and it would break θ-unity with the opening invert. Low-score DC tweaks stay research-only.
Does not: swap Frank for Dixon–Coles on the live path.
Books are not used raw. Overround is removed, the joint is fitted, display and EV may disagree on purpose.
Shin removes 1X2 overround. Power covers Asian handicap and totals, and is the Shin fallback when a book is too tight for Shin to be stable. Cleaned probabilities are the comparison sheet for tip-hug and mispricing — model 1X2 still comes from the Copula matrix, not from the sheet alone.
Does not: treat every quoted book as Sharp, or replace the joint with de-vigged prices.
Opening 1X2 plus totals, frozen once in the T−24h…T−20h band, are inverted under COM-Poisson + Frank (dispersion starts Poisson-like, then re-fits at the final ν). That invert is the market base physics soft-couples toward. It is never the official tip and never the follow quote.
Does not: invert Market execution prices into λ / μ.
Tip-hug fit reshapes the Copula joint toward de-vigged Sharp-tip 1X2 and totals. Coupling is partial by design: Fair(model) for display sits close to tip-implied fair without discarding the physics matrix. Fill-now Desk tickets are scored on a more physics-weighted joint of the same Copula family — not a second model, and not tip-hug Fair alone. The opening freeze is not the tip-hug target. Internal blowout-mass damping can ease the hug — that is not a Kullback–Leibler circuit breaker, and KL percentiles are not a default void.
Does not: throw the model matrix away, hug from opening alone, sell tip-hug Fair × Market as the Match Pick equation, or sell “beat Sharp” as the Follow story.
On-screen 1X2 bars may be display-calibrated. Every priced research ticket uses joint-matrix margins. Full-grid mass prices 1X2, totals, and Asian lines. The report heat map is a display slice — under fat tails the visible cells can sum to less than one without implying a bug.
Does not: scan expected value off the heat-map slice.
One Copula family; several readings. Public Follow is the Daily Desk — Match Pick and Watch — not Layer A stake advice. Layer A is the internal name for three research tracks (ANCHOR / ALPHA / ROCKET) on the tip-aligned joint — intelligence only, never the public Follow KPI.
Expected value is model probability times quoted price, minus one. Because WDI is dual-book, that product is taken twice from the same Copula family: against Sharp (research / gate ledger) and against Market (follow math). Match Pick fill-now uses Market as the follow quote and requires Sharp EV not to go negative; it is not “priced on Sharp alone.” A Market quote is never written into the Sharp tip, and Sharp is never sold as a fill.
The EV scan covers 1X2, double chance, totals, and Asian handicap. Totals and Asian follow quotes must line-match the tipped selection. A mismatch is a no-quote, not a guessed line.
Confidence stars are a recommendation index, not a stake instruction. Fractional Kelly and joint-fixture caps exist only as internal ceilings. No Kelly percentage or bankroll advice appears on this site. Order-flow is allowed to skip a trap in EV; it does not hard-edit λ / μ on the live path.
Kickoff-relative windows — not “once per UTC day.” Three pricing inputs (opening, tip, execution), diagnostic Sharp ticks that never enter L1, plus public PREVIEW / FINAL Desk lamps.
No Sharp tip → no live Desk. A missing map or empty board skips publish; reference ticks are never promoted into tip. If the primary Sharp tip feed is exhausted, a secondary Sharp snapshot may unlock the Desk with distinct provenance — it is not marketed as the primary Sharp path. A stamped execution miss still counts as the T−40 attempt. Preview outside its hard band is not back-filled. After T−30, including after kickoff, the stack does not stamp a new public Final. The T−40 Sharp tip is not kickoff true close.
The same Copula family prices leagues and cups (UEFA and domestic). Sample size and Follow KPIs stay separate. A sparse cup desk is never sold as a top-flight league sample.
Subscribers follow a Desk ticket on a tip-ready Final — not Layer A tracks as stake advice. Match Pick is fill-now on Market when the physics-weighted joint clears its gates; Desk Watch is a limit. Model Judgment is a directional lean only — never a priced ticket.
Hub lamps are only TICKET vs LEAN. TICKET means Match Pick or Watch cleared the execution gate — not that every Final is fill-now. Detail unlock may still show legacy Consensus / Value labels under a Match Pick; those are not separate Hub promises. Combo Desk is Elite-only Cover 3-fold research, not Layer A +EV, never marketed as Match Pick. Access detail lives on Pricing.