PuGa/docs/saturation-design.md

Saturation model design (v1 as implemented; v0 draft below superseded where marked)

Problem: PRUNplanner's ROI Overview (and our old scan) rank recipes as if the market absorbs unlimited output at top-of-book prices. Result: recipes whose market fits 1 to 2 buildings rank first with absurd ROI (e.g. 0.25 day). We need, per recipe and per CX (or universe), a number of buildings N the market can realistically support, and profit computed at prices you would actually get at that N.

Inputs per material and CX (from puga/market.py)

• Book totals: ask, bid, supply (units on sell side), demand (units on buy side).
• Flow: traded7, traded30 = average units traded per day; vwap7, vwap30.
• Live order book (per order price, quantity) via market.walk.
• MM (market maker) prices mm_buy (floor: MM buys at this) and mm_sell (cap: MM sells at this), when present. Treat as unlimited depth at that price.

Per-building daily quantities

q_out[m], q_in[m] per building per day at efficiency e (from econ.production_io), including wages/upkeep costs per building.

Capacity: how many buildings can each side support

1. Flow cap (steady state): a producer cannot take more than a share s of the market's traded flow without moving price. N_flow_out[m] = s * traded_ref[m] / q_out[m], with traded_ref = min(traded7, traded30) (conservative), s default 0.25 (parameter). Inputs identical: N_flow_in[m] = s * traded_ref[m] / q_in[m].
2. Stock cap (short horizon): standing book absorbs a one-time batch: bids for outputs, asks for inputs. Over hold horizon H days (default 7), N_stock = book_units / (q * H). Stock refills through flow, so the effective cap per side is max(N_flow, N_stock)? To be decided (flow is the steady-state truth; stock only helps ramp-up). Proposal: cap = N_flow; report N_stock separately as ramp-up buffer.
3. MM override: if the output has mm_buy (floor with unlimited depth) then N_out is unbounded but priced at mm_buy; if an input has mm_sell then its price is capped at mm_sell, unbounded depth.
4. N = floor(min over all outputs and inputs of the capacity)*. If N* < 1: flag "thin", still report ROI at N=1 but exclude from default ranking.

Price at N buildings (price impact)

• Selling: two modes. instant: walk bids for the quantity Nq_outH, avg price. patient: price = vwap7 with a discount d(N) that grows with our share of flow: d = k * (N*q_out/traded_ref) (k calibrated from book slope, default so that at share s the discount equals the walk-price deficit). Report both; default ranking uses patient.
• Buying inputs: mirror (asks, or vwap7 + premium).
• Net per building n(N) = revenue(N) - inputs(N) - wages - amortised capex (optional). Profit curve for N in 1, 2, 4, ... N*. Report N_opt = argmax total profit N * n(N) with n(N) >= a minimum ROI.

Output columns

recipe, building, N*, limiting material (which side caps), ROI/day at N=1, ROI/day at N_opt, total profit/day at N_opt, capex at N_opt, price used (mode), thin flag.

Known weaknesses / questions for review

1. Is flow-share s the right primitive? traded volume is noisy and includes our own competitors' equilibrium; what better estimate of "room for a new producer"?
2. Existing producers: a market with big standing supply relative to flow signals saturation on the producer side (price pressure). Should supply/flow ratio adjust the price or cap?
3. Stock vs flow double counting; horizon H arbitrary.
4. Input side and output side are coupled through prices (our buying raises input prices): first-order only.
5. Patient price discount model is hand-wavy; alternatives.
6. Universe scope: with --cross across CX, shipping costs ignored; how to bound.
7. Intermediate goods we produce ourselves (chains) are not modelled here (see tools/chain.py).

Review outcome (Opus, 2026-09-18) and what was implemented in puga/saturation.py + tools/scan.py

Verdict: flow-share alone is half right. The standing sell queue (supply / flow, in days) is the dominant signal; order-book walking is a red herring for saturation (selling one day of output at N* barely moves the price); what costs money is the bid vs vwap7 haircut. Implemented:

• tref = min(traded7, traded30), with a Poisson lower bound traded30*(1 - 1.96/sqrt(30*traded30)) when traded30 < 20.
• N_out = (s*tref/q_out) * min(1, T_q*tref/supply) * min(1, demand/(T_d*tref)), s=0.25, T_q=T_d=7 days. Limiting output reported.
• Thin flag: tref < 3*q_out or demand < 7*q_out (hard exclude; --show-thin overrides). NOTE: borderline. HWP BHP 7.2h variant (13.3/day vs tref 39.2) is flagged thin at exactly this threshold while the 8.4h variant passes; the 3x rule is arbitrary and should be revisited.
• Inputs: no flow cap; priced by ask-walk of N*q_in (1 day) and profit falls out negative if the book is shallow.
• Output price: p_patient = highest ask level whose units-ahead <= T_w*(tref - produced), clamped to [bid, min(vwap7, vwap30, ask)], T_w = 3 days; falls to the bid when we out-produce flow.
• MM override only when mm_buy >= 0.9*bid: unlimited depth at mm_buy.
• Bug fixed: market.walk dropped MM orders (ItemCount: null means unlimited). Later refinements (not built): supply-feedback fixpoint (our N raises supply), daily snapshot cache and d(supply)/dt, seller-count crowding (distinct CompanyCode per side), use NarrowPriceBand*/WwidePriceBand* to bound prices, 149/370 AI1 materials have traded7 < 5/day so confidence handling matters, cross-CX with freight, chains. MM-priced materials (SP, AIR, CCD, CBS, RED...) trade AT mm_buy so their volume is the MM absorbing, not player demand.

Addendum: effective supply (implemented)

Stage 1 of tools/scan.py uses flow + demand only; stage 2 (shortlist) fetches the ask book and counts only standing sell orders priced <= 1.25 x vwap7 (saturation.effective_supply). Reason: DEC at AI1 showed 2,013 units 'queue' of which 1,501 sat at 50,000 (1.5x vwap), which made the raw queue penalty call the market saturated (N=0.38) when the effective queue gives about 1.7.