--- name: project-mm-completion-arithmetic description: The maker reduces to ONE number — completion rate. PAPER-era break-even was 61.4% on +1.78c/−2.82c; the LIVE maker's constants are +$0.0666/−$0.6956, so live break-even is 91.3% (88.9% excluding over-fills) and 86.4% observed. Use the live numbers. metadata: type: project --- ## SUPERSEDED FOR THE LIVE MAKER (measured 2026-09-14) The +1.78c / −2.82c constants below are PAPER-era (242 paper books, v1–v3). They do not describe the live maker, and the 61.4% break-even they imply is dangerously optimistic — it makes a losing strategy look like it has 25 points of headroom. Live, on 191 settled maker-only books (`research/mm_book_dataset.csv`): | group | n | mean $/book | |---|---|---| | complete | 165 | **+$0.0666** | | partial (strand) | 26 | **−$0.6956** | p(0.0666) + (1-p)(-0.6956) = 0 -> break-even completion = 91.3% observed completion = 86.4% 0.864(0.0666) + 0.136(-0.6956) = -0.0371/book vs -0.0372 realised So realised P&L is fully explained by completion being BELOW break-even. There is no missing cost. Note the strand cost is −$0.696/book, which is the figure [[maker-sits-at-breakeven]] uses (11.1% break-even strand = 88.9% completion) — that note is the one to trust, and it agrees with the clean-book numbers here. By shape, complete books only: clean n=154 **+$0.0864**, ragged n=8 +$0.0218, **over n=3 −$0.8300**. The three over-fills — the duplicate-order bug fixed 2026-09-13/14 — are −$2.49, i.e. **35% of the entire −$7.10 loss on 1.6% of books**. With over-fills gone, break-even falls to **88.9%**, so the live gap to close is 86.4% → 88.9%: about 2.5 points of strand. **How to apply:** quote live EV as p*0.0666 + (1-p)*(-0.6956), never the paper constants, and watch completion against 88.9%. Everything below is the paper decomposition and remains valid for the paper era only. Measured 2026-08-09 on `research/mm_paper_results.csv` (242 three-leg paper books, 2026-07-26 → 2026-08-08, regimes v1–v3; v4 had no settled books yet). Reproduces the completion breakdown in commit 202fa59 (3/3 +1.38c, 2/3 −7.62c, 1/3 −2.27c — I get +1.37 / −7.76 / −1.89) and then decomposes it. ## The decomposition Among the 154 books that took on any risk (≥1 fill): | | n | mean | **SD** | t | |---|---|---|---|---| | complete (3/3) | 72 | **+1.78c** | **1.69** | **+8.9** | | partial (1–2/3) | 82 | −2.82c | 43.53 | −0.6 | A completed book is essentially deterministic — it collects the overround outcome-independently, which is the thesis, and it is the one thing in this whole project measured at t=+8.9. A partial book has **25× the standard deviation** and a mean indistinguishable from zero. **All the profit is a near-certainty; all the variance is partial fills.** So the strategy is a single number: BREAK-EVEN COMPLETION RATE = 2.82 / (1.78 + 2.82) = 61.4% ## What the volume gate actually buys | gate (min leg volume) | n | completion | vs break-even | c/book | t | |---|---|---|---|---|---| | none | 154 | 46.8% | −14.6pp | −0.67c | −0.26 | | ≥250 | 77 | 62.3% | +1.0pp | +1.02c | +0.35 | | ≥500 (v4) | 58 | 69.0% | +7.6pp | +1.84c | +0.55 | | ≥1000 | 44 | 70.5% | +9.1pp | +1.28c | +0.32 | | ≥2500 | 23 | 82.6% | +21.2pp | −3.83c | −0.74 | **The completion mechanism replicates; the P&L does not.** Split at the 60th percentile of book start time, gate ≥500: completion **69.2% early / 68.8% late** — about as stable as a measurement gets. Realised P&L over the same split: **−3.15c early / +5.13c late**. Every t in the table above is noise. ## THE METHOD POINT — estimate EV from the components, not the sum EV = p(complete) x 1.78 + (1 - p) x (-2.82) at the v4 gate: 0.69 x 1.78 + 0.31 x (-2.82) = +0.35c/book Direct measurement of that same quantity has SE 3.35c — a ~10x worse estimator of its own target. Realised per-book P&L needs **~841 books at the gate to reach significance** (we have 58); the unconditional series needs ~10,505. That is the same power trap as [[project_xlow_rejection_criteria]], and the same fix as `pin_accuracy_test` / `clv_realisation`: measure the low-variance component, not the high-variance outcome. **Never judge a maker rule by its realised c/book at these sample sizes.** ## The v4 cap at 500 is probably too low The reversal above 1000 that motivated capping the gate there rests on **4 partial books averaging −31c with SE ±29c**. The obvious mechanism for a real reversal — fuller books being tighter, so completing one pays less — is **dead**: complete-book payout by volume bucket is flat at +1.56 / +2.75 / +2.14 / +0.98 / +1.97c, no trend. Flat payout plus completion rising to 82.6% gives **+0.98c/book at ≥2500**, ~3x the ≥500 gate. Not acted on — it is the same in-sample reasoning that set 500, and raising the gate cuts book count from 58 to 23. Logged so the next gate review starts from the arithmetic rather than re-reading the P&L column. ## Honest weak link Break-even 61.4% is only as good as the partial-book cost of −2.82c, which carries **SE ±4.8c**. One SD in either direction swings break-even between ~0% and ~81%, i.e. between "always quote" and "essentially never". **Pinning down what a partial book actually costs is worth more than any further tuning of the gate** — and unlike P&L it is estimable from data already on disk (the 82 partial books, plus whatever the queue-aware scorer says about which leg strands and at what price). ## How to re-run Group `research/mm_paper_results.csv` by `match`, keep `legs==3`, compare `pnl_cents` sums for `fills==3` vs `0