The dial inventory: every dial, searched or not

5 Oct (T-726). tools/dialinventory.js; the machine-readable inventory is tools/dial-inventory.json. Snapshot 8dcd24032d, inputs hash dcd477d8a78c. Base: Track A (tools/ledger-benchmarks/2026-10-05-step34b-baseline.json), Track B beside. A report: nothing in the ledger moves, nothing is removed and nothing is adopted.

In plain English

Jordan's rule (5 Oct): every dial goes into the searches, and off is one of its options, never its permanent home. This is the list of every dial we have, so that nothing is left out again.

• 161 dials. That is every one of the ledger page's 118 slider keys, the 13 rule multipliers, the 4 letter cuts, 24 post dials across 10 exam post modules (plus gradeBy), the datasheet-feature family and the popularity diagnostic. node tools/dialinventory.js --check fails if a new slider key, rule kind or post module is not in the list. Beside them are 35 hard-coded constants that could become dials (CHAR_PTS, SHOCK_AMP, AIR_KILL, ARRIVE_W, ...).
• 145 are live on this snapshot. Each dial was set to a sensible value away from its default on Track A, and all 16 armies were run through the exam's own compute (wCarry 0). A strength dial was run with its switch on in both runs.
  • 89 of the live dials move units in every army, 41 in 4 to 15 armies.
  • 15 move only one to three armies. Examples: the Biovore dial, Synapse, the army-rule dials and the Orders.
  • 11 move nothing at the test value. 7 of those do act once a sibling is set:
    • threat, once threatSoak is off;
    • charsJoined, once burstKill is off, and then on Tyranids only;
    • killClassWeight, from strength 3;
    • carryCargo and carryFragRef, once a cargo part is on;
    • profileDials and profileLines, on the data tools/ledgerprofile.js prepares.
  • Run without its switch, every dial behind a sibling moves nothing.
  • 5 entries were not run: the 4 letter cuts, which never move a Value, and the feature family.
  • No dial errored.
• The cascade (tools/cascade2.js) searched 26 of them, all live. 6 more were held at one value: screenHide, screenRank, objPresence's extras and enabler, typicalSizeRule (mean) and typicalDet (0). 119 live dials were left out, including:
  • every line weight;
  • supportMeasured, preferredTargets, the life and VP dials;
  • leadersLeading, joinedMarginal, joinedShapley and leaderCredit;
  • 12 of the 15 character dials;
  • rivals, domRival, jail, steal, gradeBy and the transport dials.

On 5 Oct Jordan asked that the cascade re-run also search the measured replacements, supportMeasured and synapseMarginal (design/decisions.md). Neither was in cascade2's grid.

• Duplicates (measured or read in the code):
  • prem = wKill exactly. prem 2 and wKill × 2 give every Value to the bit.
  • Only the weights' ratios matter. Doubling all seven line weights doubles every Value, so any search should hold wKill fixed.
  • smallPiece = pointsExp with the sign turned round. They are the same formula up to a constant per army: smallPiece 0.2 and pointsExp −0.2 order all 21,313 unit pairs the same way.
  • scarceAnswers ≈ role scarcity off (ρ 0.997). Its answer gaps add almost nothing, so scarceAnswersW is in effect a strength dial on role scarcity.
  • objPresence ≈ screenScore in direction (ρ 0.963, the same 686 units). Both credit a cheap unit's OC per point; at equal strength screenScore reorders about three times as many unit pairs.
  • joinedShapley ≈ joinedMarginal at half strength (ρ 0.969).
  • typicalW is a shorthand for typicalSize and typicalDet together.
• Overlaps, not duplicates:
  • The leader dials: leaderCredit against leadersLeading 0.72, against joinedMarginal 0.53. leaderComp's penalty is a different idea, at 0.2 or below against all three.
  • supportCredit against supportMeasured, 0.52.
  • r.synapse against synapseMarginal, 0.64; 0.998 on the Tyranids alone.
  • The four transport dials, 0.1 to 0.6 with one another: different transports win.
  • screenArea against screenBlock, 0.93.
  • charLead against charEnh 0.66, against charHome 0.34. charEpic against charEnh −0.78: they are complements.
  • typicalSize against smallPiece, −0.13: unrelated.
  • objPresence and screenScore against wScore, about −0.87 at wScore 0: each is a Score weight by another route.
• Removal candidates, for Jordan to decide (nothing removed):
  • Exact duplicates: prem; pointsExp or smallPiece (keep one); typicalW.
  • Inert on every army:
    • r.arrival: every arrival rule is measured by the charge model;
    • killMargin: its field was never built;
    • armyPick: no ledger carries burstPick since the re-freezes, and armyRounds took over its World Eaters job;
    • charsJoined: inert in both tracks, and attachChars is its Burst version;
    • profileDials: superseded by profileLines.
  • Data we must not use in letters: popshare, which reads tournament popularity.
  • Jordan's call: bonusShare weights its bonus package by the share of tournament lists that run each detachment or take each aura bearer. That is not the rated unit's own popularity, but it is popularity data inside a letter dial.
• Wargear BSData forbids, in Track A best forms (flagged, not fixed):
  • Death Guard's Helbrute (11th of 36) carries both a Helbrute hammer and a power scourge (T-723).
  • Votann's Thunderkyn (5th of 22) mix a bolt cannon with two SP conversion beamers; T-724 makes every model take the same weapon.
  • The Cadian Recon Squad (Astra Militarum 25th, Cults 53rd) has two long-las with a stubber and a meltagun. Whether that breaks the long-las or weapons team rule needs a check.
  • The other T-723 units are legal in their best forms: Aggressors, Beserks, Yaegirs, Vanguard Veterans and Wolf Guard.
• The next search (proposed, not run): a space-filling screen over every live dial at once, then a full factorial on the dials that move anything. That is about 3 to 8 hours on 8 workers; plan for 6. Details below.

How it was run

• The test: each dial at one sensible non-default value over Track A, against the same setting without it. Both runs go through tools/exam.js runOf() with wCarry 0, and the post steps act on that run.
• What counts as moving: "moved" means a ranked unit's Value changes. "Flips" are the unit pairs whose order changes.
• Strength dials run with their switch on in both runs. "alone" is the same dial with its switch off, at wCarry 0.
• Rule multipliers: 1.5, or 1 where Track A's value is not 1. r.cp is 2.88, r.first 1.8, r.synapse 1.5.
• The pairs:
  • Each dial's change in Value from Track A, divided by its army's SD of Track A Values, pooled over all 16 armies.
  • Spearman's ρ over the units that either dial moves; the ρ over all 733 ranked units and the median per-army ρ sit beside it.
  • The exact check compares the two settings' unit orders directly: the unit pairs the two put in different orders, out of 21,313.
  • A pair is called a duplicate when ρ is above 0.95 or the code computes the same thing. Otherwise it is an overlap.
• Run time: 16 armies, 174 to 194 computes each. 14 armies took about 20 min on 8 workers; Dark Angels and Space Marines took another 20 min on 2 workers with a larger heap: a Dark Angels compute holds hundreds of MB, and the first pass ran out of memory. Per-compute cost, mean over the tests on one core: Dark Angels 6.1 s, Space Marines 4.1 s, Astra Militarum 2.2 s, Tyranids 1.0 s, World Eaters 0.15 s. That is 20.7 s for one setting over all 16 armies. cascade2's settings, nearer Track A, cost about 13 s.
• Commands:
  • node tools/dialinventory.js --check
  • node --max-old-space-size=6000 tools/dialinventory.js --live --workers 8 [--heap 6000] --analyse
  • --md writes the tables below.

The next search

Recommended: a space-filling screen, then a full factorial on what moves.

Factors. About 100, built from the 140 searchable live dials. wKill is held fixed, and raw, popshare, typicalW, pointsExp and prem are left out.

• Each switch carries its strength dials as levels: off, on at 1, on at a second strength.
• Each mutually exclusive family is one factor: secondaryVP, missionVP, missionBudget and vpLedger; the lifeKill modes; the screen bundle's structure.
• Every factor has 0 or off as one of its levels.

Stage 1, the screen.

• 4,096 settings. Each factor's levels are balanced and shuffled on their own, as tools/solcascade.js's sample does.
• Plus 454 anchor rows: Track A and cascade2's 240 and 213 survivors, with every other factor at Track A.
• Every row is scored on the real letters and cascade2's three scrambled sets. The post steps are chained in their stack order, not added.
• Cost: about 4,550 settings at 1,400 to 2,200 an hour on 8 workers, so 2.1 to 3.3 h.

The analysis.

• Per army and pooled, each factor level's main effect on the pairs ordered right, real letters against scrambled (cascade2's gate, applied per factor). Each level appears in about 1,400 rows.
• Two-way interactions by a lasso among the factors that pass, plus the named families: leaders, support, carry and screens.
• A factor passes when its real effect beats the scrambled seeds', either in the multi-list armies or in the clean chain's seven armies.

Stage 2, the full factorial.

• Every combination of the factors that pass. Expect 8 to 12 factors at their passing levels: from 2^10 = 1,024 to 3^8 = 6,561 settings.
• Run through cascade2's staged armies, bars and per-army gates, with each army free to take its own values as in cascade2.
• Cost: 0.5 to 4.7 h.

Why this design.

• Every dial moves in every row, so no dial is pinned at off because of an old one-at-a-time result.
• Combinations are seen statistically in stage 1 and exactly in stage 2.
• cascade2's survivors stay in the comparison as anchors.

Rejected:

• One dial at a time, then in pairs, on all 453 survivors: 126,840 settings, 58 to 91 h. On 20 representative survivors it is 5,600 settings (2.6 to 4 h), then 34,800 for the pairs among the top 30 (16 to 25 h). It is also blind to a dial that helps only when others move.
• The full factorial: about 3^100 settings.

Tables

Columns:

• Search: the values proposed for the next search.
• Track A · B: each track's value (post dials are 0 in both).
• Cascade2: the values it searched, or "held at" for a value it kept fixed.
• Live: armies moved of 16, units moved, then in brackets the unit pairs whose order flips. "alone" is the number of armies the dial moves without its sibling.

weights

base

calls

rules

cuts

switches

carry

profile

strengths

ingredients

leaders

army

screens

characters

post

diagnostic

Pairs

(21313 unit pairs in all, over the 16 armies.)

Constants that could be dials