Plan v4, step 1a: the Tyranid numbers and the walk (2026-10-03)

T-587 (design/tier-plan-v4.md sections 2, 3, 6 and 8; pre-registered in design/decisions.md, 3 Oct). Command: node tools/v4walk.js --write (about 8 s), which writes this report, its JSON and reports/tiers/2026-10-03-tyranids-v4-walk-table.md. Tests: tests/unit/v4walk.test.js. Data: BSData 374f505; the top-quarter field from tools/field.js (build/field/states.json, 630 units, 2001.9 points; its units are copied into the JSON), from tournament lists in grimstat-corpus 570b8c6 (CC BY 4.0, published by players and organisers on MiniHeadQuarters; the listhammer/ folder is not read); engine hash e2abebfd3b3b (the engine, loadout and effects files, this tool). Our own numbers from the datasheets' dice; no rules text. A report: nothing on the site changes, nothing is fitted, tuned or chosen on any panel, and no form is preferred.

In short

For the 52 Tyranid pool units at their minimum size and best legal loadout, every raw column of plan v4's feature table that the dice allow, from the matrix's cells and the one-phase targeting rule (β 6) into the top-quarter field, and the four score forms of the walk side by side, with the three Tyranid reviewers and round 13's B1 for continuity. Parity: 200 cells drawn from the 421,976 the run read, against ev.js: worst |Δ damage per attack| 2.2e−16, worst |Δ unsaved wounds per attack| 1.1e−16; on the 24 one-wound targets the long-run wounds removed equal ev.js's damage to 1.1e−16; 0 cells above it elsewhere. A second run writes a byte-identical JSON (the test). Standing lines: scaled sum -hivemind 0.04 (SE 0.15, lift +0.03), -second 0.14 (SE 0.16, lift +0.13), Auspex (tuned on) 0.26 (SE 0.15, lift +0.27), ρ(score, points) −0.35; offense -hivemind 0.10 (SE 0.15, lift +0.10), -second 0.31 (SE 0.15, lift +0.30), Auspex (tuned on) 0.18 (SE 0.15, lift +0.19), ρ(score, points) −0.17; defense -hivemind 0.10 (SE 0.15, lift +0.10), -second 0.07 (SE 0.16, lift +0.06), Auspex (tuned on) 0.36 (SE 0.14, lift +0.37), ρ(score, points) −0.35; geometric mean -hivemind 0.03 (SE 0.15, lift +0.03), -second 0.19 (SE 0.16, lift +0.18), Auspex (tuned on) 0.26 (SE 0.15, lift +0.27), ρ(score, points) −0.31.

The pre-registered lines, read as written (no form is chosen here). ρ(score, points) below −0.3 marks the cheap lean: scaled sum, defense, geometric mean are below it; offense (−0.17) is not. The critique's C3 test (the sum's order following one part at ρ above 0.9): ρ(scaled sum, offense) 0.74, ρ(scaled sum, defense) 0.83; ρ(offense, defense) 0.30. C5's six (the units over 165 points Auspex grades S: Norn Emissary, Norn Assimilator, The Swarmlord, Hive Tyrant, Maleceptor, Tyrannofex): mean rank of 52 32.2 on the scaled sum, 28.8 on offense, 29.7 on defense, 31.2 on the geometric mean, 5.8 on the absolute defense column alone (B1: 19.2).

The table

Sorted by the scaled sum's rank: a presentation order, not a choice of form. Offense and defense are in points per 100 points (offense: ranged plus melee, summed; defense: shooting plus fight, summed). The scaled sum is offense ÷ 45.50 + defense ÷ 186.18 (each divided by its standard deviation over the 52, population); the geometric mean is √(offense ÷ 45.50 × defense ÷ 186.18). Rank 1 is the highest; ties share a rank. No letters of ours: no bands exist yet.

Scaled sum. 2026-10-03-tyranids-hivemind: ρ 0.04 (SE 0.15), lift +0.03; 2026-10-03-tyranids-second: ρ 0.14 (SE 0.16), lift +0.13; Auspex (tuned on): ρ 0.26 (SE 0.15), lift +0.27. ρ(score, points) −0.35. Within one on each reviewer's shape (computed only for this line), as lift over shuffle: 2026-10-03-tyranids-hivemind −1.2 (30.0 of 45, shuffle 31.2); 2026-10-03-tyranids-second +2.7 (30.0 of 41, shuffle 27.3); Auspex +1.9 (24.0 of 44, shuffle 22.1).

Offense. 2026-10-03-tyranids-hivemind: ρ 0.10 (SE 0.15), lift +0.10; 2026-10-03-tyranids-second: ρ 0.31 (SE 0.15), lift +0.30; Auspex (tuned on): ρ 0.18 (SE 0.15), lift +0.19. ρ(score, points) −0.17. Within one on each reviewer's shape (computed only for this line), as lift over shuffle: 2026-10-03-tyranids-hivemind +4.8 (36.0 of 45, shuffle 31.2); 2026-10-03-tyranids-second +4.7 (32.0 of 41, shuffle 27.3); Auspex +2.9 (25.0 of 44, shuffle 22.1).

Defense. 2026-10-03-tyranids-hivemind: ρ 0.10 (SE 0.15), lift +0.10; 2026-10-03-tyranids-second: ρ 0.07 (SE 0.16), lift +0.06; Auspex (tuned on): ρ 0.36 (SE 0.14), lift +0.37. ρ(score, points) −0.35. Within one on each reviewer's shape (computed only for this line), as lift over shuffle: 2026-10-03-tyranids-hivemind +1.8 (33.0 of 45, shuffle 31.2); 2026-10-03-tyranids-second +1.7 (29.0 of 41, shuffle 27.3); Auspex +6.9 (29.0 of 44, shuffle 22.1).

Geometric mean. 2026-10-03-tyranids-hivemind: ρ 0.03 (SE 0.15), lift +0.03; 2026-10-03-tyranids-second: ρ 0.19 (SE 0.16), lift +0.18; Auspex (tuned on): ρ 0.26 (SE 0.15), lift +0.27. ρ(score, points) −0.31. Within one on each reviewer's shape (computed only for this line), as lift over shuffle: 2026-10-03-tyranids-hivemind +0.8 (32.0 of 45, shuffle 31.2); 2026-10-03-tyranids-second +1.7 (29.0 of 41, shuffle 27.3); Auspex +1.9 (24.0 of 44, shuffle 22.1).

Driving columns: the two or three of the scaled sum's four parts (offense ranged, offense melee, defense shooting, defense fight, each ÷ its form's SD) furthest from the army's mean of that part; the value is the raw column, the bracket the part's distance from that mean in SDs.

What each column is and how it is computed

Every number is one unit, alone, at its minimum size (the smallest size its datasheet prices), with its best legal loadout (below); no detachment, no joined character (except in Lends), marks off, no cover, no half range, Heavy weapons stationary, One Shot at a fifth (targets.js). Each unit fires its weapons' dice with its own unconditional abilities (unitfx.json, at the unit's level as the matrix reads them: a condition the engine cannot check, such as a Battle-shocked target or an objective, counts as not met: no shares). Every defender carries its own defensive abilities (the matrix's profiles). No turns alive, no delivery, no CP worth, no shares or clocks.

• The field. One meta state, the whole top quarter (T-569, build/field/states.json, its units copied into the JSON; field hash 8fd085059e24): 630 units in expected copies per nominal 2001.9-point list, each at the size the lists field it, with its datasheet's default wargear (allocate.js buildSide). 731 ranged guns and 627 melee lines. Its own shooting phase (every gun at β 6) removes 672.6 points, its fight phase 982.2; no fire is lost to saturation in either.
• The best legal loadout. Every legal squad at minimum size (docs/loadout.js, BSData's limits), scored by its offense into the field, ranged plus melee per 100 points; the first found wins a tie. 7 units differ from their datasheet's default wargear (appendix A).
• Offense, ranged (points per 100 points): enemy points destroyed per 100 of its own points in one shooting phase into the field. Each gun is a group of the kernel (allocate.js allocateTurn): one full volley's wounds into each field unit (A × e, e the matrix cell's long-run wounds removed per attack, the best of its profiles per target, Blast's extra attacks from the target's size), its fire spread σ ∝ R × (v ÷ v*)^β over the field's units (R the wounds present, v the points one volley removes, v* the gun's best), saturation and spill as the kernel does; destroyed points at points per wound (fluid targets, question 6). Every gun fires (a = 1). By class: the same with only the field's units of that class (matrix.md 6.2) as targets.
• Offense, melee (points per 100 points): the same for one fight phase, every charge landing (Lance on): the unit's blows as one line, each model its best weapon for the target, Extra Attacks on top (allocate.js's melee group); no melee into AIRCRAFT without FLY.
• Defense, per point (points per 100 points), shooting and fight apart: the field points spent to destroy it, per 100 of its own points. The unit enters the field as a marginal target: each field gun g sends it the share the targeting rule gives a target of its value, the rule's derivative as its wounds go to zero, m = q ÷ S' per wound present (q = (v_X ÷ v*)^β with v* the gun's best over the field and the unit, S' the gun's weights over the field at that v*). The points per wound it costs the field are Σ m c ÷ Σ m w (w the wounds one phase of g removes from it; c the field points that phase costs: a field unit's points split over its guns by the points each removes in the field's own phase; a melee line costs its unit's points), times its wounds, × 100 ÷ its points. A gun with nothing in the field to hurt would send it all its fire and is left out (none here). By weapon class: the same over the field's guns of one class, each gun classed by the profile it uses on the unit (Damage 3.5 or more or Strength 10 or more anti-tank; Damage 2.5 or more elite; 1.5 or more plasma; AP 1 or more or Strength 5 or more special; the rest small arms; V5's sorting), Devastating Wounds' mortal part as mortal (melee lines split by weapon). The field's mortal wounds outside attacks are not in it (their uses would be a guess).
• Defense, absolute (share of a phase): the field points needed to destroy it once by shooting, over the field's whole shooting phase (1731.7 points: every field unit with a gun).
• Lends (points per 100 of the character's points): tools/banner.js lend-only (the character's own attacks out; its rules and its wounds behind the squad in) picks the best squad by its multiplier over bodies and gives the squad's damage and durability added (wounds into the five stand-ins, hits from the five stand-in attackers, per 100 of its points). Beside it, the same squad's lend in field points: its offense with the character's attacking effects (leaderfx.json) on, less without; and the field points spent to destroy it with the character's defending effects on, less without; each per 100 of the character's points. Vouched conditions are not met, as everywhere. Bodyguards: a squad's own rule toward the character leading it, measured where the effects files give it dice.
• Mortal wounds outside attacks (the coverage's mortal kind): expected mortal wounds per use from kindfx.json's numbers (its v, else n × the chance of the roll × the damage dice), mortalfx.json where kindfx has none, × models for a per-model rule; priced into the field as one pseudo-weapon by the targeting rule (Feel No Pain and Feel No Pain against mortal wounds on), per use, per 100 points. When it fires, whether it hits every unit in range, and one-use rules are shown, never multiplied. Spawning: neither file says how much a use places, so nothing is computed (listed).
• Body: points and models at minimum size, wounds in all, Toughness (the highest of its models), save and invulnerable save (its front group), Feel No Pain, OC per 100 points (OC × models), Move, Leadership. Reach: the band of the weapon group that removes the most points in its phase (melee; short to 12"; mid to 24"; long beyond); melee worth counting when its fight phase removes at least half what its shooting phase does.

The walk (section 3), no weights: offense alone (ranged + melee, by sum); defense alone (shooting + fight, by sum); their scaled sum, each divided by its standard deviation over the 52 (population; offense 45.50, defense 186.18); their geometric mean, √ of the product of the same scaled values (which no rescaling reorders). Ranks of 52, 1 the highest. The standing lines use tools/tierbaseline.js's battery on the 52 alone (2,000 bootstrap resamples and shuffles, fixed seeds; each panel's patchDrop respected): ρ with its SE (Bonett and Wright) and lift over the shuffle; within one letter on each reviewer's own shape (our order cut at the reviewer's letter counts, ties broken at random and averaged), printed only as lift over shuffle; and ρ(score, points).

The tests

Every column

Offense (points per 100 points, one phase into the field)

Defense (field points to destroy it per 100 of its points; absolute: share of the field's shooting phase)

A class with no field gun that reaches and hurts the unit prints –.

Body, reach and loadout

Lends

Bodyguards: Tyrant Guard (Guardian Organism: noted; not in the dice: Feel No Pain on the leader's model only needs a selfFnp mod). A bodyguard's own wounds in front of its character add exactly its own defense in this fluid model (points per wound, the front group's profile), so the reverse lend is only what its rule changes in the dice.

Mortal wounds and spawning

Spawning: Biovores (Seed Spore Mines); Parasite of Mortrex (Parasitic Infection); Sporocyst (Seed Mucolids): not computed (how much a use places is in neither kindfx.json nor mortalfx.json).

The standing lines in full

Reviewers' shapes (S/A/B/C/D): 2026-10-03-tyranids-hivemind 4/12/17/9/3 (patchDrop: Pyrovores, Neurotyrant, Tyrannocyte, Toxicrene); 2026-10-03-tyranids-second 6/11/14/8/2 (patchDrop: Toxicrene, Neurotyrant, Tyrannocyte); Auspex (tuned on) 13/7/13/4/7.

What could not be computed exactly

• Spawning (Biovores, Parasite of Mortrex, Sporocyst): no numbers for how much a use places.
• Bodyguards' reverse lend (Tyrant Guard): the rule is noted in words only.
• Vouched conditions (a Battle-shocked target, an objective, a chosen enemy) are counted as not met everywhere, so effects that need them add nothing: this is the rule of no shares, not a measurement of their worth.
• Mortal wounds outside attacks are per use; how often a rule fires, and how many units it reaches, are not measured.
• The field's own mortal wounds outside attacks are left out of every defense column, for the same reason.

Decided alone

• Own abilities in, for every unit, at the matrix's unit level. Each unit (the Tyranids and the field's) fires with its own unconditional attacking abilities; a condition the engine cannot check counts as not met (no shares); a rule with a choice takes its first option; the army rule adds nothing (Synapse reaches others as an aura, which the matrix's unit level leaves out). The plan asks for abilities measured where the dice allow; the matrix's base context alone would have left out, for example, the Hyperadapted Raveners' Sustained Hits.
• The best legal loadout is the one with the most offense into the field (ranged plus melee per 100 points), first on a tie; defense does not depend on it here.
• Defense reads the targeting rule at the margin. The unit is added to the field as a target of vanishing size, so the share each field gun sends it is the rule's derivative and does not depend on how many of it there are; a field unit's points are split over its guns by the points each removes in the field's own phase (its melee line costs its whole points, since a fight phase is a separate phase). The field's units carry their datasheets' default wargear at the size the lists field them.
• By weapon class: a gun counts in the class of the profile it uses on the unit; a melee line splits by weapon; Devastating Wounds' mortal part is the mortal class; the field's mortal wounds outside attacks are left out.
• One-die re-rolls (re-roll one hit or wound roll a volley) are not a per-attack quantity: those 6,001 cells are computed at the volley's own size (the models with the weapon in one unit, the target's models), as ev.js plays them; every other cell is the matrix's size-free one.
• Mortal wounds outside attacks are priced per use as one pseudo-weapon by the targeting rule; how often and on how many units are shown, not multiplied. Spawning is listed, not computed.
• Lends: banner.js lend-only picks the squad; the field-point lend uses that squad at its own best loadout. Reach: melee worth counting at half the shooting phase's points; the main weapon is the group that removes the most.
• Presentation: the standard deviations are population ones over the 52; the driving columns are the parts furthest from the army's mean in SDs, two, or three when the third is at least half the second. The field's Tyranid units (38 of 630 lines) stay in it as targets and shooters: the field is the top quarter as a whole.

Doubts

• Defense per point leans to cheap bodies (ρ(defense, points) −0.35): cheap infantry draw the field's cheap guns, whose points per wound removed are high. It is what the measurement says, not a fault found; the absolute column is the one that tells a big monster apart.
• The cost split of a field unit's points over its guns (by points removed) is a choice; splitting by attacks or evenly would move the per-class columns and, less, the totals. Nothing here tests that.
• β stays 6, swept but not fitted; the field is one meta state; there is no cover, no range and no delivery anywhere, as the plan asks, so every gun reaches every target.
• Mucolid Spores and Spore Mines carry no weapons: their offense is 0 and their worth is the mortal wounds per use, which no form reads.

Appendix A: the default wargear rows

Defense does not depend on wargear here. With every unit at its default wargear the offense SD is 43.47. Standing lines at default wargear: scaled sum -hivemind 0.07 (SE 0.15, lift +0.07), -second 0.16 (SE 0.16, lift +0.16), Auspex (tuned on) 0.28 (SE 0.15, lift +0.29), ρ(score, points) −0.34; offense -hivemind 0.16 (SE 0.15, lift +0.16), -second 0.35 (SE 0.15, lift +0.35), Auspex (tuned on) 0.20 (SE 0.15, lift +0.21), ρ(score, points) −0.15; defense -hivemind 0.10 (SE 0.15, lift +0.10), -second 0.07 (SE 0.16, lift +0.06), Auspex (tuned on) 0.36 (SE 0.14, lift +0.37), ρ(score, points) −0.35; geometric mean -hivemind 0.08 (SE 0.15, lift +0.08), -second 0.21 (SE 0.16, lift +0.21), Auspex (tuned on) 0.29 (SE 0.15, lift +0.29), ρ(score, points) −0.31.

For the supervisor

design/decisions.md entry (paste-ready):

3 Oct: plan v4 step 1a, the Tyranid numbers and the walk (T-587)

• Built: tools/v4walk.js: for the 52 Tyranid pool units at minimum size with their best legal loadout (most offense into the field; default wargear in an appendix), offense ranged and melee (enemy points destroyed per 100 points in one phase into the top-quarter field, each gun by the one-phase targeting rule at β 6, every charge landing) and into seven unit classes; defense per point from the field's shooting and fight phases (field points spent to destroy it per 100 points, the unit as a marginal target of the targeting rule; a field unit's points split over its guns by the points each removes) and from six weapon classes; defense absolute (share of the field's shooting phase); lends (banner.js lend-only, and in field points); mortal wounds per use; body and reach. Each unit fires with its own unconditional abilities; vouched conditions are not met (no shares). tools/tyrtable.js walkTable, the fixed layout.
• Tests: parity of 200 cells against ev.js, worst 2.2e−16 (one-die re-rolls computed at their own volley, 6,001 cells); a second run byte-identical; the volleys equal allocate.js's; the shares conserved, and the marginal share equal to the kernel's for a vanishing target.
• The walk (no weights, nothing chosen): ρ against -hivemind / -second / Auspex (tuned on): scaled sum 0.04 / 0.14 / 0.26, offense 0.10 / 0.31 / 0.18, defense 0.10 / 0.07 / 0.36, geometric mean 0.03 / 0.19 / 0.26 (SE 0.14 to 0.16). ρ(score, points): −0.35, −0.17, −0.35, −0.31 (three forms below the −0.3 line). ρ(scaled sum, defense) 0.83, ρ(scaled sum, offense) 0.74: neither part above 0.9. Auspex's six S units over 165 points average rank 29 to 32 on every form and 5.8 on the absolute column alone (B1 19.2).
• Not computed: spawning (no numbers in the effects files); Tyrant Guard's reverse lend (its rule is noted in words only).
• Next: the full stop. Jordan reads the order against the three reviewers one unit at a time before step 1b or any other card runs.

design/scoring.md changelog line (paste-ready):

3 Oct

T-587, plan v4 step 1a, a report only, live scores unchanged: tools/v4walk.js, the Tyranid feature table at minimum size and best legal loadout: offense ranged and melee in enemy points per 100 points over one phase into the top-quarter field (allocate.js's kernel, β 6, no reach, every charge landing; by unit class); defense per point as the field points spent per 100 points to destroy the unit as a marginal target of the targeting rule (q ÷ S' per wound present; a field unit's points split over its guns by the points each removes; shooting and fight apart; by weapon class, Devastating Wounds as mortal); defense absolute as a share of the field's shooting phase; lends (banner.js lend-only, and in field points); mortal wounds per use (kindfx.json, else mortalfx.json) priced by the targeting rule; the walk's four forms (offense, defense, the sum scaled by population SDs, the geometric mean). Own unconditional abilities on, vouched conditions not met; one-die re-rolls at their own volley. Report: reports/tiers/2026-10-03-v4-step1a.md.