Hard to answer: does surviving everything but a burst explain what the ledger misses? (T-642 step B, 4 Oct)

A read-only check. No ledger number, page default, data file, benchmark or frozen input changes. Our own numbers from the datasheets' dice; unit names only, no rules text.

The short answer

• The idea doesn't hold, as we pre-registered it. We counted, for each Tyranid unit, how many enemy units of a typical army could wipe it (or break it below a quarter) in one go, and how many enemy points would have to take turns at it until one did. Ranking units by that ("Answer Soak") instead of by the ledger's ordinary Soak (enemy points needed to wear it down) does not move the units the reviewers rate above the ledger up, or the over-rated ones down. The correlation is −0.04 (chance alone gives that or more 62% of the time). Four of the seven named units move the predicted way (Exocrine up; Toxicrene, Tervigon, Tyrannocyte down), but Tyrannofex and Maleceptor go down and Haruspex stays put.
• Why: the two ways of counting toughness mostly agree (rank correlation 0.90). Among Tyranids, the units that take many points to wear down are the same ones few enemies can finish in one go. What Answer Soak adds is mainly points cost: the dearer a single big model, the rarer anything that removes it whole (Exposure, the share of the enemy army that can do it, follows points at 0.84).
• The Hierophant, as we feared: it becomes the hardest Tyranid unit to answer by a distance (about one enemy unit in fifty can finish it in an activation) and climbs from 6th to 1st on toughness; the Harridan goes from 26th to 4th. The reviewers rate both near the bottom. This is step 12's trap again: a finishing rule on the defending side rewards sheer bulk, and can't tell a cat-and-mouse piece from an expensive brick.
• Both halves together (the "cat and mouse" score) do lift the named units more than either half alone, as predicted (5 of 7 move the right way; average move in the predicted direction 2.1 places, against 0.7 for Answer Soak and 0.9 for step A's Burst). But across all 52 Tyranids it is still no real signal (correlation 0.13, chance 18%).
• The previews say the same. Putting Answer Soak in Soak's place makes the ledger worse on both armies (seven headline lists: ρ 0.490 → 0.465, pairwise 70.8% → 69.5%). Adding step A's Burst too (0.508, 71.6%) is below Burst alone (0.516, 72.1%).
• Recommendation: don't build the defending half. If T-642 continues, it is step A's Burst on Kill (the Space Marine signal) judged as an ordinary step; this check adds nothing to it. What the reviewers mean by "hard to answer" seems to lie outside what one activation's dice can see (range, hiding, mobility, what the enemy would rather shoot).

The numbers

The pre-registered test (Tyranids, 52 units, all graded by the headline lists)

Verdict: doesn't hold (needed ρ > 0 with p < 0.05 and at least 4 of the 7 named units; got ρ −0.04, p 0.62, and 4 of 7).

Single predictors of the consensus (Spearman, not pre-registered): Soak −0.09, Answer Soak −0.02, Exposure (lower better) 0.00. Toughness, by either count, says almost nothing about how the reviewers grade Tyranids. Answer Soak and Soak agree at 0.90; Answer Soak and points cost 0.64; Exposure and points cost 0.84.

The named units

Ranks of 52 (1 = hardest to remove; for the combined score, best by Kill + Soak and by Burst + Answer Soak).

Mean move in the predicted direction over the seven: Answer Soak +0.71 places, Burst +0.86, combined +2.14 (the pre-registered combined prediction, point 3: holds for the named units; its correlation over all 52 is 0.13, p 0.18).

The Tyrannofex is already the toughest Tyranid by Soak; by Answer Soak five units pass it: three dearer single models (Hierophant, Norn Emissary, Harridan) and two six-model squads of tough bodies (Tyrant Guard, Hive Guard). The Exocrine, Haruspex, Toxicrene, Trygon, Mawloc and Pyrovores sit together in the middle: the same handful of enemy units (big melee elites and the C'tan) can finish any of them about as often.

The Hierophant (and the Harridan)

Answers 0.02: only the Imperial Knights' big walkers have a real chance (a quarter to a third) to finish it in one fight, and the typical army holds few of them. Its Answer Soak is more than twice the next unit's, so it ranks 1st (Soak had it 6th); Exposure ranks it 1st too. The Harridan (Answers 0.08) goes 26th → 4th. The reviewers put both at 44.5 of 52. As written in the pre-registration, this is step 12's trap: the finishing rule on the defending side is mostly a reward for being one very expensive model.

The previews (not steps)

Answer Soak per phase × 0.326 (Tyranids; × 0.389 Marines) in each solo form's soak (every β), so the median ranking form's soakEnemy is unchanged; the Hold line reads Soak's shooting number and moves with it. "Both": the same and step A's Burst in Kill's slot (step A's constant). Everything else at the step-6 baseline; scored as tools/ledgerstep.js.

Moved most by Answer Soak, Tyranids: Hierophant 42 → 30, Neurogaunts 29 → 38, Termagants 36 → 44, Hive Guard 28 → 21, Hormagaunts 26 → 32 (big squads need 16 of 20 dead, which many elite enemy units manage). Marines: Terminator Assault Squad 63 → 1, Terminator Squad 60 → 2, Astraeus 75 → 28, the Centurion squads 34 → 13 and 30 → 10 (a five-model unit of tough bodies with good saves must lose four in one activation: very few enemy units do it).

Space Marines (a transfer check, no named units)

84 units. Answer shift with the residual ρ 0.136, p 0.11 (−0.069 to 0.328); Exposure shift 0.118, p 0.14; the combined shift 0.310, p 0.002 (0.104 to 0.504), against step A's Burst shift alone 0.263, p 0.008. So on Marines the combined score's signal is mostly step A's; the defending half adds a little to the correlation and, in the preview, takes agreement down.

Every Tyranid unit (by ledger rank)

Soak and Answer Soak in enemy points per 100 of ours (Soak shoot + 0.9 × fight, the page's; Answer Soak the same weighting). Shift: Soak rank − Answer Soak rank (+ harder to answer than its Soak says). Answers: expected enemy unit copies (of 15.2) able to finish it in one activation, each at its better phase. Exposure: the share of the enemy army's 2,000 points that answers it (rank 1 the least exposed). Combined: rank by Kill + Soak ranks → by Burst + Answer Soak ranks. Residual: ledger rank − consensus rank among the graded. Its likeliest answers: the enemy units with the most expected finishes (copies × chance), the chance one copy finishes it, and the phase.

"(M/V)": MONSTER or VEHICLE, finished only when every model is destroyed.

Method notes and doubts

• The same exact walk as step A (tools/burst.js walk(), checked against ev.js's exact kill calculation), now with the enemy unit firing and our form as the target. Our defending modset reaches the dice (96 of the 819 Tyranid solo forms have one, from two detachments); step A's numbers reproduce unchanged (ρ 0.079) after the change.
• No carried damage between enemy activations, by the premise (a unit that isn't finished gets away). With damage carried, Answer Soak would drift toward the ordinary Soak, which already agrees with it at 0.90.
• The enemy always activates into us, its whole phase, the charge always landing in the fight; as the ledger's Soak. Which target the enemy would rather shoot is not modelled (the colleague's "cat and mouse" is partly that).
• Fractional copies: the typical army holds 15.2 unit copies over 611 distinct rows, most at a fraction of a copy; a row of c copies survives with (1 − P)^c, a smooth stretch of whole copies.
• The likeliest answers are a short list of elite melee units (Allarus Custodians, the C'tan Shards, Vertus Praetors, Skorpekh Destroyers), the Defiler's guns and the Knights. Answer Soak leans on how many of those the typical army holds; a different meta would move it more than it moves the ordinary Soak.
• Our own abilities count only as the ledger's Soak counts them (profiles and the defending modset); a bodyguard's rules, healing and Soak effects are outside both (the page's Soak effects then act on the preview's numbers as on the ordinary ones).
• Pre-registration: committed alone (c718a81f45) before the first run that read a letter, and unchanged since (the enemy-lands weight was set to the page's 0.9 at the baseline before that commit). Step A's tables were known when it was written (so the named part was not blind; the correlation test was).

Files and runtime

tools/burst.js --defend (node tools/burst.js --defend --write: Tyranids 50 s with step A and the previews, 13 s without; --army space-marines, 4 min), tests/unit/burst.test.js (Answer Soak by hand), reports/tiers/2026-10-04-burst-defend.json and -space-marines.json (every unit's Soak, Answer Soak per phase, Answers, AnswerPoints, Exposure, ranks, combined, consensus, residual, likeliest answers; the statistics; the previews).

Pre-registration (written and committed before the reviewers' letters were read for this check)

Everything below is fixed before the first run of step B that reads a reviewer letter. The results are added in a later commit; any change to this section after that commit would be marked as such. Step A's tables (which show each unit's consensus and residual) were read before this was written: the named units come from them, so the named-unit part is not blind; the correlation test is.

The idea being tested

Jordan's colleague (4 Oct), the defending half: big chassis such as the Exocrine and the Tyrannofex are not worn down by small fire; only units that can finish them in one go threaten them. Players play cat and mouse with them, and a piece that is never finished keeps working. The step-A finishing rule, now on our side: our MONSTER or VEHICLE unit counts as removed only when every model is destroyed in one enemy activation; any other unit when fewer than 25% of its starting models remain. An activation that falls short is wasted (the target runs and hides, the premise), so damage is not carried from one enemy activation to the next.

The pieces (tools/burst.js --defend)

• Our unit's form: each Tyranid unit's ranking form at the step-6 baseline, as in step A (the same rebuild through tools/ledger.js on the frozen inputs). As a target: its allocation stages as the ledger's Soak builds them (ledger.js stagesOf: each defender group at its size, front first), each model with its wounds, each stage's profile with the member's defending modset (the detachment's and army rules' always-on defensive effects, as Soak uses them; the datasheet's own defensive abilities are in its profile): our modset is passed to the dice in place of "none". MONSTER or VEHICLE from the datasheet's keywords.
• The enemy: each unit of the ledger's typical 2,000-point army (tools/ledger.js typicalArmy and prepArmy: its sizes, default wargear, its own attacking effects), rows of the same datasheet, size and points merged (copies summed). One activation of one copy: its shooting phase (every gun its best profile into us by expected removal, as step A picks it, One Shot at a fifth all or nothing), or its fight phase (the charge lands, every model its best melee weapon, Extra Attacks on top; never into AIRCRAFT without FLY). The same exact walk as step A (no simulation).
• P_u (shoot), P_u (fight): the chance one copy of enemy unit u finishes our form in that phase alone. P_u = the better of the two (the enemy picks the phase that answers us; written down here as the choice).
• Answers = Σ_u copies_u × P_u (expected enemy unit copies in the typical army that can finish it in one activation). AnswerPoints = Σ_u copies_u × points_u × P_u. Exposure = AnswerPoints ÷ 2,000 (the share of the enemy army's points that answers it; lower is harder to answer). Reported, and tested as a secondary reading.
• The score we rank by (primary): Answer Soak, per 100 of our points, the defending twin of the ledger's Soak in the same units, so a rank shift against Soak measures "finished in one go" against "worn down", not cost: the enemy points that must activate into the form, one activation at a time, until one finishes it. The enemy draws its cheapest expected answer first (ascending points_u ÷ P_u, the twin of Soak's most efficient first), each copy once, each activation fresh; a row of c copies (c may be fractional) costs points × (1 − (1 − P)^c) ÷ P and survives with (1 − P)^c. If the whole army fails, it comes again (the expected cost ÷ the chance the army finishes it at all). Computed per phase like the ledger's Soak (shooting answers alone; fight answers alone), then Answer Soak = shoot + 0.9 × fight, the page's own weighting of Soak at the baseline (its enemyLands: enemy charges landing 0.6 × the baseline's lands scale 1.5 = 0.9). A form nothing can finish in a phase: that phase's Answer Soak is infinite (ranked hardest).
  • Why not Exposure as the primary: Exposure ignores our cost, while Soak is per point, so Soak rank − Exposure rank would mostly measure points cost (an expensive brick is rarely finished), which is step 12's trap; we report it beside, judged by nothing.
• Soak (the ledger's): the ranking form's soak["6"].shoot + 0.9 × soak["6"].fight (the page's soakEnemy at the baseline, before Soak effects), per 100 points, from docs/lab/ledger/tyranids.json.
• Answer shift = Soak rank − Answer Soak rank among the 52 (rank 1 the hardest to remove; positive: harder to answer than its Soak says).
• The combined "cat and mouse" score: the rank-sum of step A's Burst rank and the Answer Soak rank, against the rank-sum of the Kill rank and the Soak rank. Combined shift = rank(Kill rank + Soak rank) − rank(Burst rank + Answer Soak rank) (positive: it rises when both halves use finishing). Burst and Kill as step A computes them (its natural mode, β 6).

The yardstick (unchanged from step A)

Consensus: each unit's mean letter over the headline Tyranid lists that grade it (auspexFull, hivemindFull, secondFull, maelstrom, astrategas; S 5 … F 0), ranked best first, ties sharing the mean rank. Residual: the ledger's rank among the graded − the consensus rank (positive: the reviewers rate it better than the ledger). Ungraded units are left out of every statistic.

The prediction (if the idea holds)

1. Primary: Spearman ρ(residual, Answer shift) > 0.
2. Named units: Exocrine, Tyrannofex, Maleceptor, Haruspex rise (Answer shift > 0); Toxicrene, Tervigon, Tyrannocyte fall (Answer shift < 0). A unit with no move counts as not moving the predicted way.
3. Combined: the combined shift lifts the named units more than either half alone: the mean of (direction × shift) over the seven named units is larger for the combined shift than for the Answer shift and than for step A's Burst shift; and ρ(residual, combined shift) is reported beside ρ(residual, Answer shift).
4. Secondary, reported, not judged: ρ(residual, Soak rank − Exposure rank, Exposure ranked lowest first).

Tests: one-sided permutation p (10,000 shuffles of the residual, seeded) and a 95% bootstrap interval (10,000, seeded), as step A.

Verdict: "holds" when the primary ρ is positive with p < 0.05 and at least 4 of the 7 named units move the predicted way; otherwise "doesn't hold".

What we expect, honestly

• All seven named units are MONSTERs, so the finishing rule treats them alike; what separates them is wounds, Toughness, saves and Feel No Pain per point. We are not confident the named part will pass: Toxicrene, Tervigon and Tyrannocyte are big monsters too, and may well rise with the others.
• The Hierophant: we expect it to be among the hardest Tyranid units to answer (the most wounds of any, few enemy units can finish it in one activation; its Exposure the lowest) and to rise by Answer Soak, while the reviewers rate it low (it is not one of the named units, and not in the verdict). If it does, that is step 12's trap again: a measure that rewards sheer bulk lifts every big tough unit, the ones the reviewers like and the ones they don't, and the idea in this form cannot tell a cat-and-mouse piece from an expensive brick. It would say the reviewers' "hard to answer" is about something the dice of a single activation don't see (range, mobility, hiding, cost against what it threatens).

The preview (not a step)

The ledger with each solo form's soak[β].shoot and .fight replaced by its Answer Soak per phase (every β the same), × one constant c so the median ranking form's soakEnemy (shoot + 0.9 × fight) is unchanged; an infinite phase is set to the largest finite value of its army; everything else at step 6 (Hold reads Soak's shooting number, so it moves with it: said beside the result). And a second preview with both this and step A's Burst in Kill's slot. Scored on the headline lists (pairwise and ρ, Tyranids; Space Marines too if it runs in reasonable time). Previews only.