How Conquest Lab Validates Unknown Stage Power and Enemy Formations

A submission is a claim, not a verified stage

When someone submits an unknown stage, Conquest Lab receives a claim containing a stage number, enemy power, and five-position enemy formation. That row stays separate from the reviewed stage data. It does not immediately change the Stage Check, the recommender, or any verified recommendation.

The first question is not “Does this look believable?” It is whether each part of the claim survives independent checks. Power, hero identity, exact position, neighboring-stage structure, duplicate rules, and corroborating evidence are evaluated separately.

The fixed-stage assumption makes validation possible

Conquest Lab treats every Conquest stage as having one canonical enemy power and one canonical enemy formation in the order front left, front right, back left, back middle, and back right. The same stage does not rotate between alternative definitions, and one enemy formation does not contain duplicate copies of a hero.

The canonical record can be written as:

Here, p(s) is the enemy power for stage s, and H(s) is the ordered five-hero formation. A later report for a known stage must match the stored definition. A conflict is investigated rather than saved as a second valid version.

The fixed Whiteout Survival counterpart can also provide an external cross-check when the equivalent stage record is available. It is corroboration, not permission to skip manual review.

Hard checks happen before any advanced math

Some submissions can be rejected or returned for correction without estimating anything. These are structural rules rather than statistical judgments.

These checks catch many random entries immediately. Statistical analysis is reserved for structurally valid claims about stages that are not yet canonical.

What the current workbook shows

The July 19 workbook contains 693 Conquest rows covering 329 populated stages. A stage may appear in multiple battle rows because different player formations were tested against the same enemy. Wherever a stage repeats, the recorded enemy power and ordered enemy formation agree.

This repeated agreement matters. It supports the model that stage identity determines a fixed enemy definition while player attempts, outcomes, and remaining heroes can vary.

Enemy power also follows a structured progression. It does not rise by one constant amount each stage, but short local sections are smooth enough that a hidden value can be estimated and backtested. The model therefore uses nearby stages rather than forcing one equation across the entire game.

Estimating a missing stage's enemy power

Enemy power grows proportionally, so the calculation is more stable in logarithms. Let p(s) be the enemy power at stage s, and define y(s) = ln(p(s)).

When a missing stage lies between verified lower stage a and verified upper stage b, geometric interpolation gives:

This is equivalent to drawing a straight line through log power rather than raw power. It is appropriate when growth is approximately proportional and can estimate one stage or a multi-stage gap.

A leave-one-stage-out backtest temporarily hid each known interior stage and estimated it from the nearest verified stage below and above. The median absolute error was about 0.23%. Approximately 90% of estimates were within 2.0%, and 95% were within 3.1%. Larger misses were concentrated around sharper progression boundaries, which is why an estimate is reported with uncertainty instead of used as automatic proof.

A worked power example of this

Suppose two verified surrounding stages have scaled power indexes of 100 and 108, and the unknown stage sits exactly halfway between them. The geometric estimate is:

A submitted index of 104 is almost identical to the estimate. Its log residual is approximately ln(104) − ln(103.92) ≈ 0.0008, so the power is highly plausible.

A submitted index of 135 has a residual of approximately ln(135) − ln(103.92) ≈ 0.262. That is far outside the expected local movement and would be held for a screenshot, video or independent review and confirmation.

The values in this example are scaled teaching values, not private enemy powers. The point is that a random number must fit both surrounding values and the proportional rate between them.

The wider weighted least-squares model

Two-point interpolation is transparent, but a wider local window can reduce sensitivity to one unusual neighbor. Build a design matrix X whose rows represent verified stages near the unknown stage. Columns can include a constant, stage number, stage squared, and locally observed block-position indicators. Let y contain the logarithm of enemy power.

The diagonal matrix W assigns larger weights to nearby stages and smaller weights to distant stages. One possible distance weight is w(j) = 1 / (1 + |j − s|), although the final weighting rule should be chosen through backtesting rather than convenience.

The predicted log power is x(s)ᵀβ̂, and the predicted power is:

p̂(s) = exp(x(s)ᵀβ̂)

This model can follow local curves and repeated rise-and-drop behavior without declaring a universal rule such as “every fifth stage must drop.” The local data determines whether a block feature is useful.

Residuals, uncertainty, and anomaly thresholds

After predicting the power, compare the submitted value with the model:

A proportional percentage error can also be reported as |p submitted / p predicted − 1|. The log residual is preferable inside the model because equal proportional errors above and below the estimate are treated more symmetrically.

To compare residuals across different parts of the stage sequence, divide by a robust local error scale. A median-absolute-deviation estimate is less distorted by a few extreme stages than ordinary standard deviation:

z robust = |r − median(r local)| / [1.4826 × MAD(r local)]

A carefully fabricated value can be chosen near the predicted curve. That is why a low residual supports plausibility but never proves that the submitted screen existed.

Representing a five-hero formation as a matrix

Power is continuous. Hero identity and position are categorical. Matrix algebra handles that difference by encoding each formation as a 5 × N one-hot matrix H(s), where N is the number of known heroes.

• Row 1 represents front left.
• Row 2 represents front right.
• Row 3 represents back left.
• Row 4 represents back middle.
• Row 5 represents back right.
• Every row contains exactly one 1.
• Every hero column can contain at most one 1, enforcing the no-duplicate rule.

The number of exact position matches between two formations is:

The score ranges from zero to five. It counts the same hero in the same slot. A separate hero-set overlap score ignores position and measures how many heroes appear in both formations. Keeping these scores separate distinguishes “same roster, rearranged positions” from “different roster entirely.”

A weighted average of nearby canonical matrices produces a position-probability matrix:

Each cell in Q(s) estimates how often a hero occupies a position in the relevant local neighborhood. Additional one-hot matrices can encode troop type, hero generation, rarity, frontline versus backline role, and other known structural properties.

Scoring a submitted formation

Let the submitted hero in position i be hᵢ. A simple position log-likelihood is:

The small value ε prevents an unseen hero-position pair from producing an undefined logarithm. This score should be combined with structural evidence rather than used alone.

A fuller formation anomaly score can include:

A formation = w₁d position + w₂d hero-set + w₃d generation + w₄d troop + w₅d role + w₆d transition

• Position distance: how unusual each hero's exact slot is.
• Hero-set distance: how little the submitted roster overlaps nearby stages.
• Generation distance: whether the submission jumps far outside the local generation profile.
• Troop distance: whether infantry, cavalry, and archer placement is structurally unusual.
• Role distance: whether frontline durability and backline functions differ sharply from nearby formations.
• Transition distance: whether the change from the lower stage and into the upper stage is much larger than surrounding transitions.
• Stages block: stages come in block sets with slightly different increase and decrease rates. More easily identified in the earlier stages.

The weights should be calibrated on known stages by hiding formations and measuring whether the correct formation ranks above alternatives. Until that validation is strong enough, the score should be described as a screening method, not as an automatic verifier.

Why formation math cannot uniquely solve every missing stage

Nearby power values tightly constrain a missing number. Formations do not behave the same way. Several heroes can change at once, positions can be rearranged, and multiple candidate lineups can share the same generation, troop, and role profile.

Formation mathematics can reliably perform three narrower jobs:

• Reject impossible structures such as duplicate heroes or invalid slots.
• Flag a submitted lineup that is extremely inconsistent with the surrounding stage block.
• Rank several candidate formations by plausibility and explain why one fits better.

It cannot prove the exact unseen five-hero lineup from stage number and power alone. A model could rank the true formation first and still be unable to distinguish it confidently from several alternatives.

The evidence ladder

A clear screenshot showing the stage, enemy power, and all five positions is direct evidence. Two genuinely independent submissions that match exactly are strong corroboration. A matching fixed Whiteout Survival counterpart record provides another external check. None of these should overwrite an existing canonical conflict without investigation.

After verification, the stage is promoted once into the canonical stage table. Later matching reports support the same record rather than creating duplicate stage definitions.

Our end-to-end review workflow when dealing with uncertain submissions

1. Quarantine the submission. Keep it in the review queue and away from verified recommendations.
2. Run hard checks. Validate stage, positive power, hero dictionary, five positions, and no duplicate hero.
3. Check for a canonical conflict. Known stages must match exactly and are never overwritten automatically.
4. Estimate unknown power. Use geometric interpolation and a weighted local model.
5. Back the estimate with uncertainty. Compare residuals with held-out errors from similar local windows.
6. Build formation features. Measure exact positions, shared hero set, generation, troop, role, and transition fit.
7. Score rather than invent. Rank the submitted formation against plausible alternatives without presenting a predicted lineup as fact.
8. Seek corroboration. Request a screenshot, direct observation, an independent matching submission, or a matching fixed counterpart record.
9. Record the decision. Save the reason for rejection, hold, corroboration, or verification so future reviews remain consistent.
10. Promote once. Move the accepted stage definition into canonical data and leave the source submissions in the audit trail.

This approach makes random numbers easy to challenge while also protecting legitimate unusual stages from being rejected solely because they differ from a simple trend.

The current website keeps unknown-stage submissions in a review queue. The mathematical methods in this guide support that review; they do not automatically turn a submitted row into verified data.

For the related evidence model, read Understanding Power Ratios, FQI and Evidence Quality. To provide a reviewable record, use How to Submit Useful Battle Data or open the battle submission form.