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9. The break-even decides; the bands describe

Status: Accepted · Date: 2026-08 · Evidence: docs/bridge-band.md, sections 2 and 4

Decision

When upgrade_gain is measurable, bridge_advantage = ARR × upgrade_gain decides whether to bridge. The ARR bands decide which bridging answer to give. Without a measurable upgrade, the bands decide alone and the result is marked provisional.

Context

The decision rule places ARR in one of four bands and recommends from that. ARR is measured against the oracle — a full reindex — so it answers "how much of a rebuild does this adapter recover". That is not the question a user is deciding: they are choosing between bridging and doing nothing.

ADR 5 added the comparison against the current model, and it caught the case where bridging lost. It did not catch the reverse.

Evidence

Fifteen runs over five corpora searched with queries real people typed — StackExchange questions and financial questions, 222,680 documents and 5,761 human-judged queries — scored with ranx.

criterion agrees with the measured outcome
ARR bands alone 10/15
bridge_advantage > 1 14/15

Every disagreement went one way. The four runs where bridging genuinely helped:

corpus ARR gain advantage banded as measured
programmers 0.55 1.96 1.071 caution +4.2%
english 0.56 1.89 1.052 full_reindex +3.8%
gaming 0.73 1.52 1.108 caution +7.4%
fiqa 0.51 2.44 1.247 full_reindex +16.0%

The bands rejected all four, including a 16% improvement.

The mechanism is the anti-correlation in docs/bridge-band.md, section 3: gain and retention pull against each other at −0.958. A large upgrade means the old model was weak, a weak source space carries less recoverable structure, and the adapter therefore lands at a low ARR precisely when the upgrade is worth having. The bands read low ARR as "an adapter cannot bridge this" when what it actually meant was "there was a lot to bridge".

Consequences

  • T1 agreement rises from 10/15 to 13/15, and the four genuine wins go from 0/4 recommended to 4/4.
  • The two remaining misses are a −0.7% run — a tie in any reading — and one whose break-even fell inside the noise band, where the result now says the two options cannot be told apart rather than picking one.
  • The bands keep a real job: bridge_sufficient when little of a reindex is left on the table, bridge_and_migrate when a lot is. That is what ARR is genuinely good at.
  • Nothing changes at T0. There is no break-even to consult, the bands decide alone, and the result is provisional.

Alternatives

Widen the bands. Rejected: the bands are not mis-tuned, they are answering a different question. No threshold on "fraction of a reindex recovered" can express "better than what I have".

Report both and let the user choose. Rejected. The report already showed both numbers and led with the band; a reader who has to multiply two figures in their head to find out whether the headline is right is not being helped.

Replace ARR with the advantage everywhere. Rejected. ARR is what the decision bands were calibrated against, what every recorded measurement holds, and the right answer to "how much am I leaving on the table". Both numbers are worth having; only one of them is the decision.