Candidate audit · October 19, 2026 · Known regression
A win can cost
the home opener.
In a valid candidate allocation with declared rankings, a fictional team wins its title game and improves from final No. 14 to No. 13, yet changes from host to visitor. The candidate fails entry-benefit monotonicity for these allowed inputs.
Hold this candidate for repair. It is not adopted. This is an allocation counterexample, not an observed season or proof that NRR produces the supplied ranking pair.
Winning changes somebody else’s bye.
Fixture labels identify teams, not final seeds. Fixture 14 is pre-title No. 14 in both worlds. Its title-game opponent is Fixture 05. All other title-game winners stay fixed. Both declared final orders place Fixture 17 at No. 9 and Fixture 09 at No. 17; neither is an NRR refit. The winning intervention moves Fixture 14 up one place; it does not worsen its final rank.
| Item | Fixture 14 loses | Fixture 14 wins |
|---|---|---|
| Final rank | 14 | 13 |
| Selected for a champion bye? | No · runner-up | No · champion outside the selected five |
| Entry benefit | Hosts opener | Visits for opener |
| Opening game | Fixture 14 hosts Fixture 17 | Fixture 13 hosts Fixture 14 |
| Wins required for title | 5 | 5 |
| Five selected champions | Fixture 04, Fixture 05, Fixture 06, Fixture 07, Fixture 08 | Fixture 04, Fixture 06, Fixture 07, Fixture 08, Fixture 17 |
- Fixture 05’s loss removes it from the champion list, although its pre-title top-ten claim still gives it a bye.
- Fixture 17 enters the selected five champions and receives a new opening exemption. Fixture 14 won its league but remains outside the selected five.
- The single-bye capacity stays eight. Fixture 10 loses its bye claim and joins the opening hosts with a higher pre-title priority.
- Four host places go to Fixtures 10–13. Fixture 14 becomes a visitor despite its win and improved rank.
This is a spillover between champion selection and retained hosting priorities. Treating only the winner’s own ranking as the incentive check would miss it.
Inspect both complete allocations and every changed benefit
| Team | Loss world · final rank / benefit | Win world · final rank / benefit |
|---|---|---|
| Fixture 01 | 1 / Double bye | 1 / Double bye |
| Fixture 02 | 2 / Double bye | 2 / Double bye |
| Fixture 03 | 3 / Single bye | 3 / Single bye |
| Fixture 04 | 4 / Single bye | 4 / Single bye |
| Fixture 05 | 5 / Single bye | 5 / Single bye |
| Fixture 06 | 6 / Single bye | 6 / Single bye |
| Fixture 07 | 7 / Single bye | 7 / Single bye |
| Fixture 08 | 8 / Single bye | 8 / Single bye |
| Fixture 17 | 9 / Opening visitor | 9 / Single bye |
| Fixture 10 | 10 / Single bye | 10 / Opening host |
| Fixture 11 | 11 / Opening host | 11 / Opening host |
| Fixture 12 | 12 / Opening host | 12 / Opening host |
| Fixture 13 | 13 / Opening host | 14 / Opening host |
| Fixture 14 | 14 / Opening host | 13 / Opening visitor |
| Fixture 15 | 15 / Opening visitor | 15 / Opening visitor |
| Fixture 16 | 16 / Opening visitor | 16 / Opening visitor |
| Fixture 09 | 17 / Single bye | 17 / Single bye |
| Fixture 18 | 18 / Opening visitor | 18 / Opening visitor |
Only the fifth title-game winner changes. Pre-title order, participants, conference classifications, eligibility and all other title results are fixed. The complete input and reason ledgers are in the download.
52,224 controlled comparisons. Ninety host losses.
18,432same-rank comparisons · 30 regressions
33,792improved-rank comparisons · 60 regressions
0bye or berth downgrades found in this grid
The design uses thirty fictional ranked teams, eighteen participants in nine disjoint title games, all 512 winner vectors, adjacent or mirrored pairings, and two before-result orders: the pre-title order or a swap of positions 9 and 17. Each loser is changed to the winner; its final rank stays fixed or improves one or two places, with other teams’ relative order preserved. Champion selection and the full allocation are recomputed. Comparisons that would move above first place are skipped.
| Pairing and before-result order | Comparisons | Same-rank / improved-rank regressions |
|---|---|---|
| adjacent · pre-title order | 13,056 | 0 / 0 |
| adjacent · swap pre-title9 and17 | 13,056 | 0 / 0 |
| mirrored · pre-title order | 13,056 | 0 / 0 |
| mirrored · swap pre-title9 and17 | 13,056 | 30 / 60 |
The structural ordering is double bye, single bye, host, visitor, then exclusion. It expresses a preference for the entry benefit; it is not a measured welfare or title-probability ordering. No actual NRR scores, polls, play-by-play or title-game score refits were computed. These counts are not a real-season frequency, and nearby comparisons share inputs. No-failure cells do not prove a general property.
A lost host does not alone determine the whole path.
The first opponent changes from Fixture 17, final No. 9, to Fixture 13, final No. 14. Final rank alone suggests a weaker opponent after the win; the hosting reward moves the other way. To separate those effects, the same counterexample was evaluated through the complete bracket with fixed ability assumptions.
| Fixed assumption across both worlds | After title-game loss | After title-game win | Difference |
|---|---|---|---|
| Equal ability · no home effect | 3.1250% | 3.1250% | +0.0000 pp |
| Equal ability · home effect 0.2 | 2.8816% | 2.3593% | -0.5223 pp |
| Fixed pre-title ability order · home effect 0.2 | 0.0269% | 0.0164% | -0.0105 pp |
| Fixed before-result final ability order · home effect 0.2 | 0.0128% | 0.0152% | +0.0023 pp |
With equal abilities and no home effect, five required wins give exactly 1/32 in either world. A positive home effect makes the win world worse under equal abilities. Fixing abilities to the pre-title order also gives a decrease; fixing them to the before-result final order gives an increase. Actual competitive impact is therefore not established by the hosting loss or any one synthetic strength model.
Probability model, redraws and verification
Games are independent with logistic win probability from the fixed ability difference plus home advantage of zero or 0.2 logit units. Ordered ability is (31 minus the chosen baseline rank)/6. The home effect is an assumption, not an estimate. No rest effect is added, and the observed title result does not update assumed ability.
The calculation uses the candidate’s actual opening hosts, both final-rank redraws, higher-final-ranked campus hosts in quarterfinals and semifinals, and a neutral final. Quarterfinal pairing slots 0/3 feed one semifinal and 1/2 the other, matching the existing bracket sensitivity model. It enumerates 65,536 final-pair states and integrates each final analytically per world. Total mass is one; equal-neutral probabilities match every entrant’s analytic entry-round probability. There is no Monte Carlo sampling error, but there remains substantial model uncertainty.
The ability-order sensitivity and repair screen were specified after discovering the counterexample and frozen separately before their numerical evaluation. They are follow-ups, not independent holdouts.
Keep the candidate on hold. Test a repair before choosing it.
The earlier recommendation is withdrawn pending repair and validation. Keep the frozen candidate and six historical matches as evidence; matching two seasons does not erase this counterexample. No active selection rule or NRR formula changes automatically.
A post-discovery screen gave opening hosts to the four highest final-ranked opening teams while retaining the field and bye priorities. It found 0 entry-benefit regressions in the same 52,224 comparisons. In this witness, Fixture 14 changes from visitor after losing to host after winning. The repair abandons retained hosting floors when they conflict with final order. Its zero in the reused grid does not prove strategy-proofness or protect every later path.
- Build a separately versioned research candidate for final-order hosting; preserve this failing version and do not switch the active simulator.
- Expand result/ranking interventions, conference/participant configurations and explicit eligibility/cancellation cases. Use independent fixtures after the repair is frozen.
- Run actual title-game score changes through a frozen ranking generator and champion-selection pipeline before claiming that this exact ranking-pair failure is reachable in NRR.
- Compare full bracket outcomes under declared, separately validated strength assumptions; preserve reversed conclusions and missing evidence.
- Revisit the hosting/protection tradeoff with a recorded owner decision before adoption. Keep the broader historical-coverage gate.
Reproduce and inspect
Run node scripts/audit-candidate-incentives.mjs, node scripts/audit-candidate-paths.mjs, node scripts/audit-candidate-strength-sensitivity.mjs and node scripts/audit-host-priority-repair.mjs from the matching source. Each study checks its own frozen source and input hashes; earlier candidate files remain unchanged.