shadowgate report: demo-n400-s0-serve

Run demo-n400-s0-serve · mode serve · 400 decisions · tiers fast → slow

Summary

BREACHSkipped-case error vs references exceeds tolerance 5%: the lower bound 8.9% is above it. From the audit alone (weighted disagreement 10.8%, interval 5.1%-19.4%) the status would be BREACH; that is what a run without references reports.

The fast tier (fast) answered 65% of 400 tasks without escalating. On those, it disagrees with slow on an estimated 10.8% (95% CI 5.1–19.4%, 89 audits, n_eff 84). Against reference answers, the skipped cases are wrong on 12.3% (95% CI 8.9–16.9%, 260 graded). That is about 32.0 wrong answers among the 260 skipped cases (23.0–43.8).

Answered by fast tier
65.0%
260 of 400 tasks
Escalation rate
35.0%
95% CI 30.5–39.8%
Served accuracy
92.0%
95% CI 88.9–94.3%, 400 graded
Cost per task
$0.00038
Savings vs always slow
54.8%
95% CI 53.6–55.9%; always slow: $0.00084/task
Audit overhead
44.6%
$0.068 audit spend
Expected wrong skipped cases
32.0
95% CI 23.0–43.8

Audit by confidence bin

Skipped cases by served confidence (95% CI in brackets)
Confidence binSkippedAuditedDisagreement (CI)Error vs references (CI)
[0.00, 0.50)00——
[0.50, 0.70)137100% (59.0–100.0%)100% (77.2–100.0%)
[0.70, 0.80)15977.8% (40.0–97.2%)86.7% (62.1–96.3%)
[0.80, 0.90)6475.0% (19.4–99.4%)66.7% (30.0–90.3%)
[0.90, 0.95)30—33.3% (6.1–79.2%)
[0.95, 1.00]223690% (0.0–5.2%)0.45% (0.1–2.5%)

Highlighted bins have a disagreement interval entirely above the tolerance.

Skipped-case disagreement by confidence binBars show the disagreement per bin with 95% CI whiskers; the dashed line is the tolerance.0%50%100%[0.00, 0.50) n=0n=0[0.00, 0.50)[0.00, 0.50)[0.50, 0.70) 100% [59%, 100%] n=7n=7[0.50, 0.70)[0.50, 0.70)[0.70, 0.80) 78% [40%, 97%] n=9n=9[0.70, 0.80)[0.70, 0.80)[0.80, 0.90) 75% [19%, 99%] n=4n=4[0.80, 0.90)[0.80, 0.90)[0.90, 0.95) n=0n=0[0.90, 0.95)[0.90, 0.95)[0.95, 1.00] 0% [0%, 5.2%] n=69n=69[0.95, 1.00][0.95, 1.00]tolerance 5%served confidencedisagreement
Skipped-case disagreement by confidence binBars show the disagreement per bin with 95% CI whiskers; the dashed line is the tolerance.0%50%100%0.00 n=0n=00.000.000.50 100% [59%, 100%] n=7n=70.500.500.70 78% [40%, 97%] n=9n=90.700.700.80 75% [19%, 99%] n=4n=40.800.800.90 n=0n=00.900.900.95 0% [0%, 5.2%] n=69n=690.950.95tolerance 5%served confidence (bin start)disagreement
Whiskers are 95% CIs; n is the number of audits per bin.

Tier usage and costs

Decisions served per tier
TierRoleServedShare
fastfast26065.0%
slowfinal, reference14035.0%
Audit coverage of skipped cases
QuantityCount
Skipped260
Audited89
Not selected for audit171
Audit pending0
Audit errors0
Undecided (judge could not decide)0
No audit record0
Graded against references260
Unweighted disagreement (biased)19.1% (12.3–28.5%)
Audit tier (slow) error vs references0% (0.0–4.3%)
Costs (USD)
QuantityValue
Serving cost (total)$0.15
Audit cost (total)$0.068
Cost per task$0.00038
Est. cost per task, always slow$0.00084 ($0.00082–$0.00086)
Estimated savings54.8% (53.6–55.9%)
Audit overhead (audit / serving)44.6%
Decisions with unknown serving cost0
Decisions with unknown audit cost0

Threshold sweep

Offline threshold sweep over 400 eval-mode tasks (52 threshold settings); accuracy is measured against reference answers.

Accuracy vs cost per task52 simulated threshold settings (gray), the Pareto frontier (line), single-tier and oracle baselines, and the recommended point (star).50%60%70%80%90%100%$0.000050$0.00010$0.00020$0.00050$0.0010cost per task (USD, log scale)accuracyoperating pointsPareto frontieralways fastalways sloworacle (lower bound)recommendedoracle (lower bound)always slowrecommendedalways fastoperating pointsoperating pointsPareto frontierPareto frontieralways fastalways fastalways slowalways sloworacle (lower bound)oracle (lower bound)recommendedrecommended
Accuracy vs cost per task52 simulated threshold settings (gray), the Pareto frontier (line), single-tier and oracle baselines, and the recommended point (star).50%60%70%80%90%100%$0.000050$0.00010$0.00020$0.00050$0.0010cost per task (USD, log scale)accuracyoperating pointsPareto frontieralways fastalways sloworacle (lower bound)recommendedoracle (lower bound)always slowrecommendedalways fastoperating pointsoperating pointsPareto frontierPareto frontieralways fastalways fastalways slowalways sloworacle (lower bound)oracle (lower bound)recommendedrecommended
Gray: every simulated threshold setting. Line: Pareto frontier. Star: recommended thresholds.

Recommendation

Objective
max-savings
Thresholds
fast ≥ 0.89
Selection accuracy (280 tasks)
99.3% (95% CI 97.4–99.8%)
Selection cost per task
$0.00043
Selection escalation rate
42.1%
Held-out accuracy (120 tasks)
99.2% (95% CI 95.4–99.9%)
Held-out cost per task
$0.00049
Held-out escalation rate
45.8%
Accuracy vs always slow
-0.8 pp (95% CI -2.5 to +0.0 pp)

cheapest thresholds with accuracy >= 0.9900 (best single tier 'slow' at 1.0000 minus 0.01) on the selection split; validated on 120 held-out decisions (seed 0)

Baselines on all 400 usable tasks
RouterAccuracy (CI)Cost / taskEscalationTier share
always fast57.0% (52.1–61.8%)$0.0000270%fast 100%, slow 0%
always slow100% (99.0–100.0%)$0.000840%fast 0%, slow 100%
oracle (lower bound)100% (99.0–100.0%)$0.0004343.0%fast 57%, slow 43%
recommended (all data)99.2% (97.8–99.7%)$0.0004543.2%fast 57%, slow 43%

The oracle serves from the cheapest correct tier without paying for the tiers it skips; no real router can reach it.

Pareto frontier (showing 15 of 43 points)
ThresholdsAccuracy (CI)Cost / taskEscalationSkipped error (CI)
fast ≥ 057.0% (52.1–61.8%)$0.0000270%43.0% (38.2–47.9%)
fast ≥ 0.3361.5% (56.6–66.1%)$0.0000744.5%40.3% (35.5–45.3%)
fast ≥ 0.3669.2% (64.6–73.6%)$0.0001612.2%35.0% (30.2–40.2%)
fast ≥ 0.3979.0% (74.7–82.7%)$0.0002622.0%26.9% (22.3–32.1%)
fast ≥ 0.4284.0% (80.1–87.3%)$0.0003127.0%21.9% (17.6–27.0%)
fast ≥ 0.4587.5% (83.9–90.4%)$0.0003430.5%18.0% (13.9–22.9%)
fast ≥ 0.4889.5% (86.1–92.1%)$0.0003632.5%15.6% (11.7–20.4%)
fast ≥ 0.5291.2% (88.1–93.6%)$0.0003734.2%13.3% (9.7–17.9%)
fast ≥ 0.5692.2% (89.2–94.5%)$0.0003835.2%12.0% (8.6–16.5%)
fast ≥ 0.6194.0% (91.2–95.9%)$0.0004037.0%9.5% (6.5–13.8%)
fast ≥ 0.7195.5% (93.0–97.1%)$0.0004138.5%7.3% (4.7–11.3%)
fast ≥ 0.7497.2% (95.1–98.5%)$0.0004240.2%4.6% (2.6–8.1%)
fast ≥ 0.7798.2% (96.4–99.1%)$0.0004341.2%3.0% (1.5–6.0%)
fast ≥ 0.8999.2% (97.8–99.7%)$0.0004543.2%1.3% (0.5–3.8%)recommended
fast ≥ 0.99100% (99.0–100.0%)$0.0004746.0%0% (0.0–1.7%)

Calibration

Confidence calibration per non-final tier
TierScoredECEBrierAUROCAURCMissing scores
fast4000.1850.0930.9990.1140

ECE and Brier: lower is better. AUROC: how well the score separates right from wrong answers (0.5 = chance). AURC: area under the risk-coverage curve, lower is better.

Reliability: fastAccuracy per confidence bin with Wilson intervals; points on the diagonal are perfectly calibrated.0%20%40%60%80%100%0%50%100%mean confidenceaccuracyperfect calibrationobserved
Reliability diagram for fast (400 scored tasks).
Risk-coverage: fastError rate among the skipped cases as the threshold is lowered and the tier answers more cases alone.0%10%20%30%40%50%0%50%100%coverage (share answered by tier)risk (error among skipped)tolerance 5%risk
Risk-coverage curve for fast.

Caveats

Methodology

Disagreement is the share of skipped cases (answered by a non-final tier without escalating) whose answer differs from the final (audit) tier's answer to the same task, as decided by the configured comparator or judge. In serve mode only a random sample of skipped cases is shadow-audited; each audited case is weighted by 1/π, the inverse of its known inclusion probability (a Hajek inverse-probability-weighted estimator), so the estimate describes all skipped cases rather than only the audited ones. In eval mode every tier answers every task, so every skipped case is observed (π = 1). The audit tier is a proxy, not ground truth: disagreement counts differences from its answers, not verified errors, unless reference answers exist, in which case the error rate against them is reported as well. Audits that are pending, failed or undecided are treated as nonresponse: within each inclusion-probability stratum, completed audits are up-weighted by the inverse of the stratum's response rate, which assumes audits are missing at random within their stratum; strata without any completed audit cannot be represented and are excluded from the estimate (a caveat says so). Intervals are Wilson score intervals for unweighted proportions and Korn-Graubard intervals (Clopper-Pearson at the effective sample size n_eff) for weighted ones; when a stratum holding at least 10% of the skipped cases has fewer than 10 completed audits, the status is never reported as ok. The status uses a fixed-sample interval: checking it repeatedly as audits accumulate and stopping at the first ok inflates the chance of a false ok, so fix the number of audits in advance or use a stricter confidence level for repeated checks. The savings interval reflects only the uncertainty in the cost of always using the final tier. Sweep accuracies are Wilson intervals; recommended thresholds are chosen on a selection split and re-evaluated on a held-out split.