Cost Anomaly

Per-session outlier detection — the diagnostic counterpart to cost-burn's aggregate-trend signal.

Question	Skill
"Is the AGGREGATE rate accelerating?"	cost-burn
"Which SPECIFIC sessions are anomalous outliers?"	cost-anomaly ← this
"Could we have spent less in aggregate?"	cost-counterfactual
"When will we hit budget?"	cost-projection

Algorithm

Implementation: scripts/anomaly.mjs.

1. Read all session-* records from cost-tracking namespace.
2. Filter to --since window (default: all-time).
3. Compute median(total_cost_usd) and MAD = median(|x - median|).
4. Per-session modified z-score (Iglewicz-Hoaglin 1993): z = 0.6745 * (x - median) / MAD
5. Flag sessions with |z| > --threshold (default 3.5).

Why MAD and not mean + sigma?

Approach	What breaks
mean + sigma	A single $50 session inflates BOTH mean and sigma so badly that subsequent outliers hide inside the new "normal" band. Catastrophic on small samples.
median + MAD	Both estimators ignore up to 50% of the data — the outliers themselves can't shift them. Robust on n=10. The canonical cutoff |z| > 3.5 is from Iglewicz-Hoaglin (1993).

Smoke transcript (5 baseline sessions $0.08-$0.12 + 1 outlier $5.00)

| Sessions considered | 5 |
| Threshold (|modified z|) | 3.5 |
| Median spend | $0.100000 |
| MAD | $0.010000 |
| Min / Max | $0.080000 / $5.000000 |
| **Outliers found** | **1** |

## Outlier sessions
| Session | Spend | Deviation | Modified z | Direction |
| outlier- | $5.000000 | +$4.900000 | 330.505 | high |

Exit codes

$ cost anomaly --alert-on-outliers 1
⚠ ALERT: found 1 outlier session(s) (|modified z| > 3.5); threshold was ≥1
exit 1

$ cost anomaly --alert-on-outliers 5
✓ found 1 outlier session(s); under threshold ≥5 — OK
exit 0

CI integration

# Fail the build if any session this week is a >3.5σ outlier
cost anomaly --since 7d --alert-on-outliers 1 || investigate-bad-session

Most useful when paired with cost-burn:

cost burn  --alert-on-acceleration-pct 50  || page-oncall   # rate-of-change alert
cost anomaly --alert-on-outliers 1         || investigate   # point-anomaly alert

Together they cover "is the average shifting?" AND "is there a single rogue session?" — both can fire independently.

Edge cases

• n < 3: emit "Insufficient data" message, exit 0. MAD on 1-2 samples is meaningless.
• MAD = 0: ≥50% of sessions share the exact same spend, so z-scores collapse. Emit explainer instead of dividing by zero. Common cause: dry-run sessions all at $0.
• Low-direction outliers: usually crashed or dropped sessions, not over-spending. The output table explicitly labels direction so operators interpret correctly.
• Very small MAD: even tiny absolute deviations produce huge z-scores. The $5 outlier with MAD=$0.01 yields z=330 — that's correct, not a bug.

Direction column

Direction	Likely cause	Action
high	Long session, stuck in expensive tier, or runaway loop	cost report + cost conversation to investigate
low	Crash, dropped session, or unfinished work	Verify the session completed normally