Cost Anomaly

---
name: cost-anomaly
description: MAD-based outlier detection on session spend. Robust to the very outliers it hunts (unlike mean+sigma). Surfaces specific anomalous sessions with modified-z scores; optional --alert-on-outliers exit code for CI gates. Distinct from cost-burn (aggregate trend) — this answers "which INDIVIDUAL session is the outlier?".
argument-hint: "[--since 7d] [--threshold 3.5] [--alert-on-outliers N] [--format table|json]"
allowed-tools: Bash
---

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`](../../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

```bash
# 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`:

```bash
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 |