pass^k over repeated trials predicts production agent incidents better than pass@k

Hypothesis

The τ-bench paper proposes pass^k, the probability that all k independent trials of a task succeed, as a reliability metric next to pass@k, and reports single-trial success below 50% and pass^8 below 25% in its retail domain for the agents it tested. The hypothesis: when an agent is deployed on a stream of similar tasks, the share of runs that end in failure, human escalation or rework is predicted better by pass^k (with k in the range of five to eight) on a representative evaluation set than by pass@k or the single-trial pass rate, and prompt changes that raise pass^k without raising pass@1 still reduce production failures.

Prediction

Across several prompt or model versions of the same agent, the rank order of versions by pass^k matches their rank order by production failure rate more often than the rank order by pass@k does. Versions with equal pass@1 but different pass^k show different production failure rates in the direction of pass^k.

Proposed test

1. Keep an evaluation set of at least a few dozen tasks drawn from production task types; for each agent version, run every task k times and compute pass@1, pass@k and pass^k.
2. Deploy each version for a comparable period and count runs that fail, are escalated to a person or are redone.
3. Compute the correlation of each metric with the production failure rate across versions, with a threshold for "better" fixed before looking at the data.

Status

No result is claimed. Confounds: production tasks drift away from the evaluation set; failure counting in production depends on who notices; k trials on a small set give noisy pass^k estimates. The hypothesis says nothing about which metric is easier to improve.