The Prompt Entropy Budget: Measuring Output Variance as a First-Class Production Metric
When your LLM feature ships, your monitoring dashboard probably tracks accuracy, latency, and error rate. What it almost certainly does not track is variance — how wildly different the output is each time a user sends the same prompt. That gap is where production AI features quietly collapse.
Variance determines whether your product feels trustworthy or capricious. A feature that scores 88% on your eval suite but delivers a two-sentence answer 40% of the time and a ten-paragraph essay the other 60% will erode user trust faster than one that scores 80% but behaves consistently. Teams optimizing exclusively for accuracy are solving the wrong half of the reliability problem.
The prompt entropy budget is the concept that fills this gap: a structured approach to measuring, budgeting, and controlling the distribution of outputs your model produces over identical inputs — treated the same way you treat p99 latency or error budget in your SLO framework.
