Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

With no annotations, the description carries the full burden. It does add useful behavioral context: the result is expressed as standard deviations from the mean, the deviation is measured against the population, and there is a pricing/auth note (5 free trial calls per signed wallet). It stops short of error behavior, minimum population size, and whether the mean/stddev are population or sample based beyond the single word 'population'.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Is the description appropriately sized, front-loaded, and free of redundancy?

Three short sentences with the purpose and the input requirement front-loaded, no repetition or filler. The promotional free-trial line is incidental but occupies only one clause, so it does not materially dilute the definition.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

No annotations and no output schema means the description is the only documentation, and it leaves the most operationally important detail unspecified: how to encode the values array in a string field. For a two-parameter, untyped-schema math tool this leaves the agent able to guess the purpose but not confidently form the call.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema description coverage is 0% and both parameters are bare 'string' types, so the description should compensate. It names both parameters and says 'values array', but never explains the serialization format (comma-separated string, JSON array, etc.) or how non-numeric entries are treated, which is the single most likely cause of a failed call.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Does the description clearly state what the tool does and how it differs from similar tools?

The description names a specific verb and resource ('Calculate the z-score (standard score) of a value within a population') and clarifies the POPULATION variant, which is meaningful. It does not, however, distinguish itself from the sibling x402-zscore-array or x402-standardize, so an agent cannot route between them from the text alone.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Does the description explain when to use this tool, when not to, or what alternatives exist?

'Provide values array and value' is a parameter instruction, not usage guidance. There is no statement of when to pick this over x402-zscore-array (which appears to score a whole array) or x402-standardize, and no preconditions such as minimum sample size or behavior with a single-element array.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.