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

With no annotations, the description carries the full behavioral burden. It does disclose a genuine edge-case rule ('returns 0 when the variance is zero') and the free-trial quota, which are useful. However, it says nothing about accepted input format, numeric validation behavior, or return shape.

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?

One compact sentence that front-loads the operation and formula, followed by a short pricing tag. Nothing is redundant, though the pricing emoji/tag is arguably marketing noise rather than tool semantics.

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?

For a single-parameter math utility with no annotations and no output schema, the description covers the computation and one edge case but omits the input format, which is the main thing an agent needs to call it correctly. Adequate but with a clear gap.

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 coverage is 0% and the single parameter 'values' is a bare string with no description. The description never explains the expected input encoding (comma-separated list, JSON array, etc.), so an agent cannot reliably construct a valid call. With one undocumented param, the description should have compensated but does not.

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?

States a specific verb ('Computes') and resource ('excess kurtosis of values') plus the exact formula (population moments minus 3), so an agent knows precisely what operation is performed. It does not name any sibling (e.g. x402-skewness-sample, x402-stats) to route between them, but the operation is unambiguous. Minor internal tension: the tool name says 'sample' while the description specifies population moments.

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?

There is no guidance on when to use this versus the many related statistics siblings (x402-skewness, x402-skewness-sample, x402-variance, x402-stats). No prerequisites, input expectations, or exclusions are given. The only usage-flavored text is a pricing note ('5 free trial calls per signed wallet'), which does not help selection.

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