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

With no annotations, the description carries the full behavioral burden and largely fails to: it does not say what is returned (three intervals? formatted percentages?), whether inputs are raw numbers despite the string type, or whether negative/non-numeric sd is handled. The '🆓 5 free trial calls per signed wallet' note does disclose a cost/auth-adjacent detail, which is the one piece of real behavioral context.

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?

Front-loaded: the computational purpose comes first in a single sentence. The trailing promo/emoji line is extraneous but short and mildly informative about the paywall, so the overall structure remains efficient.

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?

A mathematically simple tool, but with no annotations, no output schema, and undocumented parameters, the description should at minimum state the expected input format and what the three resulting intervals look like. As written an agent knows the concept but not how to call it correctly.

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 typed as bare strings with no description. The prose mentions 'mean' and 'sd' conceptually, which hints at what each parameter means, but adds no format, unit, or parsing guidance — e.g., whether they are numbers, comma-formatted, or JSON. This does not compensate for a total lack of schema documentation.

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 (the empirical rule's 68/95/99.7 intervals around the mean in units of sd). The phrasing '68, 95 and 99.7 percent mean plus or minus one, two and three sd intervals' is slightly garbled but an agent can still identify the operation. It does not distinguish this from nearby siblings such as x402-chebyshev-inequality or x402-normal-cdf.

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 when-to-use guidance and no mention of alternatives (e.g., Chebyshev's inequality for non-normal data, or normal-cdf for exact tail probabilities). The only extra clause is a pricing/promo line, which does not help the agent decide when to invoke this tool.

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