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

Annotations already declare readOnlyHint, idempotentHint, openWorldHint and destructiveHint=false, so the safety profile is covered. The description adds genuinely new operational context: the per-call cost of 1 credit and the exact deterministic formula being applied. It does not mention error behavior for empty or non-numeric input, which is the only notable gap.

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 front-loaded sentence states the verb, the resource, the statistical variant, the formula, and the cost, with no filler. Nothing could be removed without losing information an agent needs.

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 one-parameter, no-output-schema tool with rich annotations, the description covers purpose, computation method, and cost. The only shortfall is that it never indicates the return value is a single number, which matters slightly because there is no output schema to fall back on.

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 100%, so the schema already defines the single 'numbers' parameter, and baseline 3 applies. The description adds no clarification of the ambiguous anyOf form, which permits either an array of strings or a single string — an agent must guess whether a delimited string like "1,2,3" is acceptable.

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 operation ('Calculates the population standard deviation of a list of numbers') and even supplies the exact formula, which disambiguates it from siblings like calculate_median, average, or variance-style tools. An agent can identify the resource, the input shape, and the statistical variant without opening the schema.

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?

Usage is only implied: the word 'population' signals that this is not the sample standard deviation, which is a real decision point for an agent. However, no alternatives (e.g. calculate_median, average) are named, and there is no when-to-use or when-not-to-use guidance despite a very crowded calculation-tool sibling set.

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