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

Annotations already declare readOnlyHint=true and openWorldHint=false, so safety is covered. The description adds real behavioral context beyond that: listing mode returns per-formula usage counts, detail mode returns the queries that use it, and a chart-based formula metric always resolves to the formula's current definition. Return shape itself is not described, but the semantics an agent needs are.

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?

The dual-mode behavior is front-loaded in the first sentence and the prerequisite is placed last, which is the right order. It is dense but nearly every clause carries information; the data.savedFormulaId sentence is slightly tangential to calling this tool, keeping it from a 5.

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 read-only, four-parameter listing/detail tool with no output schema, the description covers both modes, the prerequisite skill, and the conceptual meaning of a saved formula. What an agent needs to call it correctly is present; only result-shape and pagination behavior are unaddressed.

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 formulaId, search, projectId and environment are already documented in the schema. The description reinforces formulaId's dual behavior but says nothing about the search parameter's matching/ranking or the environment scoping. Baseline 3 is appropriate when the schema does the heavy lifting.

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 gives a specific verb and resource ("List the project's saved formulas") and parenthetically defines what a saved formula is, then states the second mode ("fetch one by formulaId with the queries that use it"). An agent can distinguish this from create_saved_formula or update_saved_formula without opening any 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?

It clearly states the condition that selects each mode: omit formulaId to list, set formulaId to fetch one with its queries. It also gives a usage prerequisite ("Load the insight-queries skill first") and explains the downstream usage path via data.savedFormulaId. It does not name sibling alternatives such as list_queries, so it stops short of a 5.

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