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pert_estimate

Read-onlyIdempotent

Calculate expected duration from optimistic, most likely, and pessimistic estimates using the PERT Beta distribution. Get variance, standard deviation, and confidence bounds for uncertain task durations.

Instructions

Calculate PERT expected duration from three-point estimates using Beta distribution.

Formula: E = (O + 4M + P) / 6. Returns expected value, variance, standard deviation, and 95%/99% confidence bounds with urgency categorization. Use when estimating task duration with uncertain outcomes.

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
optimisticYesBest-case duration. Do NOT use your initial optimistic guess — this should be the absolute minimum if everything goes perfectly.
most_likelyYesMode of the distribution — the single most probable outcome.
pessimisticYesWorst-case duration accounting for known risks and unknown unknowns.
unitNoTime unit for all three PERT estimates.hours
task_typeNoOptional task type for feedback matching. Enables per-task-type accuracy tracking.
ai_nativeNoDegree of AI assistance: 0.0 = fully human, 1.0 = fully AI-native, 0.5 = hybrid. Accepts boolean for backward compatibility (true=1.0, false=0.0).
Behavior5/5

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

Annotations (readOnlyHint, destructiveHint, idempotentHint, openWorldHint) are consistent. The description adds details about outputs (confidence bounds, urgency categorization) beyond annotations, fully disclosing behavior.

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

Conciseness5/5

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

The description is very concise: two sentences, formula, and output list. Every sentence adds value with no redundancy.

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

Completeness5/5

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

Despite no output schema, the description enumerates all outputs (expected value, variance, etc.). With good annotations and parameter descriptions, the tool is fully understandable.

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

Parameters4/5

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

Schema coverage is 100%, so baseline is 3. The description adds practical guidance for parameters (e.g., 'Do NOT use your initial optimistic guess'), improving clarity beyond the schema.

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

Purpose5/5

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

The description clearly states the tool calculates PERT expected duration from three-point estimates using Beta distribution. It specifies the formula and outputs (expected value, variance, etc.), and distinguishes from sibling estimation tools like cocomo_estimate or monte_carlo_schedule.

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

Usage Guidelines4/5

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

The description explicitly says 'Use when estimating task duration with uncertain outcomes,' providing clear context. While it doesn't list when not to use, the sibling tools cover alternative methods, making the usage guidance adequate.

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

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