startup-valuation

Probability & Expected Value

valuation_probability

Read-onlyIdempotent

Calculate probability-weighted expected values for startup scenarios using discrete, joint, portfolio, Poisson, or continuous formulas. Use outcome and probability lists for central estimates.

Instructions

Compute expected value and probability-weighted outcomes for startup scenarios: discrete E[X], joint probability of sequential events, probability-weighted value, VC portfolio expected return, Poisson event probability, and continuous E[X] over a range. Method selects the formula. Use for probability-weighted central estimates; for named bull/base/bear tables or option pricing use valuation_advanced, and to discount cash flows use valuation_time_value. Parameters apply per method: expected_value_discrete and probability_weighted need outcomes + probabilities; portfolio_return needs weights + returns; poisson needs mean_events + k; expected_value_continuous needs lower + upper. outcomes and probabilities must be equal length, and the probabilities should sum to 1. Routing: use valuation_advanced method 'scenario_analysis' for named bull/base/bear scenario tables, and its black_scholes/binomial methods for option pricing; use this tool for arbitrary outcome lists and probability-weighted central estimates. Only method is required; all other parameters are method-dependent, so supply those the selected method names and omit the rest (defaults apply where defined). Rate and decimal inputs are fractions (0.10 = 10%); probability and weight lists are in [0,1] and sum to 1. Returns value, method, inputs, assumptions, chapter, formula_number and calculation steps; pure arithmetic — no I/O and no external calls — rounded to 2 decimals, with no auth or rate limits. An unknown method, or a missing method-required parameter, returns an error instead of a value.

Input Schema

TableJSON Schema

Name	Required	Description
`k`	No	Number of events k for the Poisson probability P(X=k); integer ≥ 0.
`lower`	No	Lower integration bound (standard-normal domain, e.g. -1.0).
`upper`	No	Upper integration bound (standard-normal domain, e.g. 1.0).
`method`	Yes	Formula to apply. Options: expected_value_discrete = E[X] = Σ xᵢ·P(X=xᵢ) over a discrete outcome list.; joint_probability = P(total) = Π pᵢ for independent sequential events.; probability_weighted = E[V] = Σ pᵢ·Vᵢ.; portfolio_return = E[R] = Σ wᵢ·Rᵢ across a VC portfolio.; poisson = P(X=k) = e^-λ λ^k / k! for rare events.; expected_value_continuous = E[X] = ∫ x·f(x) dx over [lower, upper] on the standard normal.
`returns`	No	Return of each asset or scenario as a decimal (0.20 = 20%), aligned with weights.
`weights`	No	Portfolio or factor weights, each in [0,1] and summing to 1 (same order as the paired value list).
`outcomes`	No	Possible outcome values x_i, in any currency unit (must match probabilities in length/order).
`mean_events`	No	Poisson mean λ = expected number of events in the interval.
`probabilities`	No	Probability of each outcome or stage, each in [0,1]; the list must sum to 1 where it is exhaustive.

Output Schema

TableJSON Schema

Name	Required	Description
`error`	No	Error message when the call fails.
`steps`	No	Intermediate steps for traceability.
`value`	Yes	Computed valuation or metric.
`inputs`	No	Echo of the normalised inputs used.
`method`	No	Formula / method name that produced the result.
`chapter`	No	Source textbook chapter.
`assumptions`	No	Modelling assumptions applied.
`formula_number`	No	Source textbook formula number (e.g. '3.1').
`defaults_applied`	No	Optional parameters that were not supplied, so their documented defaults were used.

Schema Changelog

Changes observed during successful MCP inspections.

Changed2 schema fields changedv2.1.1Oct 2, 2026

changedInput schema / properties / k / description

Previous value: -"Number of events k for the Poisson probability P(X=k)."New value: +"Number of events k for the Poisson probability P(X=k); integer ≥ 0."

addedOutput schema / properties / defaults_applied

Added value: +{
+  "description": "Optional parameters that were not supplied, so their documented defaults were used.",
+  "items": {
+    "type": "string"
+  },
+  "type": "array"
+}

First observedv0.1.0Sep 30, 2026

TDQS

A4.8/5.0

Behavior5/5

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

Annotations already declare the safe read-only, idempotent, closed-world profile, and the description goes well beyond them: pure arithmetic with no I/O or external calls, results rounded to 2 decimals, no auth or rate limits, and the explicit error behavior when method is unknown or a required parameter is missing.

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

Conciseness4/5

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

Front-loaded with the core purpose and method list, and each block is useful. However the valuation_advanced routing for bull/base/bear tables is stated twice, which is mild redundancy in an already dense description.

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?

For a 9-parameter, enum-driven calculator with an output schema, the description covers everything an agent needs: which method needs which inputs, input-format conventions, and the return payload. The listed return fields are redundant with the output schema but do no harm.

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%, but the description adds a method-to-parameter mapping the schema does not encode (discrete/probability_weighted need outcomes+probabilities, portfolio_return needs weights+returns, poisson needs mean_events+k, continuous needs lower+upper) plus constraints (equal length, probabilities sum to 1, fractions). Slight leftover gap: it doesn't spell out the joint_probability parameter pairing.

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?

States a specific verb+resource ('Compute expected value and probability-weighted outcomes') and enumerates the concrete computations (discrete E[X], joint probability, portfolio return, Poisson, continuous E[X]). It explicitly distinguishes itself from siblings valuation_advanced and valuation_time_value.

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

Usage Guidelines5/5

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

Gives explicit when-to-use routing: use this tool for arbitrary outcome lists and probability-weighted central estimates, and names the alternatives with the exact conditions that select them ('use valuation_advanced method scenario_analysis for named bull/base/bear tables', 'use valuation_time_value to discount cash flows').

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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