Reference

Mini-language syntax

Statements are separated by newlines (semicolons also accepted). Each statement is a random variable declaration or a derived variable declaration. Variable names may contain letters, digits, underscores, and internal spaces (e.g. hrs per phase).

revenue ~ norm(100000, 15000)
costs ~ norm(80000, 10000)
profit = revenue - costs

Random variable declaration — name ~ distribution(params). Each simulation iteration draws a new sample from the distribution.

Derived variable declaration — name = expression. Standard arithmetic; variables resolve in dependency order regardless of declaration order.

Comments — lines starting with # are ignored:

# Revenue model
revenue ~ norm(50000, 8000)

Operators

Operator	Meaning	Example
`+`	Addition	`a + b`
`-`	Subtraction	`a - b`
`*`	Multiplication	`a * b`
`/`	Division	`a / b`
`**`	Power	`a ** b`

Precedence (highest first): ** (right-to-left) → *, / (left-to-right) → +, - (left-to-right). Use parentheses to override.

Built-in functions

Function	Description
`abs(x)`	Absolute value
`sqrt(x)`	Square root
`log(x)`	Natural logarithm
`exp(x)`	Exponential (e^x)
`min(a, b)`	Minimum of two values
`max(a, b)`	Maximum of two values

Supported distributions

Distribution	Syntax	Description
Normal	`norm(mean, std)` or `normal(mean, std)`	Symmetric bell curve
Uniform	`uniform(low, high)` or `unif(low, high)`	Every value equally likely
Triangular	`triangular(low, mode, high)` or `tri(low, mode, high)`	Three-point estimate
Lognormal	`lognormal(mean, sigma)` or `lognorm(mean, sigma)`	Right-skewed, always positive
Exponential	`exponential(rate)` or `expon(rate)`	Memoryless waiting times
Gamma	`gamma(shape, scale)`	Flexible positive-value distribution
Beta	`beta(alpha, beta)`	Bounded 0–1; good for probabilities
Poisson	`poisson(rate)`	Discrete count data
Binomial	`binom(n, p)`	Successes in `n` independent trials
Integers	`integers(low, high)`	Uniform random whole number in range
Negative Binomial	`negbinom(n, p)`	Trials until `n` successes
Choice	`choice([a, b, c])`	Picks one value from a list equally
Weibull	`weibull(scale, shape)`	Wear-out or reliability modeling (spreadsheet engine)
Constant	`constant(value)`	Fixed value — effectively a pinned input (spreadsheet engine)

Distribution parameters

normal / norm

Parameter	Description
`mean`	Center of the distribution
`std`	Standard deviation (spread)

uniform / unif

Parameter	Description
`low`	Minimum value
`high`	Maximum value

triangular / tri

Parameter	Description
`low`	Minimum value
`mode`	Most likely value
`high`	Maximum value

lognormal / lognorm

Parameter	Description
`mean`	Mean of the underlying normal distribution (in log space)
`sigma`	Standard deviation in log space

exponential / expon

Parameter	Description
`rate`	Rate parameter (mean = 1/rate)

gamma

Parameter	Description
`shape`	Shape parameter (k)
`scale`	Scale parameter (θ)

beta

Parameter	Description
`alpha`	Shape parameter α (> 0)
`beta`	Shape parameter β (> 0)

poisson

Parameter	Description
`rate`	Expected number of events (λ)

binom

Parameter	Description
`n`	Number of trials
`p`	Probability of success per trial

negbinom

Parameter	Description
`n`	Target number of successes
`p`	Probability of success per trial

integers

Parameter	Description
`low`	Minimum integer (inclusive)
`high`	Maximum integer (inclusive)

choice

Parameter	Description
`[a, b, c]`	List of numeric values; one is picked uniformly each iteration

Output metric types

Configured per output variable in the author view.

Kind	Description	Extra fields
`mean`	Arithmetic mean across iterations	—
`median`	50th percentile	—
`percentile`	Arbitrary percentile	`p` (0–100)
`probability`	Fraction of iterations satisfying a threshold	`op` (`<`, `<=`, `>`, `>=`), `value`
`std`	Standard deviation	—
`min`	Minimum sampled value	—
`max`	Maximum sampled value	—

Default metric set when none are configured: mean, P25, P75.

Output format types

Format	Display
`number`	Plain number (default)
`currency`	Dollar-prefixed
`percent`	Percentage
`duration`	Human-readable duration

User input types (parameters manifest)

Kind	Runner control	Fields
`number`	Numeric text field	`default`, optional `test_value`
`choice`	Radio buttons	`choices` (label + value pairs), `default` (option label), optional `test_value`
`distribution`	Family-locked distribution control	`family`, `param_ui`, `default` (parameter set)

test_value is author-only — it drives the editor's live preview and is never written to saved runs.

Distribution `param_ui` values

Controls the runner-facing interface for distribution user inputs.

`param_ui`	Runner controls	Supported families
`raw`	The distribution's native parameters	All
`min-mode-max`	Min, mode, max number inputs	`triangular` only
`low-high-conf`	Low bound, high bound, confidence percent	`norm` only
`presets`	Author-defined preset chips	All (each preset maps to a full parameter set)

Spreadsheet engine

Supported workbook features

Feature	Support
`.xlsx` files	Supported
Multiple sheets	Supported — switch via sheet tabs
Cell formulas	Rendered read-only via IronCalc
`.xls` (legacy)	Not supported — save as `.xlsx` first
Macros / VBA	Not executed

Assumption fields

Field	Description
Name	Label shown in the sidebar and runs table
Sheet	Sheet name containing the target cell
Cell	Single cell reference (e.g. `B4`)
Distribution	Probability distribution used for sampling
Parameters	Distribution-specific parameter values
Origin	`assumption` (sampled each iteration) or `user_input` (bound once per run)

Simulation parameters

Parameter	Default	Range
Rep count	1,000	1–10,000
Job timeout	60 s	Fixed

Output types

Output	Result display
Single cell	Histogram of scalar values across all replications
Cell range	One histogram per cell in the range

Percentile table

Percentile	Meaning
P5	5% of replications produced a value below this
P25	Lower quartile
P50	Median
P75	Upper quartile
P95	95% of replications produced a value below this

REST endpoints

Method	Path	Description
`GET`	`/api/estimator/`	List your estimators
`POST`	`/api/estimator/`	Create an estimator
`GET`	`/api/estimator/<id>/`	Retrieve an estimator
`PUT`	`/api/estimator/<id>/`	Update an estimator
`DELETE`	`/api/estimator/<id>/`	Delete (blocked if template has runs)
`POST`	`/api/estimator/<id>/run/`	Run with given bindings
`POST`	`/api/estimator/run-adhoc/`	Run any model without persisting
`GET`	`/api/estimator/<id>/runs/`	List runs of a template
`POST`	`/api/estimator/<id>/runs/`	Create a run
`GET`	`/api/estimator/runs/<run_id>/`	Retrieve a run
`PUT`	`/api/estimator/runs/<run_id>/`	Update a run
`DELETE`	`/api/estimator/runs/<run_id>/`	Delete a run
`GET`	`/api/estimator/<id>/runs.csv`	CSV export of a template's runs
`POST`	`/api/estimator/<id>/share/`	Generate or revoke a template share token
`POST`	`/api/estimator/runs/<run_id>/share/`	Generate or revoke a run share token
`GET`	`/api/estimator/shared/<token>/`	Public template view
`GET`	`/api/estimator/runs/shared/<token>/`	Public run view

/api/estimator/run-adhoc/ and /api/estimator/shared/* are unauthenticated. All other endpoints require authentication and ownership. Running a spreadsheet-engine estimator requires Pro (403 {"error": "pro_required"} otherwise).

Legacy redirects

Browser bookmarks to the old Probability Playground and Spreadsheet Sim URLs redirect permanently:

Old path	Redirects to
`/playground/`	`/estimator/`
`/app/playground/`	`/app/estimator/`
`/app/playground/<id>/`	`/app/estimator/<id>/`
`/playground/shared/<token>/`	`/app/estimator/shared/<token>/`
`/spreadsheet-sim/`	`/estimator/`
`/app/spreadsheet-sim/`	`/app/estimator/`

Simulation request and response

`POST /api/estimator/<id>/run/`

Request

{
  "bindings": {
    "n_phases": 4,
    "complexity": 1.5,
    "close_prob": {"family": "beta", "params": {"a": 2.5, "b": 3.0}}
  },
  "nreps": 1000,
  "seed": null
}

Scalar bindings become name = value prepended to the model.
Distribution bindings become name ~ family(params) prepended.
Bindings for identifiers not in the model are rejected.
Missing required bindings use the parameter default.

Response (formula engine — synchronous)

{
  "variables": ["hrs_per_phase", "rate_per_phase", "total"],
  "samples": {
    "hrs_per_phase": [22.1, 18.4, "..."],
    "total": [66300, 55200, "..."]
  },
  "metrics": {
    "total": {
      "mean": 68000,
      "p10": 54000,
      "p90": 84000,
      "pr_gt_75000": 0.34
    }
  }
}

Spreadsheet-engine requests return 202 {"job_id": "..."} immediately; poll GET /api/jobs/<job_id>/ until status == "complete", then read the same shape from job.result_json.

Mini-language syntax​

Operators​

Built-in functions​

Supported distributions​

Distribution parameters​

normal / norm​

uniform / unif​

triangular / tri​

lognormal / lognorm​

exponential / expon​

gamma​

beta​

poisson​

binom​

negbinom​

integers​

choice​

Output metric types​

Output format types​

User input types (parameters manifest)​

Distribution param_ui values​

Spreadsheet engine​

Supported workbook features​

Assumption fields​

Simulation parameters​

Output types​

Percentile table​

REST endpoints​

Legacy redirects​

Simulation request and response​

POST /api/estimator/<id>/run/​