> ## Documentation Index
> Fetch the complete documentation index at: https://docs.polystr.at/llms.txt
> Use this file to discover all available pages before exploring further.

# Statistical Model

> Quantitative modeling to estimate outcome likelihood.

Polystrat analyzes crypto price targets using multiple statistical approaches and historical behavior to generate model-based probabilities. These probabilities are designed to support better decisions, giving you a clearer sense of risk before you commit capital.

# Probability Engine Overview

This endpoint estimates the likelihood of a crypto asset (e.g. BTC) reaching a given price level within a defined time horizon.

It is designed for probabilistic decision support, not deterministic prediction.

<Info>
  The engine aggregates multiple independent probabilistic perspectives into a single bounded estimate, with explicit confidence signals.
</Info>

## High-level Architecture

The system follows an ensemble-based approach. Instead of relying on a single statistical assumption, it combines several complementary probability engines, each modeling a different market behavior.

The final probability reflects both the estimate itself and the degree of agreement between models.

## Volatility Regime Detection

Before aggregation, the engine classifies the current market into a volatility regime.

| Regime | Description                     | Effect                                |
| :----- | :------------------------------ | :------------------------------------ |
| Low    | Compressed volatility           | Tighter estimates, higher confidence  |
| Normal | Typical market conditions       | Standard behavior                     |
| High   | Elevated or stressed volatility | Wider uncertainty, confidence penalty |

<Warning>
  High volatility regimes explicitly reduce confidence, even when raw probabilities appear attractive.
</Warning>

## Ensemble Aggregation

All model outputs are combined into a single probability estimate.

Core principles:

* No single model dominates across all regimes
* Model disagreement increases uncertainty
* Model alignment tightens confidence intervals

The aggregation step produces both a probability and a model-consensus signal.

## Contextual Adjustments

After aggregation, the estimate is adjusted using market context signals.

These adjustments account for:

* Market positioning and sentiment imbalance
* Distance between spot price and target
* Time remaining to expiry

<Note>
  Adjustments are intentionally conservative and designed to dampen crowd-driven overconfidence.
</Note>

## Probability Bounding

The engine never outputs absolute certainty.

Probability bounds are applied based on:

* Target distance (moneyness)
* Time horizon
* Detected volatility regime

This ensures outputs remain probabilistic rather than declarative.

## Output Structure

<ResponseField name="probability" type="Final bounded probability estimate (0–1)">
  Represents the final adjusted probability after ensemble aggregation, contextual adjustments, and bounding.
</ResponseField>

<ResponseField name="confidence_interval" type="Lower and upper bounds derived from model dispersion">
  Indicates the uncertainty range implied by disagreement between internal models.
</ResponseField>

<ResponseField name="confidence_score" type="Model agreement score indicating estimate reliability">
  Measures how closely aligned the internal models are with each other. This reflects consensus, not predictive certainty.
</ResponseField>

<ResponseField name="model_breakdown" type="Abstracted per-model contribution summary">
  Provides a high-level summary of how different probabilistic engines contributed to the final estimate, without exposing internal mechanics.
</ResponseField>

<ResponseField name="recommendation" type="Human-readable probability classification">
  A categorical label derived from the probability range, intended for fast scanning and UI display.
</ResponseField>

## Intended Use

This system is optimized for:

* Scenario comparison
* Risk-weighted decision making
* Probabilistic hedging logic

<Danger>
  This engine is not a price oracle, trading signal, or guarantee of outcome.
</Danger>