Information Value Calculator

Overview

This pillar provides a structured, mathematical framework for updating your predictions based on new evidence. It uses Bayesian principles to calculate the precise strength of information, helping you avoid emotional overreactions and make disciplined adjustments.

What It Does

The Information Value Calculator operationalizes Bayes' Theorem to measure the power of a new piece of evidence. It computes a Likelihood Ratio, which shows how much more likely the evidence is if your prediction is correct versus if it is incorrect. This ratio is then used to systematically update the prior probability of an outcome, resulting in a more accurate posterior probability.

Why It Matters

In prediction markets, traders often overreact or underreact to news. This pillar provides a rigorous, quantitative method to determine exactly how much a market's probability should shift, giving you an edge over those relying on gut feelings.

How It Works

First, establish your initial belief, or prior probability, for a market outcome. When new evidence appears, you estimate the probability of observing that evidence under two scenarios: one where your prediction is true, and one where it's false. The pillar then calculates the Likelihood Ratio from these estimates and applies it to your prior odds to generate a new, updated probability.

Methodology

The core calculation uses Bayes' Theorem in its odds form: Posterior Odds = Prior Odds * Likelihood Ratio. The Likelihood Ratio (LR) is defined as P(Evidence | Hypothesis is True) / P(Evidence | Hypothesis is False). Probabilities are first converted to odds (odds = p / (1-p)), multiplied by the LR, and then the resulting posterior odds are converted back to a probability (p = odds / (1+odds)).

Edge & Advantage

This tool provides a systematic defense against common cognitive biases, like confirmation bias and overconfidence, by forcing a quantitative and objective assessment of new information.

Key Indicators

• Likelihood Ratio (LR)

  high

  Measures how many times more likely a piece of evidence is if a hypothesis is true, compared to if it is false. A value greater than 1 supports the hypothesis.

• Posterior Probability

  high

  The updated probability of a hypothesis after considering the new evidence.

• Information Surprise

  medium

  A measure of how unexpected the new evidence was. Highly surprising information, if diagnostic, leads to larger probability shifts.

Data Sources

• Expert Elicitation

  The primary 'source' is the user's own estimated probabilities for the likelihood ratio calculation based on their domain knowledge and research.

• Historical Data Analysis

  Past instances of similar events can be analyzed to empirically estimate the probabilities needed for the Likelihood Ratio.

Example Questions This Pillar Answers

• → Will the FDA approve Drug X by year end, after a new set of clinical trial results are published?
• → Will the incumbent win the election, after a key endorsement from a rival?
• → Will a company's stock price exceed $200, following an unexpected earnings report?

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