Bayesian Analysis

Definition

Bayesian analysis is the mathematical framework behind Bayesian pricing. It provides a principled way to combine prior knowledge (historical deal data) with new evidence (current deal signals) to produce updated probability estimates.

The process works in three steps: (1) establish a prior probability distribution based on historical data — e.g., "firms in this industry with our rate have a 40% baseline win probability"; (2) collect evidence from the current deal — budget confirmation, competitor presence, decision-maker access; and (3) update the prior using Bayes' theorem to produce a posterior probability — e.g., "with a confirmed budget and warm introduction, win probability rises to 62%."

What makes Bayesian analysis powerful for pricing is that it improves with every deal. A firm that logs 50 deals per year has 50 updates to its probability models. After two years, the pricing recommendations are grounded in 100+ data points specific to that firm's market.

ScopeMetrix applies Bayesian analysis to all client audits. The methodology does not claim "Bayesian pricing" as a proprietary term — it is standard applied statistics adapted for agency pricing decisions. The output is a statistical weighted model that quantifies uncertainty rather than pretending it doesn't exist.

Bayesian analysis is distinct from Monte Carlo simulation: Bayes handles probability updating, Monte Carlo handles outcome simulation under uncertainty. Used together, they form a complete pricing decision toolkit.