Bayesian Probability Calculator
Update your betting probabilities with new evidence using Bayes' Theorem
Your initial probability estimate before new evidence
Probability evidence appears when hypothesis is TRUE (sensitivity)
Probability evidence appears when hypothesis is FALSE
What is Bayesian Probability?
Bayesian inference is a method of statistical reasoning that allows you to update your probability estimates as new evidence becomes available. It's named after Reverend Thomas Bayes and is fundamental to making rational betting decisions when information changes.
Bayes' Theorem Formula
P(H|E) = P(E|H) × P(H) / P(E)
- P(H|E) = Posterior probability (updated belief)
- P(H) = Prior probability (initial belief)
- P(E|H) = Likelihood (probability of evidence if hypothesis is true)
- P(E) = Probability of observing the evidence
Sports Betting Applications
- Injury News: Update win probability when key player ruled out (prior: team's win %, evidence: injury impact data)
- Line Movements: Adjust probability when sharp money moves the line (prior: your model, evidence: market signals)
- Weather Reports: Update over/under probability when forecast changes (prior: model total, evidence: weather impact)
- Live Betting: Continuously update win probability as game events unfold
- Model Refinement: Incorporate actual results to improve future predictions
Example Scenarios
Prior: 60% win probability → Star QB injury news → True positive: 90% (injury correctly predicts worse performance), False positive: 10% → Posterior: Update your win probability down
Prior: 50% probability → Respected sharp bettor hammers one side → True positive: 70% (sharp correctly identifies value), False positive: 30% → Posterior: Shift probability toward sharp's side
Professional bettors are Bayesian thinkers - they constantly update their beliefs based on new information while weighing the reliability of that information. This calculator helps you formalize that process mathematically.
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Responsible Gambling
Gambling should be entertaining, not a way to make money. Only bet what you can afford to lose, and never chase your losses.
- Betting more than you can afford to lose
- Chasing losses with bigger bets
- Lying to others about gambling habits