New Evidence Just Dropped. Here Is How to Actually Update Your Probability
A headline breaks. A poll comes in. A report gets released. You have a prediction market position open and you need to figure out what this new information actually means for the probability. Most people do one of two things; they either panic and overreact to the news, or they shrug and do not update enough. Both are wrong.
Bayesian updating is the mathematically correct way to incorporate new evidence into an existing probability estimate. It was formalized by Thomas Bayes in the 18th century and is the foundation of an enormous chunk of modern statistics, machine learning, and quantitative forecasting. The core idea is simple; you have a prior belief, you observe some evidence, and you update your belief in proportion to how likely that evidence was given your prior versus how likely it was in general.
The FatNarwhal Bayesian Updater takes your prior probability, the likelihood of the evidence you just observed, and gives you the correctly updated posterior probability. It is the tool you want open every time news hits a market you are trading.
How to Use It
Go to fatnarwhal.com/bayes and set up an update.
Say you have a prediction market position on whether a company passes a regulatory review. Your prior probability is 60%; you thought it was more likely than not to pass based on the existing public information. A new report comes out suggesting the regulator has significant concerns.
Now you need to estimate two things; how likely was this report to appear if the company was going to pass (maybe 15%, concerning reports can be misleading), and how likely was this report to appear if the company was not going to pass (maybe 70%, a negative report is much more likely in a failure scenario).
Enter those three numbers; prior of 60%, likelihood given pass of 15%, likelihood given fail of 70%. The tool applies Bayes' theorem and outputs your posterior probability. In this case it would shift meaningfully downward, reflecting the fact that this kind of report is much more common in failure scenarios than success ones.
The Math Behind It
Bayes' theorem is:
Where P(H) is your prior probability of the hypothesis (the event happening), P(E | H) is the likelihood of seeing this evidence if the hypothesis is true, P(E) is the overall probability of seeing this evidence (across both the hypothesis being true and false), and P(H | E) is your posterior, the updated probability after seeing the evidence.
The denominator P(E) expands to P(E | H) × P(H) + P(E | not-H) × P(not-H), which is why the tool asks for the likelihood of the evidence under both scenarios.
What Bayes is really doing is reweighting your prior in proportion to how diagnostic the evidence is. If the evidence is equally likely whether or not your hypothesis is true (a likelihood ratio of 1), your posterior equals your prior; the evidence told you nothing. If the evidence is much more likely under one scenario than the other, the update is large. The strength of the update is proportional to the diagnostic power of the evidence.
When to Use It and When Not To
Use it any time new information hits a market you are involved in and you want a principled way to update rather than a gut reaction. Use it before making any trading decision in response to news; it forces you to be explicit about how likely that news was under different scenarios, which is a discipline that sharpens your thinking.
The main challenge is estimating the likelihoods; P(E | H) and P(E | not-H) are not always easy to put numbers on. But being roughly right is far better than not trying at all, and the exercise of estimating them forces you to be explicit about what the evidence actually means rather than reacting emotionally.
One trap to avoid is working backwards from the outcome you want. If you are trying to stay in a losing position and you subconsciously estimate the likelihoods to produce a posterior that justifies not updating, you are doing motivated reasoning, not Bayesian updating.
Try It
Next time a piece of news hits a prediction market position you hold, go to fatnarwhal.com/bayes before you do anything. Enter your prior, estimate the likelihoods honestly, and see what the math says your probability should be.
Then decide whether the market has already priced it in or whether you have an edge.