Formal Bayes gave you conditional probability, likelihood ratios, and the algebra of belief revision. Superforecasting chapters gave you anchors and decomposition. This chapter is where the symbols meet the trading week: priors from base rates, updates from tiered news, posteriors that feed expected value—not posteriors that chase the tape.
If you only remember one practice rule: no evidence, no update. Price moving is not evidence unless you treat market movement itself as a modeled input—which is a different chapter and a different claim. Superforecasting chapters gave you who updates well and how to anchor. This chapter is the bridge: Bayesian thinking in practice on real contracts—where priors come from base rates and venue prices, evidence arrives in tiers, and every move must survive expected value and a locked Brier score before you trade.
Practice versus ceremony
Ceremony is reciting formulas without logs. Practice is recording prior f₀ at entry, writing a likelihood ratio for each news item, moving three to eight points on a typical poll unless the LR truly justifies more, and refusing to revise without evidence or to hide hindsight in the journal.
Bayesian thinking here means coherent updating: beliefs are probabilities, evidence shifts odds by strength you can defend, and forbidden moves include matching price after a loss or jumping forty cents on one social post.
The live-market loop
Frame the event with resolution text. Set prior f₀ from outside base and decomposition, optionally shrunk toward consensus. List evidence with tier. Compute posterior f₁ via Bayes or odds multiplication. Run economics on executable ask, fees, slippage. Lock f₁ for scoring. Repeat on a schedule, not on every notification.
If you cannot write why f moved, you moved on mood—not Bayes.
Odds form traders actually use
Prior odds equal f / (1 − f). Posterior odds equal prior odds times likelihood ratio. Convert back: posterior f equals odds divided by one plus odds.
If prior is fifty percent and LR is 2, posterior is about sixty-seven percent. If prior is forty percent and LR is 1.5, posterior returns to fifty percent. Large LRs need documentation—base-rate neglect is letting a small prior get steamrolled by a story-sized LR without checking overlap.
Denominator discipline
Likelihood ratios require how often you see the evidence if the event is false. Rumors, leaks, and viral clips are often common when nothing happens—that keeps LRs small. Bayes is skeptical of drama when the denominator is large.
Worked example: election poll
Prior f₀ might be fifty-two percent from decomposition. A reputable poll shows candidate plus six; from historical calibration you might estimate P(poll | win) 0.65 and P(poll | lose) 0.35, giving LR 1.86. Prior odds 0.52/0.48 ≈ 1.08 times 1.86 yields posterior near sixty-seven percent.
If YES still trades fifty-six cents twenty minutes later, net edge may clear after frictions—or may not if spread is wide. Same day a viral "gaffe" clip should not get another full poll-sized LR without checking overlap; electability moved once already. Bundle or assign a small LR like 1.15.
Evidence tiers and discipline
Official resolution-adjacent releases deserve modest moves unless truly decisive. Primary data—polls, filings—can justify larger shifts within reason. Quality journalism and models sit in the middle. Social sentiment should nudge, not dominate.
A practical guardrail: the product of uncorrelated-looking LRs in one day should stay modest unless a tier-zero event occurred. Correlation control is how you avoid fake precision.
Updating when you already have a position
If price moved without news, do not rewrite f to match the tape. If news contradicts the thesis, update down before debating the stop. If you exit on a plan, post-mortem the LR table. Outcome bias treats a loss as proof you were "wrong" without comparing to f at entry.
Take-profit is not automatic evidence you were underconfident. Exit rules and belief updates are different ledgers unless new information arrived.
Rare events and noisy tips
Contract: cabinet secretary resigns within thirty days. Outside prior might be three percent. An anonymous tip might justify LR near 2.8, lifting f to roughly eight percent—still far below a forty-cent YES if retail chases narrative. Bayesian practice is often fading overreaction when resolution and base rate disagree with price.
Headline volume is not likelihood strength. The denominator in Bayes—how often you see this noise when nothing happens—matters.
Brier honesty
Lock f before trade. Revise with logged evidence. Revise to match price after loss and you fake calibration. Living at ninety-five percent when reality hits sixty percent destroys Brier tails. Superforecasters spend much of their mass in the middle band until evidence stacks.
Multi-outcome and conditional contracts
Categorical markets need vector updates that renormalize. Scalar markets shift means and should keep variance explicit. Conditional contracts update the parent story first, then the child—otherwise child Bayes fights parent base rate.
Linking updates to mispricing audits
Your compute step should output posterior belief with a paper trail: prior row, each evidence line with LR, posterior. If the audit jumps from prior to story peak without lines, you have marketing, not math.
Scheduled updates versus reactive scrolling
Superforecasters batch revisions: morning review, post-release update, weekly refresh. Reactive traders let every push notification move f by five points. Scheduling does not mean ignoring news—it means assigning each item a tier and LR before you touch the number.
If three items arrive in an hour, write one combined update with correlation noted, not three heroic jumps.
Worked example: second piece of same-day evidence
After the poll update to sixty-seven percent, a favorable fundraising filing arrives. Ask whether fundraising is independent of polling. If mostly redundant, apply LR near 1.1 and land near sixty-nine percent, not eighty. Independence checks are the difference between Bayes in practice and Bayes on a bumper sticker.
Common mistakes
Treating every bullish headline as LR 2. Ignoring P(evidence | no event)—tips and rumors are common when nothing happens. Updating on price alone. Using Bayes to justify a trade you already wanted.
What comes next
Single-track Bayes is necessary but not sufficient. Before you commit one f to the journal, superforecasting teams synthesize multiple partial estimates—the dragonfly eye.
Key ideas to carry forward
Log priors. Write LRs. Use odds form. Cap daily product of LRs. Never update on price alone. Lock f for Brier.
Bayesian practice is not optimism or pessimism—it is bookkeeping. If your bookkeeping cannot survive a skeptical reader, it cannot survive your bankroll over hundreds of events.
Practice Bayes on paper before you practice it with size. The log is the product.
Next: The Dragonfly Eye: Combining Multiple Perspectives