Predict the Future from a Single Clue with Bayes’s Trick

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When Anna launched her blog, she had no idea if her first post would go viral or sink without a trace. She’d read articles about data-driven marketing and felt overwhelmed by big analytics platforms. Then she stumbled on a simple Bayes-inspired trick: start with a guess, run one test, and update your belief with a plus-two rule. If her first post got 50 subscribers, she’d expect ⅔ of her target. If it drove zero, she’d drop to ⅓.

This rule was first sketched by Thomas Bayes and given polish by Laplace two centuries ago. It takes any prior belief and refines it with just a single data point—no complicated regressions required. If you think there’s a 20% chance a product feature will delight users, launch a quick survey. One happy customer pushes you toward 50–75% odds; one detractor pushes you down to 25–33%.

Suddenly Anna had a repeatable method. She scribbled her original hunch on a Post-it, ran her first A/B test, and applied the ratio. She’d gain confidence, pivot, or pause before investing heavily in any feature.

Bayes’s rule shows that small data need not be worthless. With a clear prior and one good clue, you can navigate uncertainty, replace guesswork with a simple formula, and learn where to focus your efforts next.

Start by committing your initial estimate to paper—even if it’s a gut hunch. Run a single, quick experiment or trial and watch what happens. Use the plus-two rule to combine your prior with that one result, and update your forecast. Treat that new figure as your fresh starting point for the next test. You’ll find that a little evidence goes a long way toward guiding your next move—try it in your next decision.

What You'll Achieve

You’ll gain clarity in uncertainty and replace vacillation with a repeatable update rule. Externally, your experiments will become more focused and your plans more agile.

Combine Beliefs with Evidence

1

Write Down Your Priors

Before you encounter new data about an unfamiliar project or trend, note your initial sense of likelihood. Be explicit: “I think there’s a 20% chance my idea will work.”

2

Collect a Single Data Point

Run a quick experiment or test—one interview, one prototype trial, one drop in the bucket—and observe whether it succeeds or fails.

3

Apply the Plus-Two Rule

After one success, estimate your probability as 2÷(1 + 2)=⅔. After one failure, 1÷(1 + 2)=⅓. If you already had a prior, multiply it by the new likelihood ratios.

4

Update and Iterate

Record your new belief as your updated prior. When you get the next result, repeat the calculation—gently steering your forecast in light of evidence.

Reflection Questions

  • What prior belief in your work could benefit from a quick data point?
  • How would using the plus-two rule change your next decision?
  • What’s one small test you can run today to gather that first clue?

Personalization Tips

  • Pitch your startup idea once and note investor feedback. Then use Bayes’s Law to update your confidence before your next pitch.
  • After speaking one sentence in a new language class, immediately adjust how likely you think you’ll become fluent using Laplace’s plus-two method.
  • Prototype a single feature of your app and use that result to reprioritize your roadmap with a Bayesian update.
Algorithms to Live By: The Computer Science of Human Decisions
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Algorithms to Live By: The Computer Science of Human Decisions

Brian Christian and Tom Griffiths 2016
Insight 6 of 8

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