Convert Probabilities Into Frequencies
Translate percentages into counts so people actually feel the odds
- Difficulty
- Easy
- Time to result
- ~days to results
- Steps
- 6
- Confidence
- 80%
Schrager's working definition of risk is a probability distribution: an estimate of all the different things that could happen and how probable they are. The problem is that whole distributions are not intuitive to anyone, and probabilities themselves only arrived with the Renaissance — Bernoulli and that generation — so no one is born with a feel for them. Her fix is a translation step. Take the probability you would normally quote as a percentage or a confidence interval, and re-express it as a frequency: a count of times out of a small, imaginable total. Ritholtz reports the same effect with clients — retirement software output as a percentile lands nowhere, while 'nineteen out of twenty' lands immediately. The research psychologists Schrager spoke to attribute it to how brains are programmed: frequencies simply resonate more.
Origin
Extracted from Masters in Business — Allison Schrager's account of asking research psychologists why frequency framings land where percentiles do not, matched against Barry Ritholtz's client experience.
Core principles
- 01Probability is a modern invention; humans have no native intuition for it.
- 02Frequencies map onto how brains already process the world.
- 03A confidence interval communicates almost nothing to a non-specialist.
- 04The same number can be honest and useless, or honest and vivid.
- 05Even specialists admit percentages often fail to move them.
How to run it
- 1
Get the underlying distribution right first
Before simplifying, establish the honest set of outcomes and their probabilities. The translation is a presentation layer, not a substitute for the analysis.
Watch out Do not let a clean frequency hide a model whose assumptions are shaky.
- 2
Identify the single number that drives the decision
Most projections carry many figures. Pick the one the listener must act on — for example, the chance of hitting a retirement goal.
- 3
Choose an imaginable denominator
Twenty, or a hundred at most. The listener should be able to picture the set of cases without effort.
Pro tip Round to the nearest clean count rather than preserving false precision.
- 4
State both sides of the count
Say how many times it works and how many times it does not. Nineteen out of twenty succeed; one out of twenty does not.
Pro tip Naming the failure count builds trust and pre-empts the accusation of spin.
Watch out Reporting only the success count turns a translation into a sales pitch.
- 5
Strip the jargon from the spoken version
Keep percentiles and confidence intervals in the appendix. Speak in counts.
- 6
Verify it landed
Ask the person to restate the odds in their own words before moving to the decision.
Pro tip If they restate it as a certainty, the framing has overshot — reintroduce the failure case.
In the wild
Ritholtz describes planning software that outputs a probability of hitting retirement goals under assumptions about inflation and continued contributions. Presented as a percentile or a confidence interval, it means almost nothing to the client sitting across the desk. Re-stated as 'in nineteen out of twenty situations we can show you you'll hit your target goals, it's only one out of twenty that you don't make it', the same projection suddenly registers. Schrager's explanation is that frequencies match how our brains are programmed, whereas whole probability distributions never will.
→ Identical underlying model, but a client who can now weigh the trade-off instead of nodding at a number.
Common mistakes
Leading with the confidence interval
The statistically correct object is the one least likely to be understood, so opening with it wastes the conversation.
Quoting only the good count
Saying nineteen out of twenty succeed without naming the one that fails converts a clarity tool into persuasion.
Using an unimaginable denominator
Frequencies out of ten thousand recreate the original abstraction problem the translation was meant to solve.
Is it for you?
Best for
Advisers, planners and analysts who must get a non-technical audience to act on probabilistic information.
Not ideal for
Technical audiences who need the full distribution and its parameters rather than a simplified count.
From the transcript
“hey, in nineteen out of twenty situations, we can show you you'll hit your target goals.”
“just something about the way our brains are programmed. His frequencies just resonate with us more.”
“but it's also when you think of probabilities converting them to frequencies.”
From the episode
Allison Schrager Discusses Monetary Policy
Allison Schrager