A boundary turns a score into a decision.

INSTRUMENTS / MEASUREMENT & FRAMING

Constructed example

Move the cutoff. Inspect the errors.

Change an input. Inspect every step. Keep a fixed record.

A working copy · changes stay here until you save

thresholds-v1

01 / THE QUESTION

What would you rather get wrong?

Twenty fictional messages have supplied labels and scores. A cutoff turns each score into a decision: flag it as spam, or let it through.

Keep a first thought

Optional. Included only when you explicitly save; excluded from shared links.

Constructed data · every relationship and outcome is supplied.

02 / OPEN THE MODEL

SpamLegitimate0255075100
Fixed supplied scores, 0–100. Circles: spam. Diamonds: legitimate. Shaded side: flagged. The cutoff includes equality.
True positive7Spam flagged
False positive2Legitimate flagged
False negative1Spam passed
True negative10Legitimate passed
FOLLOW ONE MESSAGE

S07 · score 60 → flagged → true positive

Supplied label: spam. Equality is on the flagged side.

Assign costs to the mistakes

Whole fictional points 0–100. Changing a cost does not change any classification or move the cutoff.

2False positivesmessages
1False negativesmessages
9Assigned error costfictional points

Follow the idea.

A concept, in three frames

Inspect the scores.

Scores are supplied, not calibrated probabilities.

Move the cutoff.

The decision changes at an explicit boundary.

Count both errors.

False positives and false negatives differ.

HOLD ONE VERSION STILL

What changes when you change the model?

Keep the current inputs beside your next adjustment.

A cutoff is a choice with consequences.

A false positive flags a legitimate message. A false negative lets spam through. Moving the cutoff changes which mistakes this fixed set contains.

Read the investigation →
Save this experiment

Saved only in this browser. Clearing browser data removes local copies; export a copy from your notebook to keep it.

MODEL & LIMITS

What this model leaves open

These scores are not calibrated probabilities, and twenty supplied messages do not estimate real-world performance. Assigned costs are fictional points, not objective harm.

  1. InputsWhat is supplied?
  2. DefinitionWhat is counted?
  3. InferenceWhat follows?
Inspect the exact workings
Every message · fixed labels and scores · cutoff ≥ 60
IDScoreSupplied labelDecisionOutcome
S0190SpamFlagTrue positive
S0285SpamFlagTrue positive
S0380SpamFlagTrue positive
S0475SpamFlagTrue positive
S0570SpamFlagTrue positive
S0665SpamFlagTrue positive
S0760SpamFlagTrue positive
S0855SpamPassFalse negative
L0195LegitimateFlagFalse positive
L0268LegitimateFlagFalse positive
L0358LegitimatePassTrue negative
L0448LegitimatePassTrue negative
L0545LegitimatePassTrue negative
L0640LegitimatePassTrue negative
L0735LegitimatePassTrue negative
L0830LegitimatePassTrue negative
L0925LegitimatePassTrue negative
L1020LegitimatePassTrue negative
L1115LegitimatePassTrue negative
L1210LegitimatePassTrue negative

Precision: 7/9 = 77.78%. Recall: 7/8 = 87.50%. Assigned cost: 2 × 4 + 1 × 1 = 9 fictional points.

Assumptions, sources and evidence status

Original constructed fixture: constructed-messages-v1. thresholds-v1. No empirical observations are represented by these example counts.

  • All labels and scores are supplied; these are not empirical classifier performance estimates.
  • Scores are not calibrated probabilities. Error costs are fictional points chosen by the reader.
  • Changing costs does not move the threshold or retrain a model. Precision is undefined if no messages are flagged.
Read the definition and primary background sources →