Compound-error math
Build-along · ~8 min at your own keyboard
If each step succeeds independently, the chances multiply: 0.9 × 0.9 × 0.9 × 0.9 × 0.9 ≈ 0.59, and twenty steps at 90% ≈ 0.12 — about 1 run in 8 gets through clean. Two honest caveats. The multiplying assumes steps fail independently; in real work, one bad input can break several steps at once. And your per-step numbers are guesses, so the product is a rough guide to WHERE to look, not a measurement. Use it to pick the weakest steps; then prove the fix by running the whole workflow on a fixed set of test inputs and counting clean runs.
The long version: Why chained steps fail ↗
Do this
0/4Checkpoints
- ▸You should now see a number for each step in your workflow, marked guess or counted.
- ▸You should now see the before product with the decimals shown.
- ▸You should now see two weakest steps picked with a fix named for each.
- ▸You should now see a before and after count of clean runs on the same test inputs.
The three ways this goes wrong
- You multiply the percentages as whole numbers (90 x 90). — Convert to decimals first: 0.9 x 0.9 x 0.9.
- Every step gets 99% and the total looks fine. — Be honest. Any step where you have seen it go wrong once in ten tries is 90%, not 99%.
- The measured runs don't improve even though the paper number did. — Your guesses were off, or steps fail together. Look at the failed runs and fix what actually broke.
Share what happened
Paste your step list with estimates (marked guess or counted), the before product with the decimals shown, the fixes, and the before/after count of clean runs on your test inputs.
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