Where the arithmetic stops working

Three places it fails

Demand is not fixed. The arithmetic assumes the work stays the same size. Frequently the cost falling causes more of it to be demanded, and nobody's hours go down. This is the single most common reason predicted savings do not appear.

The residual is not proportional. Taking 90% of a task does not leave 10% of the cost. What remains is often the part requiring the most context, arriving unpredictably, in the hands of somebody who now does it rarely enough to be bad at it.

Errors are not symmetric. Payback treats a wrong output as a small cost. In some tasks one wrong output costs more than a decade of savings, and the correct model is not payback at all.

Nobody's hours went down

A team automates a task that was taking 200 hours a month. A year later, headcount is the same and everybody is still busy. What most likely happened?

Break your own model

Go back to your payback figure and find the assumption that, if wrong, changes the answer most. Not the one most likely to be wrong — the one with the largest effect if it is.

Then write one sentence stating the condition under which your recommendation flips. That sentence is worth more than the number it qualifies.

The assumption that carries the answer

Name it in a few words — "exception rate", "invoice volume", "my hourly cost". You are recording which part of your own reasoning to go and check first.

What you would say now

You started this course able to have an opinion about automation. You can now have an argument about a specific task.