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adfire.digital  /  Arithmetic before spend

The arithmetic to do before any spending decision

Two numbers a business already knows — the margin it keeps on a sale and the share of visitors who buy — determine the most it can pay for a visit before the arrangement loses money. The relationship is arithmetic, not a benchmark, so it holds regardless of channel, platform or year.

Deriving the ceiling

Symbols throughout, because any specific figure quoted here would be someone else's business rather than the reader's.

margin per sale = M visitors per sale = 1 / C (C = conversion rate) break-even per visitor = M × C

Read the last line carefully: the ceiling on what a visit can be worth is the margin multiplied by the conversion rate — not the sale price, and not the revenue. Every cost that sits between revenue and margin has already been removed before this line is reached.

Two properties follow. Halving the conversion rate halves the ceiling. And a business whose margin is unknown cannot compute a ceiling at all, which is the real reason this step precedes any spending decision rather than following it.

Why an early result cannot be read

The limit is statistical and applies before any judgement about performance is possible.

A conversion rate observed over a small number of visits carries an interval wide enough to contain wildly different conclusions. With very few conversions recorded, the observed rate and a rate several times larger or smaller are both consistent with the data. No amount of dashboard refreshing narrows that interval; only accumulating more observations does.

The practical form of this limit: decide in advance how many conversions you will wait for before drawing any conclusion, and write that number down before starting. Deciding afterwards, once results are visible, converts the same data into a conclusion that the data does not support.

What the arithmetic settles and what it leaves open

Settled by the arithmetic

  • The maximum a visit can be worth, given a margin and a conversion rate.
  • The direction and size of the effect when either input changes.
  • That a ceiling cannot be computed without knowing the margin.

Left entirely open

  • Whether visits are obtainable at or below that ceiling at all.
  • Whether the observed conversion rate will hold at a larger volume.
  • How much of an observed outcome would have occurred without any spending.

What backs the statements here