Impressions count the times an ad was served, not seen, and dividing them by reach, the number of unique people, gives frequency. Click-through rate is clicks over impressions, cost per click is spend over clicks, and cost per mille is spend per thousand impressions.
Customer acquisition cost is the fully loaded spend, including salaries, tools and creative, divided by customers actually won. Lifetime value is the margin, not the revenue, expected over the relationship, and it rests on a forecast of how long customers stay. Their ratio says whether acquisition pays; the payback period says when, which is the cash question.
Work an example. A shop spends 2,000 dollars, gets 500,000 impressions and 5,000 clicks, and wins 50 customers. Click-through rate is 1 percent, cost per click is 40 cents, cost per mille is 4 dollars, and acquisition cost is 40 dollars on media alone. If each customer brings 15 dollars of margin a month, payback takes a little under three months.
Attribution models, such as first touch, last touch, linear and time decay, divide credit by assumption, so switching models reshuffles every channel's apparent performance. Only a holdout, a random slice deliberately left unexposed, answers whether the spending caused the outcome.
On a website, an engaged session is one that clears a set bar for duration, key events or pages viewed. Engagement rate is the share of sessions that were engaged and bounce rate is the rest, so broader, cheaper traffic can lower the rate while raising the count of engaged sessions.
The trap is reading a falling cost per click as progress. Suppose next month the same 2,000 dollars buys 8,000 clicks at 25 cents but wins only 30 customers. Cost per click fell by more than a third, and acquisition cost rose to about 67 dollars, because cheaper clicks are often less qualified ones.
Rule: judge every metric next to the one it trades against, and trust a channel's credit only after a holdout has tested it.