The Same Campaign Can Have a $10,000 CPA or a $100 CPA. Depends Which Model You Ask.
First-click, last-click, and multi-touch attribution don't disagree by a small margin. On the exact same spend and the exact same conversions, they can land 100x apart.
Same spend, same conversions, wildly different CPA
An attribution model decides which touchpoint in a customer's path gets credit for a conversion. On a channel where most buyers interact with an ad more than once before purchasing, strict first-click credit only counts the handful of people who converted on their very first touch. Any-click or last-click credit counts far more of the same conversions as attributable. Same total sales, same total spend. The denominator used to calculate cost-per-acquisition is the only thing that changed, and it can move the reported number by orders of magnitude, not a rounding difference.
Why this isn't a rare edge case
Any channel playing a discovery role rather than a closing role shows this pattern: prospecting formats, upper-funnel video, anything that introduces a brand rather than closes a sale. A small number of people buy on the first exposure. A much larger number buy later, after seeing the brand again somewhere else. A model that only credits the first touch makes that channel look nearly worthless. A model that credits any touch makes the same channel look like the primary driver of revenue. Neither read is wrong. They're answering different questions and reporting the answer as if it were the only one.
What to check instead of picking a 'better' model
Arguing over which single attribution model is most correct is usually the wrong fight. Every model produces a defensible number by its own logic. What settles the argument is a reconciled record: how many verified conversions actually happened, and whether the customer's real path can be reconstructed rather than assumed by a model built for a different purpose. The model choice will always output something. Only an owned, reconciled record tells you whether that output reflects what actually happened.