Attribution allocates credit for conversions that occurred. Incrementality asks whether they would have occurred anyway, and only the second question tells you whether spending was worthwhile.
The counterfactual is the entire point
Every conversion has two possible histories. One where the advertising influenced it and one where the person would have bought regardless.
Reporting cannot distinguish these, because it only observes the history that happened.
An experiment creates the missing comparison by withholding advertising from a group that is otherwise identical, which makes the difference observable.
How a test is constructed
A population is split at random into an exposed group and a control group, and the advertising runs only for the first.
Randomisation is what makes the comparison valid, because it ensures the two groups differ only in exposure rather than in anything correlated with buying.
The difference in conversion rate between the groups is the incremental effect, and everything above that level was going to happen anyway.
Geographic splits are the practical version
Where user-level control is not available, markets can be split instead, with the channel switched off in a set of regions and left running in comparable ones.
This works well for national campaigns and requires the regions to be matched on size, seasonality and historical trend rather than simply divided.
It also requires patience, since regional sales data is noisier than user-level data and needs a longer period to separate the effect from normal variation.
Why results are usually lower than reported returns
Attribution assigns full credit for conversions that were partly or wholly determined elsewhere, so any attributed figure includes a share of activity that was not caused.
Incremental results are consistently smaller, and the gap is widest in channels that advertise to people already close to purchasing.
Knowing the size of that gap per channel is what makes budget allocation a decision rather than a preference, and it is why the test is worth its cost.
The limits of a single test
A test measures the effect of a specific level of spend, in a specific period, with specific creative, and does not generalise beyond those conditions.
Doubling budget after a positive result does not double the effect, because returns diminish as the reachable audience is exhausted.
Tests also measure the short window they run in, which understates channels whose effects accumulate over longer periods than the test allows.