I think this is probably where you get the room to juice the numbers like this. If you were tracking online conversions, people would easily be able to compare with an incrementality study run by the provider (say Google) and see that you are lying/wrong.
It is impossible to actually observe what would have happened, had there been no advertisement, because there in fact was an advertisement.
Thus, the estimation of incrementality must be inferred statistically.
I can see how you would have that perspective as a third-party analyst of conversion.
It's actually easy to do if you are the exchange/sell-side provider of the advertising space. In your logic, where the advertiser requesting the incrementality study would have won the auction, just randomly remove their bid from some won auctions, have the second highest bidder win, and then track that user as the "control" for conversion purposes vs. users you did display the ad to. Voilà!
This is how Google in-house incrementality studies are run, for instance.
I can see how you would have that perspective as a third-party analyst of conversion.
It's actually easy to do if you are the exchange/sell-side provider of the advertising space. In your logic, where the advertiser running the incrementality study would have won the auction, just randomly remove their bid from some won auctions, have the second highest bidder win, and then track that user as the "control" for conversion purposes vs. users you did display the ad to. Voilà!
That's not observation. That's statistical inference. I am referring, strictly, to direct, empiricial observation. With any kind of statistical inference, you get into a pissing match about assumptions, model quality, etc... Is the "control" a good stand-in for the behavior of the "test", etc.
Incrementality is able to be estimated, but unobservable. And therein lies the potential for fraud.
You can observe the results of the experiment and then make statistical inference about the "true" incrementality. You don't even have to perform inference necessarily, you can just provide the direct results of your experiment to the advertiser and let them do the inference.
But I do fail to see how a third-party could possibly infer this measure, given that they have no capacity to do a true incrementality experiment on the platform.
To riff off the average height example - you can get a pretty darn good estimate based on sampling and good statistical practice... unless the people doing the sampling have a reason to bias the measurement, or - if you're sampling on your own - people who control where you go and who you meet...
I think my usage of "you" was confusing because I work in sell-side advertising.