Ads that "work" are more a case of "can we show numbers that the people upstairs will consider ok?" than "can we prove these ads have contributed to our bottom

Ads that "work" are more a case of "can we show numbers that the people upstairs will consider ok?" than "can we prove these ads have contributed to our bottom line?". The old "I know half of what I spend on advertising is wasted but the problem is I don't know which half" still applies, despite all the promises of digital advertising.