In mathematics—as in other forms of communication—terms should retain their precise meanings
First, let’s get this straight: ROI is not synonymous with “whatever results.”
ROI (return on investment) refers to a financial return on a financial investment (in dollars, or pounds, or rands, or whatever your currency is) and it’s expressed as a percentage—the percent you made on your money. That’s what ROI is. If someone tells you differently, they’re either lying or intentionally obfuscating. Or, to be generous, they’re not really sure what they’re talking about.
Yes, yes, yes: Nowadays PR and social media people are always “ROI for this” and “ROI for that.” And they are almost always in error. In an effort to sound businesslike, they’ve borrowed a term from the hard-nosed guys in accounting. But what gets lost in translation is their credibility. (See Shel Holtz’s blog for an excellent discussion of this problem.)
Counting is not measurement.