When you're setting up an authentication method for access to an enterprise information system or to the enterprise premises, you don't want to just worry about false positives. You need to worry about the false negatives also.
Think about the logon screen of an application or website, asking for your username and password. The biggest worry of IT people behind that screen is to make sure the wrong people do not access the system. I think they should also care about the number of times the right people can't access the system either.
That's no big math, but suppose you would change a logon screen with 0.1% of false positives and 1% of false negatives (each losing the company 0.5$ because of the time lost for work) for a new logon screen with 0.01% of false positives and 3% of false negatives. Additionally, suppose the logon screen is used by 10,000 employees five times a day, 300 days a year.
The change would represent a loss of:
2% of additional false negatives
x 0.5$ each time
x 10,000 employees
x 300 days a year
x 5 times a day
which equals 150,000 $ per year.
It makes sense to acquire the new logon screen (let alone its own cost) if dividing by ten the losses due to intrusions in this system saves you more than 150,000 $ each year, that is, if the losses due to intrusions are above 170 000 $ per year, roughly.