How does a board objectively evaluate that a potential CEO is worth say $25M/year over a candidate who will take the job for $4M/year?

Previous job performance isn't that reliable since countless CEOs have been great at one company in terms of raising stock price/revenue/profit/whatever, and then flamed out at a future company. How does one know in advance that one CEO will increase revenue by a few percent more than another, and justify such an expensive compensation package?