How exactly do you establish the %likelihood that a particular CEO will save your company to the degree of precision that you could actually meaningfully incorporate it into a business model?
(Yes, I'm ignoring the time value of money, risk, etc, to simplify.)
The best you could ever hope to do is "CEO candidates with this kind of background tend to have this kind of record when taking over this kind of company", which I'm sure is quite an illuminating sample.
I really don't get the point you are making. Are you telling me that a struggling company shouldn't try to get what they believe is the best possible CEO, provided his pay package is vastly smaller than the variance in possible outcomes for the company?
You realize that with the narrow exception of a few quant traders, you've pretty much described all business decisions.