We need to adjust by the probability that you are indeed the best choice for CEO, conditional on the board thinking you were.
You don’t actually care about the probability that you’re the best CEO. If you chose not to work there, the company wouldn’t necessarily hire the best CEO in your place. Instead you care about how much better you are in expectation versus who the board would hire instead of you. Even if you’re unlikely to be the best CEO, you might still be better in expectation than any other candidate.
You’re right, you’ll presumably be better in expectation than the next candidate. But the research that yields the high CEO impact numbers tends to look at actual performance differentials, rather than expected—clearly their expectation will be much lower, so we need to scale down the statistics these studies provide.
Nice analysis, Larks!
You don’t actually care about the probability that you’re the best CEO. If you chose not to work there, the company wouldn’t necessarily hire the best CEO in your place. Instead you care about how much better you are in expectation versus who the board would hire instead of you. Even if you’re unlikely to be the best CEO, you might still be better in expectation than any other candidate.
You’re right, you’ll presumably be better in expectation than the next candidate. But the research that yields the high CEO impact numbers tends to look at actual performance differentials, rather than expected—clearly their expectation will be much lower, so we need to scale down the statistics these studies provide.