From Thinking, Fast and Slow. Emphasis mine.
A very generous estimate of the correlation between the success of the firm and the quality of its CEO might be as high as .30, indicating 30% overlap. To appreciate the significance of this number, consider the following question:
Suppose you consider many pairs of firms. The two firms in each pair are generally similar, but the CEO of one of them is better than the other. How often will you find that the firm with the stronger CEO is the more successful of the two?
In a well-ordered and predictable world, the correlation would be perfect (1) and the stronger CEO would be found to lead the more successful firm in 100% of the pairs. If the relative success of similar firms was determined entirely by factors that the CEO does not control (call them luck, if you wish), you would find the more successful firm led by the weaker CEO 50% of the time. A correlation of .30 implies that you would find the stronger CEO leading the stronger firm in about 60% of the pairs - an improvement of a mere 10 percentage points over random guessing, hardly grist for the hero worship of CEOs we so often witness.
If you expected this value to be higher - and most of us do - then you should take that as an indication that you are prone to overestimate the predictability of the world you live in. Make no mistake: improving the odds of success from 1:1 to 3:2 is a very significant advantage, both at the racetrack and in business. From a perspective of most business writers, however, a CEO who has so little control over performance would not be particularly impressive even if her firm did well. It is difficult to imagine people lining up at airport bookstores to buy a book that enthusiastically describes the practices of business leaders who, on average, do somewhat better than chance.