What a wonderfully succinct way of expressing this - it also captures why "control-motivated" people for want of a better description struggle so much with even the first steps of ceding that control. Great expression!
But if control is "indistinguishable from noise" then it sounds like control=impact, which means I don't understand your overall point and distinction at all. It seems like it gets all muddled along the way.
So I think of being an individual contributor as playing chess for $100 and being a CEO as playing a hand of poker for $100,000.
And to take this analogy further you gain a lot of information about a chess player's skill by whether he wins, but very little from a single hand of poker. Did the poker player lose because he got a band hand or because he's a bad player. There is a similar difference between CEOs versus developers. You can figure out if a developer is any good by seeing how successfully he completes a project or task. But it is very hard to figure out how well a CEO is doing by just looking at his performance.
Brilliantly articulated!!
(I logged in after years just to up-vote this comment).
I have an alternative theory.
When you're a single contributor you have total control over your productivity and success, but very little impact on your the company's success. Then when you're promoted your control decreases, but impact rises. As you move up the ladder you are constantly trading control for impact.
Eventually you end up as CEO and these numbers converge with a large impact relative to a single contributor but little control over the success of a company. Little enough control that its sometimes hard to distinguish from noise. But your affect on perceived success drops off at a slower rate than actual success. This means to get promoted at higher levels it is more impactful to focus on perceived success over absolute success, and people who are better at this will have more luck getting promoted at high levels. Basically it's a lot easier to convince the board of AT&T that you're doing a 3% better job than to actually get the company to perform 3% better.
This would explain why most non-founder CEO's are so polished.