If that is true (forgive me, I'm not from America and know nothing about NFL at all), then forgive me for being an ultra cynical bastard.

At some level, I'm taking it you're still telling me that they at least all played the game to some level, which is still a distinctly different level from common corporate messages that you wouldn't even have had to play or understand the game of the team you're managing. So it sounds to me like there's still some level of fundamental skill attribution there, though maybe not to the levels found in other sports/professions.

It is also true that the correlation between coach and skill is not perfectly bi-directional/symmetrical. Great skill does not necessarily imply great manager/coach. But my contention is that great manager/coach has some necessary correlation/causative connection with having great skill and that this connection grows stronger the more an activity relies upon high skill and the direct measuerable application thereof.

It is the nature of this connection, that one (coach) requires the other (skill), but that one (skill) does not imply the other (coach), that makes such positions so rare in highly valuable high-skill-verifiable games.

Of course, the other dimension of this analytically is the supply side: what is the shape of the skill curve (does it taper off quickly or is there a long tail), and how many people/resources are put towards producing people in this game.

As an ultra cynical bastard though, I think it would raise for me some interesting questions about the nature of NFL coaches, remuneration, players, how easy or hard it is to measure their skills and value their contribution to a team's success, how directly their skills affect an outcome of a game, how important/connected this application is to a team's success, and how much such things are the things being chosen for.

Now I should state that I've done a little bit of analytics on sports (primarily rugby and tennis) in my own time over the years, so the notion that such positions and remuneration in team sports is tied more to stereotypes, marketing, showmanship, reputation advertising and superstition in the team sports vs the individual ones/frequent contest/high-verifiable ones is actually what I would expect to see, rather than as something I think invalidates my theory. If you put sports on a spectrum, the variability and difficulty in finding empirical relationships between skill and game contribution does become increasingly difficult the more you move away from the frequent contest, high skill (by which I mean in a technical sense: the amount of variance in an outcome directly attributable to some kind of notion of measurable skill rather than randomness), individual participant games.

There's a whole lot more I haven't touched on.

/I also think, although I haven't put effort into analyzing it, so I accept it as a personal bias/belief at this stage, but I haven't found anyone else that has been able to demonstrate it, so I think i'm pretty safe, that there is almost no demonstratable connection between higher corproate executive remuneration and actual measurable skills/outcomes, and that this is this culture/phenomenon that explains where the "non-technical manager" idea comes from...