In response, several correspondents pointed out that while this
might be the case in an idealized organization, most managers inherit
their teams -- they don’t build them from scratch. Beyond that,
excellent leaders are demonstrably able to achieve superior results
with mediocre team members.
The world is generally more complicated than the idealized space within which geometricians construct their proofs.
Nonetheless, the proofs are important. So here’s a quasi-geometrical
analysis to clarify the situation, this time in the form of a matrix:

Excellent leaders can achieve strong results with less-than
excellent teams. They also take responsibility for the quality of their
teams, developing employees who have more potential than ability, and
replacing those who aren’t doing their part and clearly never will.
Adequate leaders might not add much to an excellent team’s ability
to deliver results, but they do generally have enough sense to stay out
of the way. The team knows what it has to do, and gets the job done.
Until, that is, the situation changes, and what the team knows no
longer fits. Then, a team’s strength becomes its weakness. It takes
strong leadership to steer an excellent team in a new direction. Merely
adequate leaders will either fail to recognize the need for change,
won’t understand how to adapt to the change, or will be unable to get
their teams to buy into the new program.
That leaves poor leaders. If it isn’t obvious: No matter how strong
a team they inherit, poor leaders will eventually deliver dismal
results, because they’ll drive out strong team members and hobble
everyone else.
Those who lead scientists, engineers, and other technical
professionals have an especially tough challenge. They must be
excellent leaders, and also can’t escape the need to be literate in
their fields. Among the reasons, these three stand out:
First, leaders have to be in a position to assess the strength of
the individuals and teams who report to them. The more abstruse the
field, the less likely it is that a generic leader will figure this out
with any degree of accuracy. If you don’t know who’s strong and who
isn’t, the teams reporting to you won’t improve because you won’t know
what “improve” looks like.
Second, leaders have to set direction, and to recognize when a
change in context demands a change in direction. They have to know, for
example, when it’s time to abandon object-oriented analysis and design
in favor of a services model.
Okay, that’s a bad example, since nobody seems to have a clear idea
of what the actual differences are, if in fact there any differences
other than OO’s link-time binding vs SOA’s run-time binding … but the
principle still holds. Anyway …
Third, leaders then have to allocate assignments to achieve the
organization’s goals. If they don’t know the trade, the assignments
they hand out will be reasonable only by accident.
What will happen when those receiving the assignment to, say, build
a perpetual motion machine object because they’d need to violate the
laws of physics?
Answer: The leader, unable to evaluate their objection on its
merits, and unwilling to back down for fear of being judged weak, will
be forced to rely on coercion (by, for example, firing the complainers).
Which means that in addition to being the first refuge of the lazy, coercion is also a refuge of the ignorant.