Let’s say one of every five coaches is considered ‘good’. A good player responds to either kind of coach while a bad player only responds to a good coach.
A good player...
1/5 chance of a good coach
4/5 chance of a bad coach
Improves under all coaches
Odds of improvement are 5/5
A bad player...
1/5 chance of a good coach
4/5 chance of a bad coach
Improves only under a 'good coach'
Odds of improvement are 1/5
This roughly approaches my experience from high school. It just seemed like an unwritten rule that one out of every five teams was always tough to play. I assume now that these teams just had good coaches who elevated the performance of their worst players. The other four out of five teams were sometimes good and sometimes bad – it just came down to whether they had star players at the time.
A good way to see if a high school has a good coach is to see how reliant a good team is on teachable skills. At the high school level, most of the kids are either good athletes or they are not. Therefore, a good team with a superior level of athleticism might not necessarily be led by a good coach. However, if a good team is highly skilled in the sport, it is almost always a sign of good coaching (and at minimum a better sign of it than a team full of great athletes).
A similar logic should be used to assess any form of leadership. The surest way to identify the best leadership is to look at the teams or organizations under their command and determine how closely success is linked to the skills presumably taught or cultivated by the leader.
