In which professional sport (NHL, NBA, MLB, NFL) does the coach matter the least?

Coaches matter the most in the following order:
1. NBA
2. NFL
3. MLB

There is some seriously flawed logic going on with the folks who claim NBA coaches matter little. The remarkable successes of Gregg Popovich, Phil Jackson, Pat Riley, Red Auerbach, Jerry Sloan and others offer empirical evidence of the sustained benefit superior coaching provides at the NBA level. 

While it is true that the NBA game is more improvisational than the NFL, that does not make it any less cognitively demanding for players nor coaches. 

NBA basketball is a lot like jazz, while football and baseball more closely resemble classical music. A tightly diagrammed football offense and defense functions like sheet music. If the plays are effective, called appropriately and executed by quality players, football teams generally do well (also, it's important to note that many NFL coaches do not call their own plays--specialized assistants do that for them). 

The unscripted nature of an improvisational sport like pro hoops adds an incredible level of complexity to the coaching position. Lineups, matchups, playing style and adjustments are all more difficult to maneuver. 

It is relatively easy to determine when a left-handed reliever will be statistically more effective in a certain situation--or when a nickel defense makes more sense than a 4-3. But it is more difficult (and risky) to determine that JJ Barea and Jason Terry, both undersized guards, can be effective on the floor at the same time against a specific opponent (Miami) as long as Dirk and Chandler remain in the game and a zone defense is employed. 

Because there are fewer players, more confined playing surfaces and more direct interaction among teammates in basketball compared to football and baseball, chemistry is more important on the hardwood than it is on the gridiron or the diamond. The best basketball coaches (and the best business leaders) are masters of developing chemistry and putting their personnel assets together in combinations that best ensure successful team outcomes across widely differing situations.    

Also, a coach's ability to motivate and get the most out of his players is more  critical in the NBA. Unlike NFL coaches and MLB managers, NBA coaches do not have highly-trained specialized assistants on their staffs. With smaller rosters and fewer assistants, NBA coaches spend more time one on one with their players and are therefore more directly responsible for individual players' growth and performance on the court.