The NBA Coach of the Year award doesn’t often generate controversy, and for good reason. The choice is almost always a coach from a playoff team that has shown dramatic improvement. When there are several good choices, the man selected usually comes from the team with the fewest superstars, which was the case last season when Toronto’s Sam Mitchell won the award.

If you apply those criteria to this season, there are three rather obvious choices: Doc Rivers of the Boston Celtics, Byron Scott of the New Orleans Hornets, and Maurice Cheeks of the Philadelphia 76ers. Each took a team from the lottery to the playoffs. But there are problems with each candidacy, and voters should seize the chance to reward the coaches who did the most to improve their team. A broader look at the league suggests that nontraditional choices such as Washington’s Eddie Jordan, Portland’s Nate McMillan, or Sacramento’s Reggie Theus are more deserving than the usual suspects.

Rivers received a completely revamped roster and coaching staff from his boss, the general manager of the Celtics, Danny Ainge. Admittedly, he made it work out very well, but it was hardly heavy lifting to adapt a game plan to suit two team-oriented All-Stars such as guard Ray Allen and forward Kevin Garnett. In addition, Boston’s biggest improvement was on defense, and Rivers delegated that responsibility to assistant coach Tom Thibodeau.

Scott did a good job in New Orleans, but he has been doing a good job for several seasons. This campaign marked the best run of health that the team has had during his tenure. Also, the Hornets’ rise was fueled by an ascension to superstar territory by point guard Chris Paul. Scott has always been a good coach: He took two rather mediocre New Jersey teams to the finals. His best case is based on his body of work rather than anything specific that he did this season.

Despite changes in the executive suite and much adversity, “Mo” Cheeks did an impressive job in crafting a nucleus of young players in Philadelphia. At the beginning of the season, Cheeks seemed like one of the coaches most likely to be fired before the All-Star break. Instead, he warded off the buzzards and got his charges to focus on defense while using a novel offensive scheme that relies heavily on alley-oop passes. But his Sixers faded down the stretch and now face a bad seeding, which could result in an early exit from the playoffs.

What any of these three standard Coach of the Year candidates did pales in comparison to the work of coaches such as Jordan. On the surface, Washington has shown only a modest improvement over last season’s 41–41 record, but when you look at their injury list this season, the Wizards look more like a MASH unit than a basketball team. Guard Gilbert Arenas, a perennial All-Star, missed 68 games, forward Caron Butler missed 23, and forward Antawn Jamison missed two and played hurt in several more. These three players comprise the nucleus of the Wizards. But rather than fold, Jordan kept the Wizards in the hunt with the personnel equivalent of duct tape and bailing wire, and now with their big three healthy, they could be a dangerous, under-seeded team in the playoffs. Jordan deserves a load of credit for that feat.

When Portland center Greg Oden suffered a knee injury before the season and required surgery that would delay his rookie campaign for a year, most pundits wrote the Blazers off. Some even forecast 50–55 losses. Instead, Portland contended in the rough Western Conference for most of the season (and they would be playoff-bound in the East). While some of the credit deservedly goes to second-year stars Brandon Roy and LaMarcus Aldridge, a big part of Portland’s improvement was on defense (amazing what can happen when you get rid of Zach Randolph). The Trail Blazers went from a miserable 26th in Defensive Efficiency (points allowed per 100 possessions) last season to a mediocre 17th this year. Defense is almost always a sign of good coaching, and McMillan also deserves credit for his team’s rise.

Theus deserves consideration on the same grounds as the Wizards’ Jordan. Sacramento missed their best player, guard Kevin Martin, for 21 games. Forward Ron Artest missed 25 and behaved erratically when he was present, and guard Mike Bibby was in uniform for only 15 games before being traded to Atlanta. Despite that instability, Theus led the Kings to a five-game improvement on last season’s record, and at 38–44, their record would qualify for the playoffs in the Eastern Conference, though they played a much tougher slate in the West.

I doubt any of the voters will think deeply about these coaches. The postseason awards tend to be a way of offering trinkets for the teams that go deep in the playoffs. In reality, some of the best coaching jobs were done by men whose players will be home long before Memorial Day. It doesn’t mean the coaches did a worse job; in this case, they just had less to work with.

mjohnson@nysun.com