NBA coaching is about x’s and o’s, sure, but it’s also about psychology. It’s about encouraging a group of 15 players that the system works, and will work, even if it just failed. It’s about walking into a deflated locker room and becoming a dragon that breathes hope. It’s about walking into a joyous locker room and letting everyone know there’s still plenty more work to do. It’s about knowing how to relate to each of your players and letting them know you care, not just about the team, but about them.

Doc Rivers has made some mistakes in the Eastern Conference Finals. He began the series with Kevin Garnett defending Shane Battier, an obviously poor decision that severely limited Garnett’s omniscient help defense. He took too long to realize that this wasn’t the series for Ryan Hollins. Rivers has also made some glorious decisions. He all but scrapped the pick-and-pop in favor of sending Garnett cutting hard to the hoop, utilizing Garnett’s unrivaled size in this series. He junked up and disguised his defenses in Game 5, leading Erik Spoelstra to say the Celtics had the Heat “twisted in the mind” during a sideline interview.

But perhaps Rivers’ most crucial contribution came in the moments following Game 2. The world wondered how the Celtics could ever respond to falling down 0-2 after dropping an overtime contest in which Rajon Rondo scored 44 points. Rivers stood, or sat, in front of dozens of microphones and proclaimed that the Celtics were still confident. They would make adjustments, they would play better, they didn’t feel like they’d given their best effort yet. Rivers swore to everyone that the Celtics would not surrender after such a devastating loss. No, they were confident, he said. They would improve and they would provide a better showing in Boston. Rivers was a leader who wasn’t so much interested in describing his team’s actual thoughts — after Boston took Game 3, Keyon Dooling admitted Game 2 “was a disheartening game for us” –as he was in paving the way to its recovery.

Erik Spoelstra sat in a similar situation following Game 5. His Heat were down and they were down in devastating fashion, blowing a six-point lead over the final six minutes to lose home court advantage and fall within one loss of elimination. But where Rivers projected confidence, Spoelstra projected weakness.

“It’s a loss,’’ Spoelstra said following Game 5. “That’s all it is. And that’s what our focus is right now, to fight any kind of noise from the outside or any human condition, and to collectively come together strong enough to prepare for the next game.’’

Assuredly, Spoelstra’s telling the truth. His task is to make sure his team fights any kind of noise from the outside or any human condition. During the past two days every analyst has counted out the Heat, has wondered where LeBron James went in the fourth quarter, has asked why Dwyane Wade has been so hesitant in first halves, has praised Boston’s toughness while wondering when Miami will find its. These players, however famous, are human. They hear the criticism, and it must be tough to respond.

But Rivers never would have been so weak. He would have become a dragon breathing hope. He would have stepped up to the mics and said his team would be ready for Game 6 even if he wasn’t entirely sure himself, because that’s what his team needed in a time of doubt.

Anything could still happen in this series. The Celtics still need one more win, while the Heat have already proven themselves capable of winning two straight against Boston. But if the Celtics do survive and advance, it will have a lot to do with their coach. He thrives in x’s and o’s, yes, but his biggest contributions might come elsewhere.

“I told them, we’ve done nothing,’’ Rivers told the Celtics after a Game 5 win. “We’re playing a heck of a basketball team. So just because we’re going to Boston, I told them, we have to play. They’re not going to give it to us. We have to go get it.’’

A great coach tells his team what it needs to hear.