BOSTON — Coaching is a funny profession, especially in the NBA. Coaches go through the whole regular season with relatively little scrutiny, only to see it suddenly magnified a hundred times over in the playoffs. We’ve seen multiple examples already in the first round.

But there’s a reason for this: Tactical errors in the playoffs can be much more costly than those in the regular season. During the course of 82 games, what a coach does in other departments — player relations, teaching, etc. — is vastly more important than his tactics in any individual game.

In the postseason, however, that turns on its head. All the teaching has been done, and the only remaining way for a coach to impact the game is through the use of good strategy — or, too often, bad strategy.

The first round of this year’s playoffs has been amazing for the number of times that otherwise solid head coaches have bungled the percentages and cost their team in the process.

Here in Boston, we had a good example Wednesday night, when Hawks coach Mike Woodson sat star Joe Johnson for 11 minutes of the first half because he had two fouls. He’s not the only coach that does this; indeed, Hall of Fame coach Larry Brown is famous for pulling players for the half when they’ve picked up a quick two.

But as a percentage move, this is horrendous. The major negative consequence of foul trouble is that a player may foul out of the game, thus preventing a coach from using him. You’ll notice that taking a player out for a huge chunk of the first half has a remarkably similar effect: It was as though Woodson decided to foul out Johnson in the first half rather than the second. With their best player watching, the Hawks fell behind 15 by halftime and were eventually routed by Boston, 110-85.

Coaches seem to have trouble reconciling the odds of a player getting up to five or six fouls with the cost of removing the player from the lineup. In general, the latter is much more costly than the former. There are exceptions, especially with players who are particularly foul-prone or those who, like Phoenix’s Amare Stoudemire, immediately stop playing defense any time they’re in foul trouble.

But for the majority, a quick hook for early foul trouble just doesn’t make sense. In Johnson’s case, only five shooting guards had a lower rate of fouls per minute than he did in the NBA this season. He didn’t pick up another foul the rest of the night.

Woodson wasn’t the only one to leave me perplexed. In the Washington-Cleveland series, Wizards coach Eddie Jordan made a similar head-scratcher when his team didn’t intentionally foul Cavs free-throw clunker Ben Wallace during the fourth quarter of Game 4. Jordan said he preferred not to do the “Hack-a-Ben,” and instead play straight-up basketball — as though it was an affront to the basketball gods if he didn’t let LeBron James dunk on their heads instead.

Fortunately, somebody must have had a little talk with Jordan before Wednesday’s Game 5. His team did intentionally foul Wallace in the fourth quarter. He missed both shots, and Cavs coach Mike Brown immediately took him out of the game lest the Wizards foul again. It ended up being a difference-making decision for Washington, who won Game 5 by a single point to stave off elimination.

Then there’s the choice made by Phoenix coach Mike D’Antoni (who seems likely to be the former Phoenix coach within the next week or two). His decision not to foul against San Antonio at the end of overtime in Game 1 — even as the Spurs were dribbling inside the 3-point line — was another example of a coach not understanding the percentages.

The odds of the Spurs making a foul shot, missing the second, grabbing the rebound, and scoring were much less than those of making a single 3-point attempt — even with Tim Duncan attempting the 3. Unfortunately, that choice may have ended up costing the Suns the series, which they lost in five tough games.

There are other examples I can point out. Those are just the three most prominent. But with so many coaches screwing up the percentages, here’s a thought for the masses: Why don’t more teams give the coaches a little help?

You would think that a general manager would want to sit down with his coach and talk through these situations before they happen, especially heading into a playoff series. There’s plenty of data out there to show just how poor these three particular choices were. If teams would just analyze situational odds based on historical in-game situations, they could help their coaches better understand the relative merits of certain choices.

A couple of clubs do this, but the vast majority do not. There’s an old-school, Wild West sentiment in many NBA front offices that this is the coach’s domain and it might be an affront to talk it out with him.

Obviously, every individual game presents its own singular situations, and that can skew the odds. But a coach can still benefit from understanding the big picture. If Jordan saw the odds of Wallace making free throws against the odds of Cleveland scoring against his half-court defense — two pieces of data that are readily available — he would have quickly seen that hacking Wallace would have been a huge benefit to his team as long as it didn’t create foul problems for his own side.

Similarly, if Woodson knew how slim the odds were of Johnson getting into serious foul trouble, I doubt he would have benched his best player for so long — especially in a situation where his team needed to play far beyond its limits to leave with a win.

Instead, the coaches are left to their own devices. Most are former players, and they don’t have backgrounds in probability modeling and statistical methods. They tend go by instinct, which sometimes produces the right choice, and sometimes produces a terrible choice.

We end up blaming the coaches for this, but maybe our blame is misplaced. The part that’s really baffling is why more teams don’t give them some help in making these crucial decisions.

jhollinger@nysun.com