In Game 2 of the NBA Finals, he checked in and drilled a 34-footer with time running down against the Mavericks. Then in Game 5, with the Celtics already in command and en route to their first NBA title since 2008, he hurried upcourt before the end of the second quarter and drained a half-court shot that gave the Celtics a 21-point lead.

The stage was not quite as grand when the Celtics faced the Wizards on Thursday night, but Pritchard nearly added to his ever-growing highlight reel anyway. After Jonas Valanciunas hit a hook shot with 0.2 seconds left in the third quarter, Pritchard took the inbounds pass and banked in a shot from about 70 feet away.

It did not count, because at least 0.3 seconds are required for a catch-and-shoot. But Pritchard thought the clock operator let a few precious tenths of a second drip away after Valanciunas’s shot, potentially robbing him of yet another inconceivable and successful heave.

“It is an incredible shot,” Pritchard said. “It’s low percentage and I’ve hit it at a high rate. So I kind of amaze myself at times.

“Even that one tonight, I’m like, ‘I don’t know how I hit it,’ because if I go to the gym and practice it 100 times, I probably don’t hit it. But then in the game it comes. I guess it’s just being in the moment.”

Pritchard’s long-range heaves have become so stirring and consistent that they are almost expected, with TD Garden fans buzzing when he gets the ball far from the hoop with the clock running down. And now he has a suggestion that would benefit heavers such as him, and add to late-game drama across the league.

“I honestly think maybe past half court they should look at adding it as a 4-point play,” Pritchard said. “I mean, it could be interesting. I’ve seen rules overseas that they have a 4-point line.

“I don’t think we’ll ever do that, but make the half-court line, if it’s behind half court, a 4-point play. I don’t know. It’s interesting to think about.”

After Pritchard stumped for the rule change Thursday, Celtics guard Derrick White was asked whether he could see a place in the game for the 4-pointer.

“We’ve got Payton Pritchard,” White deadpanned, “so, yes.”

It is unlikely that commissioner Adam Silver will heed Pritchard’s advice any time soon, of course. But there is at least some growing momentum in support of the heave-4.

Players are often reluctant to fire up the low-percentage shot because it will most likely dent their shooting numbers, which are important for things such as contract negotiations and awards. So this year the G League instituted an experimental rule in which heave misses would count as team attempts and not be charged to the individual.

The heave is defined as a shot that takes place in the last three seconds of the first three quarters, with the play originating in the backcourt and the shot coming from at least 36 feet.

“I think they should implement that in the NBA,” Pritchard said. “Obviously, it’s not a normal 3-point shot. Some guys don’t take it because it might hurt their percentages. I don’t worry about the percentages because it can change the whole momentum of a game. But it’s not a bad rule to maybe look at.”

But Pritchard has made it clear that he does not need any rule alterations or extra motivation. He plans to keep firing away.

“I feel like it’s just like a moment,” he said. “Like, you get it and I really just believe I can make it. That’s probably half the battle is just believing in it and giving it a chance.

“Now I’ve seen a couple go in and I’m going to take them every time. I feel like it just changes the momentum. Even if I hit it after the buzzer, the crowd gets into it.”

Hauser out again

Celtics forward Sam Hauser will miss Saturday’s game against the Pistons because of lower back pain, his second absence in a row.

Adam Himmelsbach can be reached at adam.himmelsbach@globe.com. Follow him @adamhimmelsbach.