NEW YORK — In the course of a pregame explanation of why he’s not a big fan of certain defensive statistics — like, say, the one that says his Knicks finished 19th in points allowed per possession during the regular season, the lowest defensive rating in his three seasons in New York — Tom Thibodeau was gracious enough to offer some insight on which numbers he does look at when evaluating the quality of a defense.

“The rating systems that some people use, I don't go by,” Thibodeau told reporters before Game 1 of the Eastern Conference semifinals on Sunday. “My markers are, you know, field-goal percentage, defensive field-goal percentage, 3-point percentage, rebound margin, points in the paint, fastbreak points allowed. When you look at those markers? [We’re] pretty strong.”

By some of those markers, the Knicks turned in a pretty strong performance to open their second-round matchup with the visiting Heat. Miami shot just 42.4% from the field in Game 1. The Knicks outrebounded the Heat, 59-49, and gave up just 38 points in the paint while scoring 62 themselves. And yet, four days after finishing off a stunning upset of top-seeded Milwaukee, Miami came into Madison Square Garden and stole home-court advantage from the hosts, scoring a 108-101 Game 1 win, thanks in large part to one of Thibs’ markers that didn’t break New York’s way.

“The thing is, the discrepancy on the threes,” Thibodeau said after the loss. “There's a lot of ground to make up if they're making 13 and we’re making seven.”

3-point edge gives Heat a big boost

New York shot just 7-for-34 from long distance in Game 1, while the Heat went 13-for-39 — an 18-point chasm that the Knicks’ superior interior finishing couldn’t overcome. (It didn’t help matters that a Knicks team whose recipe for offensive efficiency all season long has been predicated on taking care of the ball and getting to the free-throw line more than the opponent took nine fewer freebies than Miami and coughed the ball up five more times.)

Game 1 hero Gabe Vincent made as many long balls by himself (five) as the entire Knicks’ starting lineup — and four of those came off the fingertips of Obi Toppin, making his first career playoff start in place of the injured Julius Randle, who’s still working his way back after reaggravating his ankle sprain during Game 5 of New York’s opening-round win over the Cavaliers. Toppin finished with 18 points and 8 rebounds, shooting 7-for-15 from the floor in 31 minutes.

But while it’s good for New York that Toppin made four 3s, it’s probably even better for Miami that he took 11 — and that Josh Hart (who shot 30.4% from distance in Portland before the trade deadline) took four, and that R.J. Barrett (31% during the regular season, 25% in Round 1 against the Cavs) took five.

“I think it was good-look 3s,” Hart said. “We just didn’t make shots.”

That’s what Miami is counting on.

New York was able to get out to an early lead Sunday, thanks to a steady diet of paint touches. With Barrett attacking off the bounce and star point guard Jalen Brunson finding his preferred matchups in the pick-and-roll, the Knicks shot 20-for-24 in the lane in the first half, racking up 40 points in the paint — the highest postseason paint total in a half of any Knicks team in the last quarter-century.

“That number jumped out at halftime,” Heat coach Erik Spoelstra said.

The script flipped from there, though: just 22 points in the paint for New York on 11-for-22 shooting, which Spoelstra credited in part to improved point-of-attack defense from the likes of Vincent, Jimmy Butler, Caleb Martin and Kyle Lowry. (More on him later.) The cranked-up ball pressure came paired with more aggressive help defense behind the play, too.

“Every time we got in there, they were swarming,” Barrett said.

Much like the Knicks did against Cleveland in Round 1, Miami’s weak-side defenders pinched in off the corners to put extra bodies between Brunson and Barrett and the basket, effectively daring New York’s ballhandlers to try to either weave through a thicket of swiping arms or pass the ball to comparatively non-threatening shooters. The gambit worked: After shooting 77.8% inside the arc with five turnovers in the first half, the Knicks dipped to 52% with eight turnovers for the balance of the game, allowing the Heat to turn the tide.

Thibodeau might come to rue the decision to leave what were effectively his two best shooters, Toppin and the just-back-from-injury Quentin Grimes, on the bench during that decisive fourth quarter. Toppin played just over two minutes in the frame, with Miami mostly playing smaller lineups that Thibodeau said he felt required more wing players to match up with. Of Grimes, who played just over 10 minutes in his return from a shoulder injury, Thibs only said, “We're still working Quentin back.” (Brunson, for his part, took responsibility for the offensive malfunction, including his 0-for-7 mark from 3-point land: “Today I was horrific. Very uncharacteristic by me.”)

A jumper or two here or there could’ve swung the game. Instead, the Knicks will have to live with the cold comfort of knowing how close they were and hope that their jumpers thaw by Tuesday.

“You feel encouraged by the fact that, late in the game, it was still a one-possession game and we still had the opportunity to win the game. … We played well. We didn’t make shots. And I think that’s encouraging,” Hart said. “None of us are going to waver. None of us are going to lose confidence. We’re going to continue to be aggressive, take the right shots. If they go in, cool. If not, we’re going to keep battling.”

A tale of two halves for R.J.

Barrett battled from the opening tip, beginning Round 2 against Miami the way he ended Round 1 against Cleveland: putting his head down and trying to take smaller, overmatched defenders to the basket at every opportunity. Matched up primarily with the 6-foot-2 Vincent, Barrett repeatedly got to his spots and scoring in rhythm, pouring in 13 points on 6-for-7 shooting to go with 5 rebounds and 4 assists — precisely the kind of production New York needed from him with Randle, its All-Star finisher and complementary facilitator, watching the game in street clothes.

Come the second half, though, Miami’s increased physicality and paint-packing defense took away his rhythm looks and easy reads, forcing the 22-year-old to make difficult decisions and shots in traffic. The results weren’t pretty: 4-for-13 in the second half, with three assists against three turnovers, as he consistently struggled to generate good shots for himself and others against an elite defense trained on him.

“I mean, sure, they made adjustments,” Barrett said. “They picked up the intensity a little bit, played hard. They made shots and we didn’t. In my experience, playing them throughout the course of the year, you know, they’re never going to give up. That’s one thing that I personally enjoy about this series: It’s going to be hard-fought, it’s going to be tough, you’ve got to go out there and kind of take it.”

While he couldn’t take it on Sunday, Miami could — with the help of a few open-court haymakers just after halftime.

Heat turn it up in transition

After clawing their way to within five entering halftime, the Heat changed the game early in the third quarter in part by using the Knicks’ errant shooting and penchant for pounding the offensive glass against them.

“Second half, we were able to get a lot more defensive stops that I think took a little bit of pressure off our offense and made some timely plays,” Spoelstra said. “I think it probably started with Kevin Love’s rebounding and outlet passes.”

Three times early in the third quarter — once after a missed Hart 3, once after a missed Brunson 3 and once after a missed Barrett runner — Love grabbed a defensive rebound, turned his head up-court, and saw a teammate streaking into open space with nary a Knick in his way. So Love did what he’s been doing for years: flicked his wrists, launched a pass the length of the court and set Miami up for some easy early offense.

Max Strus muscled in a layup over a back-tracking Brunson. Butler slammed down a pair of dunks. He might have had another if not for the refs swallowing the whistle after he’d leaked out and managed to get behind the Knicks following a made free throw.

It was a neat bit of transition jiu-jitsu, using New York’s hardwired aggression against it, and it paid off, helping fuel a 24-7 third-quarter run that changed the game.

“It literally gave us just an extra boost of energy and jolt,” Lowry said. “I mean, I know you guys have all watched the highlights of him being able to do the full-court stuff. He’s been doing that forever, pinpoint passes like that. And to have a guy like Jimmy to go get it, Max to go get that one, it gives us those leak points that we always want.”

Despite only getting into transition on fewer than 9% of their possessions, the Heat finished with 15 fastbreak points, a couple of buckets above their season average, and finished Game 1 scoring 1.62 points per play in transition and 2.25 points per play on the break off a live rebound, according to Cleaning the Glass — elite numbers that helped them wrest control of the run of play. They wouldn’t give it back.

Kyle Lowry over everything, yet again

Lowry’s had an up-and-down tenure in Miami, marked by extended absences due to injury and for personal reasons; rarely has he been able to perform like the kind of championship-level contributor he was in Toronto. On Sunday, though, he offered a reminder of exactly why the Heat brought him in.

“Kyle, fourth quarter, was so important,” Spoelstra said. “You know, we gave the ball to him and he made a lot of important plays … in the fourth quarter, [he] made three or four veteran, physical, heady plays. You know, savvy plays, defensively, that you can’t really teach. You have to match competitive wills with competitive wills, and Kyle is one of those kinds of guys.”

After going 2-for-5 in the first half, Lowry was the first player out of the locker room when it was time to warm up before the third quarter. He certainly saved his best work for the second half, scoring 12 points after intermission and serving as Miami’s primary table-setter after Butler sprained his ankle midway through the fourth quarter.

Over the final five-plus minutes, Lowry:

• Took the ball away from Knicks center Mitchell Robinson to extend a Heat possession, which ended with a Vincent 3 to put Miami up by six;

• Tied up Brunson on a drive, forcing a jump ball that Miami won, scuttling another Knicks possession;

• Set Bam Adebayo up in the pick-and-roll for a short jumper that pushed Miami’s lead to eight;

• Drilled a tough fadeaway jumper in the corner over the outstretched arm of Immanuel Quickley to put New York down 10 with less than three minutes to go;

• Stripped Barrett on a drive with two minutes to go, prompting the Knicks’ Canadian forward to say after the game, “You know, I’ve watched Kyle Lowry enough times with the Raptors, just watching them growing up, and he’s a guy who’s going to get strips and get steals”; and

• Fouled Robinson to prevent him from getting a dunk, forcing him to go to the line for a pair of free throws, which he split.

When the game was tight late, one team struggled to get good possessions, and the other one didn’t. There are plenty of reasons why; Lowry, though, might be the biggest, with those half-dozen winning plays down the stretch, capping off a pristine night: 18 points, 6 assists, 5 rebounds, 4 blocks and a steal in 30 minutes off the bench. Miami outscored New York by two points with Lowry on the floor; the Heat won his minutes, and they won the game.

Spoelstra wouldn’t say Game 1 was the best Lowry had played for the Heat this season, though he would allow that it might be the healthiest that the veteran has been all year.

“He’s an absolute warrior,” the coach said. “He’s been able to do some amazing things, even on one leg this year. But those five weeks where he was able to step away and just really focus on getting himself healthy for these kinds of moments was critical. But he’s a winner. He’s just an absolute winner. And when you need it most, that’s when it’s going to show up. In these kinds of environments, at this point in his career — you know, this place was electric — this is all that Kyle wants, at this point in his career, are these kinds of opportunities, and the chance to hopefully win some games in the playoffs.”

Winning more games promises to be even tougher, though, if Miami’s main man sees that balky right ankle swell up like a beach ball before Monday morning — which makes the way the Knicks approached him down the stretch all the more curious.

Why not make Jimmy run?

Injuries are a grisly part of the game. After all of Butler’s heroics to propel Miami past the Bucks in Round 1, and how excellently he’d played to stake the Heat to their lead in Game 1, the sight of him splayed on the ground after stepping on Hart’s ankle with just over five minutes to go in the fourth quarter was enough to turn your stomach.

He got up, though — stepped gingerly to the line, made his free throws … and didn’t check out of the game.

“Great decoy,” Lowry said with a laugh. “Nah, man, it just shows the toughness of him. It shows the toughness of our team. It’s pretty evident that he was like, ‘I’m not going out the game.’ I asked him, I said, ‘Are you going out?’ He said no. And that was that.”

When Butler stayed in — with a pronounced limp, clearly struggling to move up and down the court — a Knicks team trying to make a comeback and seize an advantage in this best-of-seven series faced the kind of cold, calculated decision that comes up in the heat of competition. If Miami was going to keep Butler out there in that compromised state, why not attack him? Put him in an action and force him to defend; if he can’t, force Spoelstra to take him out of the game and put someone else in the game who is, y’know, less terrifying than Jimmy Butler.

The Knicks never did that, though. In fact, at one point, they actually ran a screen to get Butler off Barrett, inviting Lowry to guard R.J. one-on-one; the result was the strip that Barrett later said he should’ve seen coming.

From the Heat’s perspective, it didn’t seem like the Knicks were doing them any favors. (“Do you think they were being passive?” Spoelstra replied, with a laugh. “It did not feel like they were being passive. At all.”) In the cold light of day, though, the Knicks allowed the Heat to effectively defend them 4-on-5 in crunch time and didn’t capitalize.

“Tricky situation,” Brunson said. “Obviously, he wasn't 100%. He's one of the best defenders in the league, so even if his feet aren’t moving fast side-to-side, he has great hands. As a team, we’ve got to do a better job of recognizing what's going on, especially late in the game, and like I said, it starts with me.”

Whoever it starts with — the point guard on the floor, the coach on the sidelines, whoever happened to have the ball with an opportunity to target the limping All-Star in red and black — it ended badly. New York went 4-for-11 from the floor over those final five minutes with three turnovers and didn’t make Butler guard the ball once.

“It's always easy to play Monday morning quarterback when you lose a game or a team goes on a run late in the fourth,” Hart said. “We’re going to watch film and see where we can get better at. Maybe we could’ve did something. Maybe not.”

What shows up in New York’s film session is likely of less import than what the Heat’s medical team finds when they check in on Butler’s ankle.

“Yeah, no idea,” Spoelstra said. “You know, you just don’t know with ankle sprains. We’ll know more about it tomorrow. We’ll just have to see. We’ll be waiting.”

The Knicks will, too — only they’ll have to wait knowing that they might have squandered an opportunity to grab control of this series with two hand, and allowed a tough-as-nails Heat team that needs no charity to survive, get across the finish line and continue their stunning and sensational start to this postseason.