Instead, Harden was intent on something else: getting referee Tony Brothers to blow his whistle. And that’s exactly what Brothers did, sending Harden to the line for three shots while Mills stood stunned, arms raised over his head and Spurs Coach Gregg Popovich expressed his feelings so loudly that were picked up on TNT’s broadcast.

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“We’ve had to be smart about it and moving for it and not buying into it. We’ve done a decent job with it,” Mills said recently about trying to guard plays such as Harden’s. “We’ve still put them on the foul line a couple of times, but we’re really making it a focus for us to make us keep our hands up and play solid defense.”

The truth, though, is that no one was wrong here. Harden smartly saw a chance to initiate contact, and did so. Mills kept his hands up, but because he stepped toward Harden, he allowed Houston’s superstar to create contact. Given the rules, Brothers made the correct call. And Popovich had the proper response: utter disbelief.

Welcome to the murky and uncertain world of three-shot fouls, a topic that has divided NBA players, executives and fans into two camps: those who believe these plays are legitimate, and those who don’t.

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Over the past 15 years, the NBA has undergone a three-point revolution. As teams have embraced the entry of analytics and big data into the sport, they have tried to maximize their offense by focusing on the two most efficient places on the court: at the rim and beyond the three-point arc.

As a result, the number of three-pointers attempted by NBA teams leapt from 34,913 during the 2002-03 regular season to 66,421 this year — a 90.2 percent increase. And those increases aren’t likely to stop anytime soon.

But while the number of threes has risen steadily each season, the spike in three-shot fouls has been extraordinary. Over that same span, three-shot fouls have surged from 174 in 2002-03 to 1,045 this season — a 500.6 percent increase, including a jump of 349 instances of three-shot fouls over just the past two seasons, according to data provided by the NBA.

So what happened? Well, in short, players and teams found a loophole in the rules, a way to game the system, and have begun exploiting it as much as possible.

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“Well, usually what happens in everything, not just with fouls, is that offensive guys and coaches or whatever, they find a way to play that’s a little different, and then the defense takes awhile to adjust,” Rockets Coach Mike D’Antoni said. “This is another thing.”

D’Antoni’s Phoenix Suns teams a decade ago were a big part of the NBA’s three-point evolution, and his Rockets this season have had a similar impact on the dramatic increase in three-shot fouls. Harden and fellow guard Lou Williams — acquired the Los Angeles Lakers at February’s trade deadline — have become the poster children for the play, excelling at it more than virtually anyone else.

After listening to Williams explain his thought process in how he’s able to trick players into fouling him behind the arc, it’s easy to see how he’s become so successful and why defenders have had so much trouble adjusting.

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“Just guys being aggressive on the defensive end,” Williams said, “knowing they can’t use their hands, can’t body check.

“So, naturally, a defender’s first thought when you jab step or something is to push up on you, and so as an offensive player your first thought is to go past them.

“But, for me, it’s to run into them.”

It’s a simple concept — initiate contact, as opposed to letting a defender fly by. But it has become virtually impossible for defenders to stop. Because the NBA has become so heavily focused on three-point shooting, defenders have become hyper-focused on trying to make sure they don’t allow open looks.

Their aggression, however, helps players such as Boston Celtics star Isaiah Thomas notice when defenders are chasing them hard over screens on the perimeter. Thomas can then take advantage — baiting his man into a foul the defender has virtually no way of avoiding.

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“When I’m coming off screens and they’re trailing me kind of fast, I watch them and see when they can’t stop on a dime like I can,” Thomas said. “It’s just something I picked up.”

Not surprisingly, the many talented guards have followed suit. The result has been an unprecedented preponderance of stoppages and a parade of players going to the free throw line for three shots.

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Against the Rockets, the Spurs encountered a three-shot foul situation that begged for a solution.

In its five-game series against the Oklahoma City Thunder, Houston racked up 17 such fouls, and garnered four more — including Harden’s ridiculous half-court heave in Game 2 — during the opening two games of its series against San Antonio. Those four were the only three-shot calls Houston earned during the series.

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So what did San Antonio do to limit what had been such a crucial weapon in Houston’s arsenal?

“If there was a magic bullet, and I knew it, I probably wouldn’t share it,” Popovich said with a smile before San Antonio’s blowout victory in Game 6 to close the series. “But there is no magic bullet, and we’re trying to do the best we can in not giving that foul.”

Mills said San Antonio had a clear plan: Give Houston’s offensive players as few opportunities as possible to bait defenders into foul calls. The Spurs even had a name for it — keeping their hands out of the “strike zone.”

“It’s all about getting your hands up,” Mills said, “and keeping them out of the strike zone, as we call it.

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“As soon as your hands get into that strike zone where someone can grab your arm, then it’s a foul. When they call it, there’s no arguing … your hands are in the strike zone. That’s been our mind-set throughout this series: hands out of the strike zone.”

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Not surprisingly, the dramatic increase in three-shot fouls has led to calls for the NBA to do something.

“Well, obviously we’re aware of it,” said Kiki Vandeweghe, the NBA’s executive vice president of basketball operations. “It’s a difficult play to officiate. It really is.

“In real time, it happens very quickly, and like with most of our tough calls, it requires a lot of judgment. We’re going to take a look at it this summer [when the competition committee convenes during the league’s meetings in Las Vegas].”

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The debate over what to do varies wildly. Virtually everyone agrees that the fouls and the subsequent free throws are not exactly easy on the eyes. But it can be argued that drawing such a foul either is a player shrewdly utilizing a loophole to his advantage, or a level of distasteful trickery that needs to be weeded out of the game.

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“It’s never been done before,” D’Antoni said, “but they’re fouls. They can change the rules, but that’s tough. Now how do you determine was that somebody who outfoxed the defense or the defense making a bad mistake?”

It’s that last question that seems to be the crux of the issue: Will the NBA wind up looking at this and saying that these are players simply forcing defenses into mistakes? Or will the league determine that these are plays that violate the spirit of the rule, and make changes?

One possibility, as Washington Wizards star John Wall suggested, is to make such plays non-shooting fouls. Wall likened it to the “rip-through move,” which sees players swing the ball quickly past their body if they catch a defender’s hands in front of them, drawing contact and earning a foul in the process. Golden State Warriors star Kevin Durant perfected it a few seasons ago as a way to get an easy pair of foul shots, but it was eventually changed to a non-shooting foul.

“I think the NBA is going to look at some of the calls they’ve made, and make adjustments to it,” Wall said. “Like they did with the rip-through call, you don’t get free throws for that, you get the ball on the side.”

Such a rule change wouldn’t sit well with the likes of Williams, who said that defenses should simply avoid giving players such as him the opportunity to goad them into a foul and three free throws.

And, given the success San Antonio had defending against Houston, perhaps he has a point.

“Yeah, there’s a lot of complaining,” Williams said. “But you’ve just got to be smarter. You’ve just got to be smarter. I mean, Patty Mills got me with my own trick last night. It happens.

“It’s chess out there. You’re just trying to find ways to trump teams, and you just have to deal with it. A lot of guys are complaining about being able to fight over screens … but you’ve got to pick your poison.”

Still, given the amount of attention that’s been paid to these plays over the course of this season and the playoffs, it seems likely that some sort of change will be coming.

Even Thomas, who has become one of the most successful players in the league at drawing such fouls, believes a tweak will be made.

“They’re going to have to change that rule, probably,” Thomas said. “I mean, everybody is doing it.

“It’s tough to officiate, but they definitely are fouls. I know that.”

Everyone knows this, too: The debate over these plays, and how to call them, is far from over.