There are times at the end of an NCAA basketball tournament game when I not only want the ref to swallow the whistle; I’d like to garrote him with the cord. Then again, it’s just as aggravating when a ref refuses to call anything down the stretch, and by omission settles a game. Which is better, fairer? A dead-silent whistle or a shrieking intrusion?

We argue this issue annually, each time someone in a zebra-striped shirt makes a late call that swings a final score one way or the other. Last weekend a couple of seemingly ticky-tack lane violations helped decide the outcomes of two games, Xavier’s 67-63 win over Notre Dame, and UNC Asheville’s failed bid to upset Syracuse, 72-65. Something similar will probably happen again this weekend. Charles Barkley summed up how a lot of people feel about officiating intrusions from his analyst’s chair on TNT.

“My head is going to explode,” he said. “Man, these referees are killing me. You cannot call those calls with the game on the line.”

It’s an uneasy supposition: A rule is a rule early in the game, but when it’s late, especially inside the two-minute mark, refs should overlook minor infractions and “let the players play.” Most of us share this murky sentiment, though we don’t really know why and feel half-guilty about it. But University of Texas law professor Mitch Berman has set out to explain and justify it, by applying legal theory. In an article for the Georgetown Law Journal entitled “Let Em Play: A Study in the Jurisprudence of Sports,” Berman asks why we incline toward what he calls “temporal variance.”

“Why should the optimal degree of laxity differ in crunch time? Why ‘let them play’ at this particular time?” he said.

Berman contends that organized games are really legal systems. When we consider the NCAA tournament that way, it clarifies what we’re really after with temporal variance: justice.

“My project was to figure out what could be said in favor of it,” he says. “I started with this instinct that says it seems sort of right. But it wasn’t obvious, to put it mildly, what reason or evidence could support that view.”

In the 2011 book “Scorecasting: The Hidden Influences Behind How Sports Are Played and Games Are Won,” economist Tobias Moskowitz and sportswriter L. Jon Wertheim argued that we show a subtle but powerful “omission bias” in how we want final scores determined. We tend to prefer outcomes determined by a ref’s omission — a failure to blow the whistle — because we tell ourselves that inactions are less blameworthy than actions. We’ve incorporated this bias on an outright systemic bias by congratulating refs for “no-calls.”

But is this gut preference legitimate and fair? Berman takes the argument one step further and says yes. One rationale for it is aesthetic: We don’t want a bunch of whistles halting the flow of play, which is irritating during moments of high drama. Also, we want excellence to determine the score, not luck. But more importantly, we sense that as time wears on in a game, the impact of a penalty changes.

“The expected impact of outcome-affecting events varies in inverse proportion to the distance remaining to the end of the game,” Berman argues. Like it or not, whistles for minor infractions matter more to the final score with two minutes remaining in a tied game than they do at the start.

A point arrives when the penalty for an infraction has a greater impact on the final score than the infraction itself.

Take the lane violation by Notre Dame’s Jerian Grant with 2.8 seconds to go and the Irish down by two against Xavier. His teammate Eric Atkinswas at the line for a front end of a one-and-one, and made the first. But then the whistle blew. The free throw was waved off, simply because Grant left his position from beyond the three-point arc too early. Technically it was the correct call. But it deprived Notre Dame of a chance to tie and force overtime, ensuring a loss.

A penalty for an infraction is meant to give the other team restitution. But was that really fair restitution? Berman argues, the offender was unduly penalized in comparison to the minor rebounding advantage he might have gained by starting from beyond the arc too early. “The penalty becomes overcompensatory in absolute terms,” Berman says. Meantime, Xavier received excessive restitution, the huge gift of avoiding overtime.

None of this is meant to argue that refs should overlook contact fouls late in games; some things you can’t let go. Nor does it say there aren’t powerful arguments for calling a game with no variance based on time and score. Purists believe the tighter the rules are enforced, the better the quality of play down the stretch. Also, refs have to make instantaneous decisions in the heat of competition — unlike lawyers and judges, they don’t have weeks to sort out issues of remedy and restitution.

Too much variance can make for chaos; witness the incoherent officiating in the women’s game, which is simply an atrocity, with one game like rugby and another like badminton. Tuesday night a crew awarded Notre Dame’s Natalie Novosel 20 free throws all by herself in a second-round game against Cal. That was two more than Tennessee’s entire team shot in a bruising game of tackle with DePaul the previous night.

But Berman’s application of legal theory gives us a sensible, rational argument for why refs should exercise discretion in regard to time and score when deciding whether to blow the whistle on minor offenses. It’s not just a matter of exploding heads.

The law endorses such a principle in all sorts of ways. We refuse to overturn verdicts in cases in which judges may make a “harmless error” ruling. In cases of civil wrong, we tell people they may sue only for “material breach,” and not for minor breach. When we object to a ref making a minor call that has a major impact late in a game, it’s based, Berman says, on “an aversion to the awarding of windfall remedies disproportionate to the harm suffered.”

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