An empty net with 1:38 left in the game. That’s a sight the Lightning, winner of a record-tying 62 games during the regular season, is used to seeing.On Wednesday night, however, Tampa Bay found itself having to defend the empty net rather than attack it. Coach Jon Cooper, his team trailing 4-3 in its playoff opener, had called Andrei Vasilevskiy over to the bench and substituted an extra skater.It was too late. The Lightning ran out of time.When should Cooper have pulled Vasilevskiy? With two minutes left? Three minutes? Four?The optimal moment, according to a pair of probability experts, was immediately after Blue Jackets defenseman Seth Jones scored the go-ahead goal. Time remaining: 5:55.Utter nonsense, you say? Maybe according to public opinion, but hedge fund manager Clifford Asness and New York University math professor Aaron Brown followed the numbers. They recently shared their findings in “Pulling the Goalie: Hockey and Investment Implications,” a paper published on the Social Science Research Network website.Asness and Brown found that teams down by one goal should pull their goalie with 6:10 left in the game, teams down by two goals should pull with 13 minutes left and teams down by three goals should pull with 3:40 left in the second period . (Though teams become desperate this time of year, no one will dare try pulling his goalie during the second period.)Cooper’s slow trigger in Game 1 against Columbus wasn’t typical. Nor was his decision to leave Vasilevskiy in net when Tampa Bay fell behind 4-1 halfway through the third period in Game 2. During the regular season, he defied traditional thinking on goalie pulls — not because of Asness and Brown’s paper, but because it’s in his nature to be more aggressive.• • •As the third period winds down, you won’t see Cooper on the bench calculating expected point values and win probabilities. But you won’t hear him parroting conventional wisdom, either.“Who decides that when you have to tie a game up it has to be with 30 seconds left?” he said. “Why not give yourself more of an opportunity to have that happen?”Cooper has a point. Since when did waiting until the last minute to pull a goalie become standard practice anyway? Since 1931, when Art Ross, whose Bruins were losing to the Canadiens 1-0, benched Tiny Thompson in favor of a sixth attacker.Cooper’s pull times this season won’t completely satisfy statisticians, but they were earlier than most of his peers’ pull times.When the Lightning trailed by one goal late in the third period — which was rare — he pulled the goalie, on average, at the 1:52 mark, the eighth most aggressive. Tampa Bay’s opponents waited about 10 more seconds.Even when the Lightning trailed by two goals, Cooper still outpaced his opponents. In such situations, he pulled the goalie, on average, at the 2:32 mark. Tampa Bay’s opponents waited about 20 more seconds.Cooper’s appetite for risk has been trending upward. In 2015-16, his average pull time when down by one goal was 1:22. In 2016-17, it was 1:28. In 2017-18, it was 1:45.Not every aspect of the goalie pulling strategy can be measured, of course.“There’s a ton of things that can go into it,” Cooper said. “How’s the game going? Are you dominating the game and it feels like just a matter of time? Or are you struggling, can’t get anything going and you need something like that to ignite a team? I’m not going to argue any of the numbers that go up, but the numbers don’t dictate feel, they don’t dictate momentum.”• • •The NHL as a whole is beginning to realize the obvious: The downside of an early goalie pull (a lopsided loss) doesn’t outweigh the upside (a better chance at winning). Few people have had a closer view of this trend than NBC analyst Pierre McGuire, who during the network’s national broadcasts is situated between the team benches.“The early pulls have become very apparent, no question,” McGuire said. “More people spend time on setting up plays with the goalie pulled in terms of keeping the puck away, not turning it over, bringing it back to the neutral zone to regroup — almost like soccer. Teams have figured it out so that it has became more of a weapon.”The strategy helped Tampa Bay steal a game against Ottawa in November. Down 3-2 with 1:40 left, Cooper pulled Vasilevskiy and sent Brayden Point onto the ice as the extra skater. Point scored with 27 seconds left to force overtime, and Yanni Gourde scored the game-winner 14 seconds into the extra period.In extra-skater situations, the Lightning has seen relatively little dropoff defensively. It has allowed only six empty net goals, or 13.6 per 60 minutes of play, the fourth-lowest rate.“It’s hard to argue with (Cooper), especially when you have players that have puck possession skills like Tampa does and shooting ability like Tampa does,” McGuire said. “One of the other things Tampa does really well, because of how big their defense is and how well they skate, they keep pucks alive at the offensive blue line as well or better than almost any team in the league. All those things lead to the ability to pull your goalie.”• • •Pulling the goalie sooner rather than later would seem to be a common sense move. Not pulling is near certain death. Pulling is a chance at survival. Why then, if coaches truly value winning above all else, aren’t they pulling their goalies earlier than they are now? What is it that holds such power over their decision-making?They’re human. And humans don’t like to be humiliated. “Winning ugly,” Asness and Brown write, “is undervalued versus losing elegantly; losing ugly can be career suicide.”All coaches across all sports reflect this bias. It’s loss aversion, the idea that we feel more pain when we lose a dollar than we feel joy when we gain a dollar.That’s why baseball managers save their best relievers until the ninth inning even if the team would benefit from them being used in a high leverage situation earlier in the game. That’s why basketball coaches bench star players once they reach five fouls to prevent them from reaching six and fouling out. That’s why football coaches punt on fourth and 1 instead of go for the first-down conversion.There’s a price to pay for shunning the status quo, Tobias J. Moskowitz and L. Jon Wertheim write in Scorecasting: The Hidden Influences Behind How Sports Are Played and Games Are Won . Follow convention and fail, face fewer questions. Defy convention and fail, look out for the torches and pitchforks.“Many coaches ultimately are motivated less by the potential of a Super Bowl ring than by the potential loss of something valuable they possess: their job. And in sports, there are few faster ways to lose your employment than by bucking conventional thinking, trying something radical, and failing.”Former Buccaneers coach Dirk Koetter admitted as much earlier this season when he was asked about his fourth-down strategy.“The percentages say you should go for it almost every time,” he said. “We’ve studied the analytics on it, and the problem with looking at it like that — those are all looking at all fourth downs over the course of the season. You might get three in a row, but if I don’t get it in this particular game, we might be losing, and I might be out of here.”That fear of job loss drives coaches wait to act until they realize they have nothing left to lose. Cooper is the exception. It helps that he just signed multiyear contract extension.“For me, an early pull is probably better than a later pull,” he said.We checked the math, coach. You don’t have to say “probably.” Goalie pull times courtesy of Meghan Hall of ballsandsticks.com . Contact Thomas Bassinger at email@example.com . Follow @tometrics.