In Indianapolis, where the Big Ten opened its men’s tournament on Wednesday, Brandon Johns Jr., a sophomore at Michigan, led the Wolverines into a largely empty Bankers Life Fieldhouse and jokingly acknowledged the crowd that was not there. Moments later, the players from Michigan and its opponent, Rutgers, were ushered off the floor, their game and the rest of the tournament canceled.

“I don’t want to have any regrets,” Kevin Warren, the Big Ten commissioner, said afterward. “I want to make sure as a conference we do the right things because if something had gone awry here, I don’t want to be in a position looking back saying, ‘If only we would have canceled this tournament.’”

In an interview on Thursday afternoon, Greg Sankey, the Southeastern Conference commissioner, expressed a similar perspective after canceling the league’s championship events: “We viewed stopping now, given the information, as being the proactive step.” Someday, he said, he hoped the decision would be judged a well-intentioned overreaction.

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The sudden ends of the conference basketball competitions — from the mighty Atlantic Coast Conference, home to many of the men’s national champions over the last decade, to smaller leagues like the Southland and the Sun Belt — made the cancellations of the national tournaments only a matter of time. The eventual outcome became even clearer as some of the national basketball powers, like Duke and Kansas, signaled that they would not travel for any athletic events.

The N.C.A.A.’s sweeping cancellations came as a surprise to many people, even those who had believed the basketball tournaments were all but certain to be called off.

For a few hours on Wednesday, some sports executives believed that the basketball tournaments would go on in sparsely populated arenas from Sacramento to Atlanta, which was scheduled to host the men’s Final Four in April. Mark Emmert, the N.C.A.A.’s president, said in an interview on Wednesday evening that he was “very confident that we’re at the right place,” even as he declined to rule out the possibility of cancellation.