Opportunities to avert disaster don’t come often. Right now, the NFL and its union, by agreeing to a 24-hour extension of their collective bargaining agreement, have taken a step back from the edge. Let’s hope it is progress, not just gamesmanship.

As NFL owners and their players find themselves at the first of what may be many brinks in their negotiations, they should learn from baseball’s horrid battle of 1994-95. That dispute cascaded into failure, in part because both sides thought they’d win before anything awful happened.

In baseball, as in the current NFL ruckus, the owners spent years laying the groundwork to roll back gains made by the players. In both cases, the players felt sure that labor law was on their side. The owners felt they were getting squeezed and had the financial muscle to change that balance. Both sports were enjoying boom times. That cushion of overconfidence, plus so much money to be split up, proved a perfect prescription for a brawl.

Baseball set deadlines, extended them, then let them pass. Both sides postured, pretended to be negotiating seriously while actually playing for advantage with the public and in the media. There were many baseball days back then that felt a lot like Thursday’s NFL talks. Marathon meetings, new last-minute proposals: There’s progress! Don’t fret.

Yet the 1994 World Series was lost; the aftershocks are still shaking the sport today. Reflect on this cautionary tale, lords of football and players, too.

And reach a deal fast, even if it’s far sooner than your original battle plan.

At the moment, both sides are acting serious, but is there really any sense of urgency? The owners have been planning their strategy since 2008, when they reopened the CBA two years early. Aren’t they tempted to see how their brilliant strategies will play out? Baseball’s owners sure were.

As for players, you already hear quotes about, “Oh, no games until September.” When they get their first paychecks. Who cares about missing OTAs? I’ve covered 10 sports labor battles for The Washington Post, including two NFL lockouts in the 1980s. Ignore history if you want. But the longer you wait, the harder to deal, the easier to go to the mattresses.

There’s another side of the coin: our side. Fans of the NFL, even the most ardent, should also learn something from baseball’s misery: Don’t care. Or care as little as you can. Don’t live and die with the latest twist in talks. If the current 24-hour extension leads to progress, that’s great. But if this moment of hope leads to nothing, be prepared to mock both sides and, when you can, try to laugh. That’s the only pleasure we’re going to get.

Because there is one certainty when labor fights get this intense: Neither side cares about you. If you pick a favorite and scream your opinion, then you’re probably the sucker. The owners will only listen to those who back them. The same goes for the players.

The sound that really worries them is silence. Try to provide it.

Perhaps the scariest parallel between baseball then and football now is the idea that the healthier the sport, the less likely a disaster. That’s backward. Lots of money on the table brings out the worst in people, seldom the best.

Back in 1994, baseball had been setting attendance records every year. The sport had never been so healthy. Revenues were high enough to make players rich and owners even richer. Does that sound like the NFL now with an average franchise value of $1.02 billion and 111 million people watching the Super Bowl? President Obama has said he won’t get involved now. Why should he? Any president should have better things to do that settle a fight about who gets how much loot out of a $9 billion treasure chest.

NFL owners should remember their baseball counterparts who replaced moderate Fay Vincent as commissioner with Bud Selig and spent two years figuring out every permutation of what might happen. Baseball owners hired fine minds with fancy degrees to analyze their options.

Yet they totally miscalculated everything that ultimately mattered. They asked: Which side will ultimately give up? Wrong question. Neither side ever did. A U.S. District Court judge, Sonia Sotomayor, who was appointed by a business-friendly, baseball-loving President George H. W. Bush, issued a preliminary injunction against Major League Baseball in 1995 that, essentially, ended the strike and gave the players a Pyrrhic victory.

No owner, not one, ever dreamed of that last act. Some muttered, “What does she know about baseball?” Plenty, it turned out. And she’s now on the Supreme Court.

The players got up, bleeding, and agreed among themselves: “If that’s a victory, then let’s never have another one.”

For the last 24 years, the NFL has had labor peace. But part of the reason is that retired NFL commissioner Paul Tagliabue and the late union boss Gene Upshaw remembered the strikes of 1982 and 1987. They remembered “replacement players.” But they’re not around anymore.

The NFL’s reputation, one that’s well earned, is that it is generally smarter at marketing its product, at controlling its players and at avoiding disasters than baseball. If that’s still true, then this week’s developments may lead to serious progress. We can hope. If they mess up, we can mock.

Football is flying high right now. So was baseball in 1994. Here’s what the NFL should take away from the history of labor conflicts in pro sports, especially baseball’s disaster:

Both sides always think they know what’s going to happen because they, or their hirelings are so smart. But they don’t. They’re all guessing.

Both sides think they’ll win because they truly believe they are right. But that’s irrelevant because, usually, they’re both just rationalizing greed.

Finally, and perhaps worst, both sides think that they can foresee the worst-case scenario that may afflict their sport if they are somehow wrong. “Manageable,” they say. But they’re wrong. History doesn’t play fair. Bad decisions create their own chain reactions.

The NFL and its union don’t have to flirt with these enormous risks. Instead, they can use this window of opportunity to divide up $9 billion.

That sounds like such an easy obvious choice. But it seldom is.