NEW YORK — David Stern was deep in the bowels of Staples Center, holding an impromptu press conference next to the loading dock when he should have been in a luxury suite upstairs getting ready to enjoy Game 3 of the NBA Finals.

His message that day was that Tim Donaghy was a renegade crackpot and that he wasn’t worried at all about his allegations that NBA referees conspired to fix at least one playoff series and may have influenced even more.

“Why should I be worried?” Stern asked.

Turns out Stern was worried, at least about the growing public perception that NBA officials were incompetent at best, crooks at worst. Worried enough that just a few weeks later he hired a two-star general to take charge of the league’s referees and make sure whispers of impropriety never overshadow another championship series again.

The NFL saw that general and raised a state police chief this week. Jeffrey Miller is technically only a colonel, but he’s been given broad powers to make sure things like Spygate don’t cloud another Super Bowl.

Again, it was a hire driven more by perception than anything else. The preseason begins next month and the last thing commissioner Roger Goodell wants is more questions about whether stealing signals may have altered the outcome of games.

The stakes were so high for both leagues that they really didn’t have a choice. They each have only one product, and if there’s even a perception that product is tainted, they have a serious issue.

The question is why it took them so long to realize how serious it could become.

In the NFL’s case, it has been nearly a year since Bill Belichick was fined $500,000 for taping signals in violation of league rules. Goodell likely thought the hefty fine would mean the end of the scandal, but his decision to destroy the videotape and notes from his investigation not only led to more questions but eventually drew the attention of a U.S. senator from Pennsylvania.

With Arlen Specter calling for an independent investigation and threatening a Senate hearing on Spygate, it wasn’t going to simply go away. Even though Specter recently backed off his call for a hearing, Goodell hired the top cop in Pennsylvania to guard against any future Spygates or other improprieties that might harm the league.

The hiring came just a few days after Stern brought in Ron Johnson to bolster his league’s credibility in the wake of charges against Donaghy and the ones he has raised in court filings.

Johnson has no experience in sports and no background with referees, but his image as a no-nonsense army general who will tolerate no shenanigans was what Stern was after.

Some of Donaghy’s allegations — like the one where the referees gave the Lakers a playoff win against Sacramento because the league wanted the series to go seven games — seem preposterous. But if they’re repeated enough among already skeptical fans, some are going to believe them.

The problem with both leagues is the arrogance that comes from being too fat for too long.

Goodell thought he could declare the case closed because the NFL is the NFL, untouchable because it is by far the country’s most popular sport. He thought he didn’t have to answer to anyone but his owners, who are usually too busy counting their assorted billions to worry about things like that.

As for Stern, all his talk about transparency was mostly just talk. While it’s true the NBA will tell you to the exact penny what the new salary cap is ($58.68 million), and the price of Jack Nicholson’s courtside seats ($2,500), it can’t explain why its referees have a pattern of favoring the home team in playoffs or even what a foul really is these days.

There’s a credibility crisis in sports right now, something Stern and Goodell are apparently just now beginning to understand. We watch a 41-year-old mother, Dara Torres, break a swimming record and immediately wonder if she’s juiced, see bad fouls called in an NBA game and wonder if the referees are on the take, and watch football wondering if the other team has stolen signals.

So when the NFL declared Spygate dead, it wasn’t. When Stern said one rogue official shouldn’t taint the league, it did.

We’ve been burned too much, seen too many things we can’t explain.

Unfortunately, it will take more than a general and a colonel to change that.

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