With his towering home runs and unsurpassed athleticism, he could have been any baseball fan’s dream player.

Yet Alex Rodriguez was regularly booed at the ballpark and vilified in the press. He was called selfish, aloof and overpaid. His very public dalliance with Madonna, after an abrupt split with his wife, seemed to tarnish his image even further. And when it was reported earlier this year that he had used performance-enhancing drugs, he seemed irredeemable.

Then, a strange thing happened. ARod came back. It began with a full-fledged mea culpa, without any hint of defiance or denial. Then he played, as brilliantly as before, but with a quiet, understated efficiency. He became a team player and in the process helped the New York Yankees win their 27th world championship.

The fans roared their approval. It seems a straightforward formula for anyone on the rebound: an honest apology followed by hard work and success. Yet when seeking the elusive second act, there may not be any clear rules.

“Where did I go wrong?” asked Adnan Khashoggi, the former Saudi arms dealer. “Nowhere.”

So much for mea culpas.

Known for his exceedingly lavish lifestyle, Mr. Khashoggi may have been the world’s richest man at one point in the 1980s. That is, until a plethora of scandals led to bankruptcy.

Today, he is reinventing himself as a consultant, using the connections he cultivated while peddling weapons, The Times reported. Though he once owned his own jet, he now flies commercial. But he still stresses image and perception.

“It is all part of the mechanism for impressing people,” he told The Times, “with your talk, with your views, with your appearance.”

Image and perception have also aided Mullah Omar, without the opulence. The one-eyed, poorly educated Taliban leader fled Kabul in 2001 after an American assault, but has staged what Bruce Riedel, a former C.I.A. officer, called “one of the most remarkable military comebacks in modern history.”

As The Times reported, Mullah Omar’s “reputed humility,” along with his legend as a fierce fighter against the Soviets in the 1980s, helps to inspire unrelenting devotion in his followers, who view him as one of their own.

“His followers adore him, believe in him and are willing to die for him,” Rahimullah Yusufzai, a Pakistani journalist, told The Times.

Ironically, the same “he’s-one-ofus” dynamic may aid Mullah Omar’s nemesis in his own comeback bid. Toward the end of his presidency, as his approval ratings sank to dismal lows, George W. Bush boasted that he would make “ridiculous” amounts of money on the lecture circuit. So far that hasn’t happened .

In late October, however, Mr. Bush stepped out to speak at a Get Motivated seminar in Fort Worth, Texas. There were no A-Rod-like apologies, but while comedians poked fun at the $19 admission price for the event, the former president still seemed to strike a chord with those attending.

One told the Washington Post that his lack of speaking abilities sounds “incompetent if you are president. But here it can be inspiring. It makes him seem like a regular guy, no better than me.”

Comebacks come in many different varieties. With a good year on the baseball field, Alex Rodriguez of the New York Yankees won back the fans he had lost. / ASSOCIATED PRESS