The worst-person citations eventually riled Mr. O’Reilly enough that he began a petition drive directed at Mr. Olbermann (though he did not mention him by name; he has apparently never mentioned Mr. Olbermann’s name), suggesting that he be replaced by a long-ago MSNBC host, Phil Donahue. Mr. Donahue’s ratings, Mr. O’Reilly said in February, eclipsed anything MSNBC had achieved since. By the next day, Mr. Olbermann was celebrating the petition and offering to sign it himself. Now he gleefully notes that Mr. O’Reilly (whose name he has no trouble uttering) only helped his cause by taking the bait and responding to the gibes.

“You don’t punch down,” Mr. Olbermann said. “If you’re in my position,” he added, referring to his initially microscopic ratings next to Mr. O’Reilly’s, “you punch upwards.”

Every time Mr. O’Reilly took umbrage at the slams, it seemed to add a bounce to Mr. Olbermann’s ratings — one reason, perhaps, that Mr. O’Reilly’s reactions seem to have tailed off more recently. Nobody at Fox News wants Mr. Olbermann to get any more of a draft from Mr. O’Reilly’s popularity.

Mr. Olbermann thinks he knows one reason behind his gains. He believes that Mr. O’Reilly’s audience, which is still huge, is aging. He noted that Mr. O’Reilly’s total viewer ratings are basically flat, while his numbers in the younger audience group have been dropping — down about 15 percent for the last quarter. “There is no other conclusion to draw than he is not adding younger viewers,” Mr. Olbermann said.

Of course, in terms of numbers of viewers in that younger age group, Mr. O’Reilly is still playing in another league, with about three times as many as Mr. Olbermann. But that does represent a small slice of the total audience for Mr. O’Reilly.

MSNBC’s research claims that the median age for Mr. O’Reilly’s audience is 71, while Mr. Olbermann’s is 59. (Fox and CNN both report that the only figures they get for median age of shows with older audiences is “65 plus,” and that Mr. O’Reilly’s audience falls into that category.)