Before his big mouth and licentious ways cost Charlie Sheen his job on “Two and a Half Men,” he boasted about converting the writers’ tin cans into comedy gold. If so, he’s hardly the only actor to apparently possess such Rumplestiltskin-like magic.

There’s a widely held perception “Men” has disappointed creatively with Ashton Kutcher sliding into Sheen’s shoes (in more ways than one, perhaps). In a scorecard of fall shows that underwent major cast changes, a New York Times critic gave the sitcom a “D” — the lowest grade among five series featured, including “The Office” and “CSI.” Every week more emails drift in from viewers insisting they hate the revised version and Kutcher and won’t continue watching.

By the measures that truly count, though, 10 weeks into what everyone perceived as a crapshoot, the new-look “Men” appears to be, to borrow a favorite Sheen phrase, “winning.” And in an entertainment year with little cause to give thanks, viewed through the prism of a business that often rewards or turns a blind eye toward bad behavior, it just might be the feel-good story of the season.

Even tossing out the inflated two-part premiere, tune-in for the series has consistently surpassed the corresponding weeks last year, with the overall average up more than 10% in viewers and nearly 20% in the key demo of adults 18-49.

Moreover, with the considerably younger and Twitter-friendly Kutcher joining what’s now even more of an ensemble, the median age of “Men” viewers has not surprisingly dropped by a few years, down to about 48. Although that could owe something to the youthful skew of the CBS comedies preceding it, it’s nevertheless an accomplishment as the networks generally keep graying.

At his Comedy Central roast, Sheen suggested he got fired because “I told my boss to fuck off.” That conveniently ignores a list of PR nightmares due to proven and alleged transgressions — mostly involving women — too long to mention, as well as other complications related to his personal excesses. If Sheen was the equivalent of Dorian Gray for most of the show’s run, that magic began to fade, and his lifestyle started showing up in his haggard appearance.

Sheen obviously didn’t endear himself to his heretofore patient bosses by publicly taunting them — series co-creator Chuck Lorre, CBS and Warner Bros. — and one can argue the wrong straws helped break the camel’s back. Even so, ousting him represented a sizable risk.

For CBS, the gamble went beyond just “Men.” The series is the linchpin of its Monday lineup. Had the show cratered, it would have likely dragged down the four programs surrounding it.

Normally in such standoffs, after the finger-pointing and harshly worded letters from lawyers, the parties would find a way to make up. When there’s this much money at stake, change is feared, and paying big salaries to miserable people becomes just another psychic and spiritual cost of doing business.

At last week’s Hollywood Radio and Television Society luncheon, CBS Corp. CEO Leslie Moonves resisted the temptation to gloat, but he did say, “With these numbers, I’m hoping this show will last for many, many years.” Given the potential for Sheen flaming out, that would almost certainly provide more mileage than “Men” looked to have in its tank.

As for Sheen, whatever happens with his planned FX show, he has gone from highly paid TV star to carnival sideshow, perhaps irrevocably. Meanwhile, everyone associated with “Men” can spend less time dreading phone calls that begin “Did you hear what Charlie did?”

So if there’s an underlying lesson in “Two and a Half Men,” it’s that you needn’t always cling desperately to the status quo. When somebody’s really acting like a jerk, under the right circumstances it’s possible to roll the dice and reload. Assuming the ratings hold, that ought to put a tiny shiver up the spine of divas and prima donnas everywhere.

Of course, new players can amass their own baggage — as Kutcher has already demonstrated — and success has a way of bringing out the worst in people. For now, though, there’s reason to be thankful about who’s “winning.” Because for once, protecting a golden goose didn’t mean settling for a turkey.