As the abundance of adoration for Sammy Davis Jr. continues to swell in Leslie Bricusse’s massive tribute musical now at the Old Globe, there comes the moment when everybody just gives up and calls him the greatest entertainer in history.

It’s hard to evaluate such a claim, of course. But Davis certainly was one of a kind.

The old golf-handicap gag about him being a tiny one-eyed black Jew doesn’t even cover the whole subject. Davis was painfully wiry, not at all handsome and tiresomely pushy.

But he did things that astounded audiences. He didn’t so much dominate his material as obliterate it, making the content trivial compared to the form.

Davis was only 64 when he died of cancer in 1990, but he was a veteran of 60 years in the show business, thanks to a vaudeville debut at 4 with his father and his Uncle Will Mastin. It was the early appearances with the Will Mastin Trio on tiny black and white television screens that launched Davis on a superstar career that climaxed in his uber-hip Las Vegas reign with Frank Sinatra and Dean Martin as “the Rat Pack.”

Davis danced a lot and sang in a surprisingly supple and resonant baritone but it was his sheer animal presence that blasted through all those handicaps into legend.

Bricusse flat-out worships the guy. He’s written book, music and lyrics for this show, called inevitably “Sammy,” and borrowed seven additional songs that he wrote with his old partner, Anthony Newley.

That’s 23 different numbers, some with reprises. And that, plus all the usual biographical arc, makes for a long 150 or so minutes.

The songs, in busy, brass-and-percussion arrangements by conductor Ian Fraser, are heavy, either seeped in period swagger and rutting bathos or soaked in cloying angst.

The handsome female chorus spends over half the show in prototypical chorine outfits, strutting and squealing in the presence of stud potency. The mythology of excess dissipation is tired and a bit musty now but Bricusse doesn’t seem to notice.

A big, bold show like this needs some conflict but all Bricusse can find are a couple of old stalwarts, substance abuse and racial bigotry.

The booze and the pills make for some production numbers while the prejudice stuff is limited to a couple of awkward, depressing dialogue scenes. Back in the day, Davis seemed to soar untouched above such things. Probably not.

It’s unlikely that a better choice for the title role than Obba Babatunde’ could be found. (I’ve loved his name since “Dreamgirls” in 1982.)

Both his singing and his dancing are quite adequate; he’s captured the star’s buoyant charm and irresistible drive, and he even contrives to look like Davis. The part should be forever his.

Not so Adam James, who has neither the pipes nor the look of Frank Sinatra, though he does have the breezy self-satisfaction down pat. Troy Britton Johnson is likewise as Dean Martin, with lots less to do. But Perry Ojeda is a weak whiff as Eddie Cantor, assuming anybody remembers.

Ted Louis Levy as Sammy Davis Sr. and Lance Roberts as Will Mastin are genial and useful. Ann Duquesnay plays the big mama role with dignity and an astounding if erratic voice.

None of the other ladies in Davis’ life – Kim Novak, May Britt, Lola Falana, etc. – are played with much accuracy or impact but the nine ladies of the ensemble are the true spine of the show.

In a show essentially devoid of subtlety, choreographer Keith Young finds some surprising quiet and tender moments, such as a balletic duo for Babatunde’ and Mary Ann Hermansen as Kim Novak. Otherwise the dances are cheerful, casual and, well, organic. To the period. The periodS.

Director Keith Glover, on the other hand, just struggles to keep some sense of time and place alive as the numbers troupe past. Given Alexander Dodge’s set design – various corners in the Land of Glitz – and Chris Lee brooding design of light puddles, that’s probably the best plan for a stage director.

Which brings us back to Leslie Bricusse. He’s nothing if not earnest and sincere. But his dialogue – “Slowing down is one show business trick I’ve never learned.” – sounds like notes for further pondering and his lyrics – “Sammy huggin’ Nixon, that’ll take some fixin’!” – often seem right out of the rhyming dictionary.

Ultimately, though, he’s certainly done his duty for Sammy Davis Jr. Nobody is likely to do more.

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