Jack Black in “The Brink.” (Merie W. Wallace/HBO)

Part “Wag the Dog” and part “Dr. Strangelove,” HBO’s unfortunately flaccid new comedy “The Brink” (premiering Sunday) is a caper set in the midst of a Pakistani coup d’etat. Jack Black stars as Alex Talbot, a low-level diplomat in the American Embassy in Islamabad. As a military revolution against the country’s newly elected president begins, Alex is out scoring weed with his reluctant driver Rafiq (Aasif Mandvi). A mob attacks their car, and the men are forced to flee on foot.

In Washington, Secretary of State Walter Larson (Tim Robbins) is interrupted from his afternoon dalliance with a prostitute to get to the White House situation room, where an indecisive American president (Esai Morales) is being urged to bomb the bejesus out of Pakistani military targets before the new regime can sell off the country’s nuclear weapons to terrorists. On a Navy carrier in the Red Sea, a pair of hapless fighter pilots (Pablo Schreiber and Eric Ladin) are scrambled in preparation to attack — but they’ve accidentally taken morphine instead of Xanax.

Larson, fighting off a painful (but somewhat funny) kidney-stone emergency, hops on a plane with his long-suffering aide (Maribeth Monroe) in an attempt to undermine the coup and avert the crisis. All hopes hinge now on Alex, who, after he’s captured and waterboarded, finds himself at the center of the action.

“The Brink” is a little too stale and disorganized to act as the “Veep” of foreign diplomacy, but it does provoke a chuckle here and there. Black sets the pace with his shopworn shtick, while Robbins clearly enjoys another chance to play a comically egomaniacal government official. The funniest scenes involve the two fighter pilots, particularly Schreiber’s Zeke “Z-Pak” Tilson, a decorated ace who’s failing to juggle his personal crises (he’s the ship’s drug dealer and has impregnated a colleague) and probably welcomes the opportunity to crash land in the middle of a Taliban-infested nowhere.

Geoff Pierson, left, and Tim Robbins in HBO’s new show. (Merie W. Wallace/HBO)

Pablo Schreiber and Eric Ladin play hapless fighter pilots. (Merie W. Wallace/HBO)

“The Brink’s” problem isn’t that it has too much going on at once but that it seems to have too many cooks in its kitchen. The credits are heavy with a larger-than-usual array of writers, producers and directors, which may explain why the show fails to locate a coherent tone from episode to episode. Whatever “The Brink” is trying to say about the state of world affairs — and as things progress, the show does seem determined to make a point — is lost in the execution. Soon enough, this brand of globally minded satire coalesces into a giant cornball.

Dwayne “The Rock” Johnson in “Ballers.” (Gene Page/Courtesy of HBO)

The moves in HBO’s other half-hour show premiering Sunday, “Ballers,” should be instantly recognizable. (Hint: It’s basically another “Entourage,” set in the world in professional football instead of the film industry.) Just as familiar is the tone of moral ambivalence: With one hand, “Ballers” seeks to celebrate the excesses and exploitations of the NFL, and with the other (weaker) hand, it attempts to indict the same system.

Dwayne Johnson stars as Spencer Strasmore, a recently retired player trying to reinvent himself as a money manager in Miami, where pro ballers (not just Dolphins) and their wives, mistresses and hangers-on flock like preening birds. Hired at an investment firm by a fame-obsessed jerk of a boss (Rob Corddry), Spencer is under pressure to pull all his connections and persuade top players to invest their millions with the firm.

His big target is a rising Dallas Cowboys star, Vernon (Donovan Carter), who is beholden to his childhood friend and manager, Reggie (London Brown), and a large retinue of relatives and friends who’ve quickly spent all his rookie money. Spencer and Vernon’s agent (Troy Garity) work to get a $71 million, five-year contract renewal, but there’s still a danger their client will ditch them. “Ballers” makes clear that the only change in the nearly 20 years since Cuba Gooding Jr. coaxed Tom Cruise to scream “Show me the money!” in “Jerry Maguire” is that there is so much more money involved now — and that “bling” is still a word.

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Anticipating its audience’s desires, “Ballers” mainly fixates on cars, yachts, houses, topless women and raunchy sex — and a nominal amount of football. It’s hard to tell whether “Ballers” means to make the high life seem as rote and empty as it does (my hunch is that the producers and writers are given more to bouts of envy than sermonizing), but the show and its actors are so much better when zooming in on serious matters, such as the possibility that the Vicodin-popping Spencer suffers from neurological damage from his years on the field.

Better still is a storyline that seems more of an afterthought, in which Spencer’s friend Charlie (Omar Miller), newly retired from the Tampa Bay Buccaneers, takes an entry-level sales job at a Chevrolet dealership — which is a more interesting story as the basis for a series than the ceaseless joy rides, hookers and blow that “Ballers” feels obligated to provide.

Ballers (30 minutes) premieres Sunday at 10 p.m. on HBO.

The Brink (30 minutes) premieres Sunday at 10:30 p.m. on HBO.