As physical spectacle, the relationship between sport and dance goes back at least as far as the Olympic athlete. A fifth-century Athenian sculpture depicts youths playing a popular ball game as they balk and chivvy in bas-relief. On Sunday evening at the City Center, Terpsichore wore her sneakers in a very different kind of game: the postmodern pastime of precision ball passing.

In the final program of the Fall for Dance Festival, Charles Moulton premiered his “48 Person Precision Ball Passing.” Positioned on stadium risers, the performers handed off orange, yellow, and green balls in a feat of coordination and teamwork. At times, they even achieved a certain visual brilliance in the patterns they created. They either passed the balls speedily in one direction, or politely across the rows. They imitated “the wave” at sporting events, spoofed cheerleader combinations, and raised their arms as if on an amusement-park ride. Among other things, they glorified the role of spectator as athlete.

In a live performance, Matthew Pierce kept score with reiterative pizzicato on his violin, quickening in tempo or else slurring a melody that suggested at times the bluegrass vistas of Middle America.

Mr. Moulton first originated precision ball passing in 1980 for only three performers. Today the activity has spread to other companies around the world. As a form of theater, it really doesn’t get more decadent than this; for that reason it is delightful to watch.

Compagnie Marie Chouinard’s “24 Preludes by Chopin” describes itself as “a vast terrain of forbidden games sculpted by light.” Ms. Chouinard treats the lilting melodies of Chopin’s piano music with ironic disdain – associating them with the “ballet music” of every young ballerina striving to realize the neo-Romantic ideal of “Les Sylphides.” But instead of white tulle, the dancers wore black leotards, their hair knotted in dreadlocks. Hunched forward in silence, they curved their arms with prickly fingers. Whenever they interacted with the music directly, a soloist rearranged her foot positions sarcastically, another mock conducted, and still others mimicked the hammering on the piano.

At one point, a soccer ball rolled onto the stage, perhaps in a ballet reference to the tennis ball bouncing between the love triangle in Nijinsky’s famous “Jeux.” In that ballet, tennis represented, among other things, the sexual politics of Bloomsbury. The use of a strobe light in one variation of Ms. Chouinard’s work evoked that era with the fast-forward flickering of silent movies. Although the purpose of the soccer ball remains unclear, the work did come back to the theme of rebellion against ballet orthodoxy. Conceptually slight, it gained a burlesque charm.

Possibly the most thought-provoking piece on Sunday’s bill was “7 x 7 x 7 x 7 x 7” by Yoshiko Chuma & The School of Hard Knocks (which has my nomination for the best name of a dance company). The work was a game of rules and restrictions, using seven dancers, seven trombones, and, most important, four 7-foot cubes. The activity onstage was deliberately confounding; as a prime number, it remained divisible only by Ms. Chuma and itself.

But the large cube-frames had an elegance about them. When the eclectic group of performers manipulated them, lines intersected and the quadrilateral planes became three-dimensional diamonds and triangles. For the most part, they adopted significance as autonomous zones, where individuals moved comfortably at will. The trombone band, for its part, offered impetus to movement, but quickly became a dissonant pest threatening the wayward troupe. The work closed with Ms. Chuma triumphantly removing one trombonist’s U-shaped slide.

Also on the program was an excerpt from South African choreographer Vincent Mantsoe’s “Ndaa.” To the tribal percussion of drums, Mr. Mantsoe encroached onto an arena staked out with bamboo. At first he stalked forward cautiously, as if on a hunt, but soon he began to share the instinctual quickness and avidity of an animal. Ultimately, in his commanding performance, Mr. Mantsoe depicted, and overcame, the struggle between spirit and flesh.

For the valedictory event of the festival, the Joffrey Ballet returned to the stage it called home for nearly three decades. Based in Chicago since 1995, the company has earned a reputation in recent years for its phenomenal renditions of early 20th-century reconstructions, especially the “lost” works of Nijinsky (including his aforementioned “Jeux”) reassembled by Millicent Hodson and Kenneth Archer.

The dancers entered the stage to a warm reception, but the choice of Gerald Arpino’s “Suite Saint-Saens” was inauspicious. The only dancers of the evening in point shoes, they looked shaky. They beamed promise, striking out in energetic diagonals, but the large stage repeatedly deflected their extensions. The pas de trois to the saccharine melodies of “Serenade” – complete with studied enchainments and traveling arabesques – read like Balanchine-lite. And although the final “Minuet” held a few surprises – a crouching walk, vigorous turns, and a soulful duet between Brian McSween and Stacy Joy Keller – the work never redeemed itself. In addition to the uninteresting choreography, the company was also put at a disadvantage coming at the end of a particularly iconoclastic program.