ball has 19 distinct synonyms spread across 7 of its 13 senses. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. WordNet records no antonym for it — antonymy is a relation between word forms rather than concepts, so it is deliberately sparse.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
round object that is hit or thrown or kicked in games
“the ball travelled 90 mph on his serve”
a solid projectile that is shot by a musket
“they had to carry a ramrod as well as powder and ball”
the people assembled at a lavish formal dance
“the ball was already emptying out before the fire alarm sounded”
a spherical object used as a plaything
“he played with his rubber ball in the bathtub”
United States comedienne best known as the star of a popular television program (1911-1989)
a lavish dance requiring formal attire
a more or less rounded anatomical body or mass
“the ball at the base of the thumb”
a ball game played with a bat and ball between two teams of nine players; teams take turns at bat trying to score runs
“he played baseball in high school”
a pitch that is not in the strike zone
“he threw nine straight balls before the manager yanked him”
form into a ball by winding or rolling
“ball wool”
Synonyms, antonyms and the broader and narrower relations for ball come from Princeton University’s WordNet. Full sources and licences.