The only free and comprehensive online etymological dictionary of the Spanish language
pelota (1) f. (Noun) "ball"
13th cent. Old Spanish pellota. Borrowed from either Old French pelote or Old Occitan pelota 'id.' It replaced the native Old Spanish pella (pellota also existed, though rarely used). From Vulgar Latin *pilotta "little ball," a diminutive of Latin pila "ball." Of unknown origin.
Indo-European
Romance
Catalan pila, French pile, Italian pila
Italic
Latin pilus "hair," compilare "to steal"