Is one allowed to play ball on Shabbos?
The Midrash (Eichah Rabbah 2:4) says that this is why Tur Shimon was destroyed:
טור שמעון הוה מפיק תלת מאה גרבין ולמה חרב אי תימא מן הזנות והלא לא היתה אלא ריבה אחת והוציאוה משם אמר רב הונא משום שהיו משחקים בכדור בשבת
Tur Shimon would distribute 300 baskets to the poor. Why was it destroyed? If it’s because of harlotry, there was just one [such] girl in that town, and they had sent her out from there! R’ Huna said: because they would play ball on Shabbos.
It should be noted that Yerushalmi Taanis 4:5 cites this story in regard to Beitar, and it cites it without the word בשבת. Karban HaEidah explains that either the text should be emended to match the Midrash, or it means that it was destroyed because they played ball regularly, i.e. instead of learning Torah.