DY: Riding a bike is a separate issue. Playing ball is a decent split among those who mention it (that I’ve seen). The M”B quotes the Yerushalmi, but it is not at all clear what the Yerushalmi means. And even if P’shat is for playing ball on Shabbos, it would seem much more likely to be a case where that constitutes Chillul Shabbos (either because the ball is Muktzah because it’s dirty and wasn’t M’yuchad before Shabbos or because there is no Eruv; I think R’ Ovadia or the Tzitz Eliezer has a long T’shuvah trying to be M’varer why the M’chaber says balls are Muktzah). It’s a Pele that I haven’t seen anyone who Assurs playing with balls on Shabbos be Misyacheis to 301:2. But I think that most agree that in a situation where there is an Eruv and the ball is relatively clean that it should be okay.
Some people (not Poskim) say that it’s Assur to sweat on Shabbos, but that’s only because they don’t know what the word “L’hazia” means.