The answer really depends on how Jewish the person is.
Saturday is the Sabbath for the Jews, while Sunday is the Sabbath for Christians. Most Orthodox Jews do not play sports on Saturday, (because they feel it is wrong to do so), while most Conservative and Reform Jews think it's okay to play sports on Saturday, just as most Christians feel it's okay to play sports on Sunday.
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There are Modern Orthodox responsa that conclude that playing Baseball (within an Eruv, so you can carry your bat, ball and glove to the ball field) is permissible. Rabbi Saul J. Berman's "Playing Ball On Shabbat And Yom Tov," published in The Edah Journal Volume 1:1 addresses this, concluding that "Ball playing on shabbat and yom tov is a vacuous, pointless activity, almost as useless as sleeping hours on end. But it is halakhically permissible and serves a perceived need for relaxing, enjoyable and physically energetic activity time. Let’s not take that away from people until we can replace it with something that serves approximately the same purposes, and also serves to enrich their religious and ethical beings."