Quote Originally Posted by Lady Rikku
On my game, I had Lulu throw the blitzball. On my cousins game, Rikku did. I think you can kinda tell depending on that one scene where they're driving to Macalania Temple and the person behind Tidus is usually the person who throws the blitzball. Hey, that's just my theroy. xD
Yes, and that in turn depends on the "affection level" you've attained for that character.

By affection level, I mean who you've spoken to first the most amongst your party members, what answers you give in conversations. There's also speculation that healing a certain member in battle often can raise the affection level, as well.

One thing I noticed, that during the scene in Guadosalam, when Lulu asks you if you've fallen for Yuna, the only playthrough I answered "You're more my type, Lulu", was the only playthrough in which Lulu rode on the ski-doo (snowmobile) at Lake Macalania with me. As well, on this playthrough she tosses the ball during Blitz Ace to me, and none of the females were in my fighting party.