I have come to the realization that my DS10 is really lacking in initiative. I think this is a hard one. I would think his sports will help. Any ideas to get him going more in the right direction?

Ah - this is such a hard one! I have had to work incredibly hard to keep D11 motivated. While she did well in Math, she missed being in the GT classes due to her Eng scores. But she is very happy to settle at the easiest levels. Setting small goals, with just that little bit of challenge has worked best for us. Finding a peer who is similarly inclined, getting involved in Battle of Books, Science Bowl kind of competitions also helped us.

This is the key, I think! Your child has talent and brains, but if they don't want to use those talents, they may not do as well as they could.
Positive reinforcement is always good. We have found sports to be very helpful. My son is very small and for him, just being on the swim team is a success. He's never going to be in the Olympics, LOL! Pointing out how he dropped time at the meet, or noting in a good way how another kid has swum fast after he has worked hard in practice.
Gradually, my son has become motivated in other areas. He has really embraced a reading contest at school, trying to read a certain number of books in a specified amount of time. As he has slowly achieved that, we make a big deal about it, going out to dinner or something like that.

I work with my son by setting goals for myself as well. We then recognize success and I acknowledge when something is difficult or I don't want to do but complete anyway. He seems to like that I go through the same type of things as he is.
just an idea

This has been such an issue for us too! I get frustrated because my DS8 "could do so much more if he just...." (fill in the blank with just about anything. But, what I have found by just listening to him a little bit more and letting him be in that quite a bit goes on in his head that he does not share with us. Imagine my surprise when he went through a long and complex discussion with his chess coach about the personalities of different pieces and what pieces he really enjoyed. There was a lot of thinking and initiative that went into that that we were not aware of!

Seadoneam (and new!)