part of why we stay living where we live. 25 years ago, I went to a stake president who was adament against it, and had shut it down. I promised him, that if he would let me take it on, we would have well officiated games with sportsmanship, and a ton of non member participation. Finally, he allowed it, and the rest is history." Mormon ball " for our young men, is the talk of the local high school, and every team in our stake, has at least 3 non members on their team, many who have been baptized, and rarely do we have any challenges. We have two members currently serving missions, who were first exposed to the church through basketball. I remember asking the stake president to come up with any other activity that would have 12-15 non members in our building, all having a prayer with us, while their wives rubbed shoulders with other member wives.
Our mens league, is well supported, and most wards get 8-12 brethren out every week, as well as several non members. While I am not personally aware of many ( actually just remembered one from last year ) baptism's that were helped along by church basketball, many reactivations, and several husbands in part member families come and rub shoulders. Once in a while we have a sportsmanship issue, but that is the exception, and not the rule.
We also play softball, and coming to the ball park is a great part of the summer social scene for many of our members.