This game was specifically designed as a team building activity. The principal of the game was to have the tennis ball touch every team member before shooting your hands in the air and yelling "engineering"!
My team beat the other team because our design was vastly superior. Our first idea to move the ball from person to person involved a zigzag type motion where the ball touched every persons' hand only once and every other hand was either face up or face down. We then since modified the idea to a staircase meathod, where as the ball just uses gravity to move around the circle.
If you can view the image I incorperated that was the basic concept of how we moved the ball from person to person. The only other way I could see it being faster was to maybe have the ball touch less fingers. Gravity is the key factor to controling the speed the ball can travel.