Kara, he could alter his design to have a cross bar near the top with bumpers but the hole idea sorta fails for this problem.
Frame Perimeter is the polygon made by string wrapped around (Robot Definitions)
R19 and G46 if it penetrates Frame Perimeter over 3" you get penalized.
As long as it fits in 3" or less it could work in which case your hole is probably too deep.
Number crunching time
9" Diameter Ball, 4.5" Radius Ball
http://en.wikipedia.org/wiki/Circular_segment
Using this page.
h=R(1-cos(theta/2)) thus 3=4.5-4.5cos(theta/2)
-1.5=-4.5cos theta/2
1/3=cos theta/2
arcos 1/3 =70.53 degrees = theta/2
Theta = 141.06 degrees
Now Find the length of the Chord
C=2Rsin(theta/2)
C=9 sin 70.53 degrees
C =8.89"
Using radians for precision as wolfram alpha gets a lot of them you get 8.5"
Now this is the line C in the wikipedia page and there is some space if you extended c to the tangent line perpedicular to it (the ground)
9-8.5 = .5 .5/2 = .25" on top and .25 below so you need a bar at 8.75" if not lower to stop the ball from going in over 3"