It’s worth clearing some of this up... the bigger the capacity, the higher the roof and the more leakage of sound occurs...
Tosh.
The mathematical formula you are looking for relates reverberation time to the volume and the amount and reflectivity of the internal surfaces. Enjoy...
http://webphysics.davidson.edu/faculty/dmb/py115/ReverbCalc.htmlAs I explained hopefully in simpler terms above, if you have a big box, with lots of solid walls, floor and ceiling and a relatively small opening, the sound can be "bigger".
Unfortunately the largest of these areas by far is people, who are soft and squidgy and absorb sound, so the reverberation effect is relatively small compared to shouting directly at the pitch. I dare say, the sound coming back off the underside of the roof comes back to the crowd and makes it sound louder to them, which encourages them to shout directly at the pitch even louder. The angle of the roof can have more effect (
if it doesn't vibrate - but being light, it will) ie., as long as you can see the pitch to shout directly at it and there's lots of you, your going to make a big noise.
It is also doubtful that you can increase capacity with a double tier because of the increased rake and sightline requirements. so unless you want boxes in the kop, forget it.
If you really want the roof to do the job as a reflector - angle it upwards rather than down and build it out of smooth concrete (see Hollywood Bowl) or this (unfortunately it's tiny - concrete being so bleedin' heavy...
Of course it doesn't matter so much in Spain (or LA) when it rains...