And look at our stadium with the roof opened. The opening is barely a little hole in the center over the field. It's not like the whole lid slides off or something. There is a TON of "stadium" to reflect sound back downwards towards the field.
The whole debate about whether it's louder with the roof opened or closed could be easily solved with an SPL meter at the sidelines. Check it both ways, opened or closed. Having attended every game there (minus 2) since the stadium opened, I don't notice ANY difference in noise one way or another. But measure it at field level - and if it is quieter down there, then fine, close the damn roof. But, if as I suspect, there's no difference or minimal difference - then it should always be open the last half of the season when the heat is gone.