Listening tests show that floor bounce causes coloration. That coloration though was above 500 Hz. So you need something that starts there and goes to limits of audibility.
Here is a simulation I ran on a 25 mm/1 inch absorber. The graph shows amount of absorption at every frequency with 1.0 "alpha" being perfect absorption:
As you see, it starts absorbing around 200 Hz and by 1000 Hz it is in full swing.
Here is what happens when we cut the thickness to half inch/12.5mm:
Now absorption barely starts at 500 Hz and we never achieve perfect absorption.
Last is quarter inch or 6 mm:
This is why you don't want to cover all of our walls with fabric as some people do in home theaters. You effectively will be putting an EQ in the system with the above shape, absorbing a lot of your mid to high frequencies, resulting in a very dead room.
This is why Shag carpet if you can deal with its look is so good. Otherwise put a porous pad below the carpet to give it an air gap.