I don't know anything about games but at least in cameras the relation you want between the bit depth and dynamic range is determined by what you want to measure rather than a formula. An eye tracker I have is a 10-bit IR camera because a normal 8 bits are insufficient to both note that IR LED reflections are way brighter than everything else, while also having sufficient detail in the lower values that the edges of the pupil are easy to detect. At least, without having the scale be logarithmic or discontinuous or otherwise compressed.
I don't know anything about games but at least in cameras the relation you want between the bit depth and dynamic range is determined by what you want to measure rather than a formula. An eye tracker I have is a 10-bit IR camera because a normal 8 bits are insufficient to both note that IR LED reflections are way brighter than everything else, while also having sufficient detail in the lower values that the edges of the pupil are easy to detect. At least, without having the scale be logarithmic or discontinuous or otherwise compressed.