The math from 8 bit to 10bit is sound.
Just like the color is sound. You have to change your perspective.
Everything operates in groups of 4. 4 boxes have the same color value...each box has a different luma value in example:
1: 50 2: 100
3: 25 4: 220
But all 1 - 4 have the same color value whatever that may be.
They all share the same full range color, aka 10 bit color which is why we have a "4" in front of 4:2:0,
So add the values together when you down sample to 10bit and you get 395 in a 10 bit luma space. Do the math and you hit 38.57% of the full 10 bit range.
Now take the values and average them 1-4 and guess what you hit the same 38.57% Which is more accurate however, the 10bit is. Why? not only does it expand the space but it also retains all the data. When you average the values you will lose data as it rounds off information. The funny part is, I bet this is even more accurate then just strait captureing 10-bit at 1080p...you should get better roll off and easily exceed the range of 10-bit 4:2:2. Anyone who thinks other wise needs to check their math.