Right, sorry. I know LTRLI's formula is not a downsampling formula, what I was trying to say is I don't think it takes into account the realities of downsampling properly. To put it another way, I think it produces a result without context, which is why it seems to produce much higher numbers for DR than would seem realistic when computing DR for a downsampled image. In its own right, taken at face value (without any context) its certainly not an invalid formula...but do the results produced by it have real-world applicability? Do they represent something real, or is the formula too simplistic? I used to believe that DxO's Print DR numbers, which are derived the same way, were simply demonstrating that once you eliminate noise, you are then realizing the sensors full potential. Kind of tough to keep believing that, though, when the D800's Print DR numbers are BETTER than the sensors full potential...its not quite like a star trek warp drive...you don't get 120% of maximum out of a 14-bit sensor. 
Imagine you have 32MP sensor and you then averaged every 16 pixels into 1 and got 2MP output. And you then measure the Std Dev of the black frame. It's measure lower from the 2MP version than from the 32MP version but the white frame max saturation will measure the same in both cases. Plug into the DR formula and it goes up. It's not magic because the 2MP file also shows a heck of a lot less detail than the original 32MP file did so you traded that detail away for the higher score on the other aspect in a sense, what you are really trying to do it just compare the two files at the same scale. Even if the simplistic normalization didn't quite match in practice and over-stated something a little, the thing is in practice used use advanced NR to equalize them which would be doing better anyway, so there would be no problem there at all.
I understand the nature of scaling, that wasn't in question. Perhaps we just need to qualify what we mean by DR when we discuss these things. When it comes to "hardware DR"...I consider that a fixed constant, and an intrinsic attribute of the camera. If a camera has 14-bit hardware and X amount of overhead, it is going to be capable of a fixed, unchanging amount of "hardware DR"...or lets call it "true DR". If you saturate pixels beyond the True DR, say 15000 ADU, no amount of software-based tuning will be able to recover what you lost.
When we normalize two source images to a common image size, were affecting what I'd like to term "perceptual DR", or perhaps "virtual DR". You are not actually changing the characteristics of the hardware...there is still a hard limit on what a 14-bit camera can do. Virtual DR can only help you fully realize what that hardware is capable of, up to, but not exceeding the limits of, the hardware itself. I don't have a problem with the idea that with normalization of LOTS of pixels into FEW pixels, you might be able to fully realize 13.2 stops of DR, and possibly get a little bit more than that because your mitigating noise. I wouldn't be surprised if Virtual DR for a 13.2 stop sensor ended up being 13.8 stops, and if you had some REALLY GOOD algorithms to handle your normalization for you, I'd be ok, albeit surprised, if your normalized results achieved exactly 14.0 stops...but ok, fine...your making more effective use of data in the "noise floor" of your dynamic range. To achieve 14.4 tops, your somehow creating information...additional levels of luminance (over 5000 of them) to achieve a higher dynamic range than your sensor is capable of. Your adding information above and beyond the maximum number of ADU the ADC is capable of producing for a single pixel at maximum saturation.
Saying the D800 is capable of 14.4 stops, even though that is based on "normalized" data, is misleading. The camera itself is NOT capable of 14.4 stops...its capable of 13.2. Sure, it still wins the DR contest even with 13.2, but were were talking about over a full stop here...thats not within the margin of error. There is something wrong with the methodology here...something extremely UNrealistic about the way DR is being calculated from normalized data. Its not even remotely realistic when your claiming the D800 is capable of more than DOUBLE the dynamic range it ACTUALLY IS capable of
at a hardware level. This also begs the question why a mere 36.3mp sensor from Nikon gains SO MUCH MORE than say a 60mp sensor from Hasselblad when downscaling. According to the approach you and DxO use, the more megapixels you start out with, the better the ultimate results when you downscale to an 8mp image. There is obviously a serious disconnect when a FF DSLR sensor with half the resolution as a MF sensor achieves several stops better results, when if the key factor that determines normalized results is how much information you started with. The hassy should win hands down every time, even against a D800, if that was the case...and in visual comparisons even a 40mp hasselblad offers far more highlight recovery room and far better color rendition than a D800. There is a disconnect somewhere in the approach DxO uses and real-world results...and its not an insignificant disconnect.... I'm not sure if I'm portraying my point well enough here... I think sarangiman gets it, but I'm not sure if anyone else does.
As for SNR stuff they want to compare at the same noise scale otherwise you might be comparing a 32MP file that has lots of high frequency noise to a 2MP file that all the higher powers of noise automatically clipped away so it's not fair to compare the two images as if they were at the same noise scale. So they are really just normalizing the power scale of the noise between the two to not unfairly make the higher MP cameras look worse. You are reducing noise and signal so it's not like the image really improves any, it's actually a worse output really, yeah but you are just trying to do relative noise comparisons here and to compare it to the other file fairly that already had all the high frequency noise clipped away otherwise you are comparing the total noise over a larger frequency range than for the other one where the upper end of the range was hard clipped off which isn't fair. To do it well (not talking in terms of processing images for use but just for this relative comparison) you want to first gaussian blur away the high freq noise and then downsample to the scale you blurred it away to. or maybe more simply upscale the lower MP cam to the match the higher. Or you could just look at both at 100% on a monitor but stand back farther from the screen for the higher MP camera whatever distance is needed to make it's detail the same as what the lower one can capture. i think i garbled that a bit
I get your meaning there. I think, however DxO is doing it, that their "normalization" overcompensates for higher resolution and undercompensates for lower resolution, thereby unfairly making the lower MP cameras look worse than they really are. You effectively apply noise reduction to the higher MP camera, and none to the lower MP camera. I completely understand the value of normalized comparisons, but is the process of normalization valid? Scaling a smaller image up is actually not the same as scaling a larger image down. The former would actually leave noise characteristics largely in-tact for both images, without giving either of them a clear advantage. The problem with that is its harder to keep things consistent, as with each new higher resolution sensor, you need to reprocess old data to the new larger size and recompute the results. I get that, however I also believe it would still be more accurate...it would eliminate a lot of bias towards higher megapixel sensors (assuming that is the only bias...as I mentioned before, if the normalization process caters to higher resolution sensors because your factoring multiple source pixels into each output pixel of an 8mp target image, then medium format cameras should be trouncing everything else...as they well should...but there is clearly something else far less obvious going on with the D800's results.)
Do you think the D700 has much better ISO1600 than the 5D2? Because if you don't normalize, and you now seem to say that normalization doesn't make sense and isn't fair, then the D700 will stomp your 5D2, when the reality is it isn't fair to say that it does.
At a hardware level, I would say the D700 and 5D II have roughly the same performance at ISO 1600. I think the D700 wins by about 1/4 of a stop. That doesn't surprise me, and sensitivity and dynamic range
are strongly correlated with larger pixel area. Both cameras are full-frame, so the D700 certainly has a lot more area per pixel than the 5D II. I would EXPECT the D700 to offer more DR at any given ISO setting, since DR is closely linked to maximum saturation and standard deviation of read noise. (Barring any other improvements, making a pixel's total area larger will always allow for a larger maximum saturation level, and assuming all other things remain equal, I would expect the noise characteristics of two identical sensors with differing pixel sizes to be the same.)
Now, from a NOISE standpoint, which is obviously something we regularly correct with software, normalizing the two images to the same dimensions makes sense, and will help the 5D II's standing
from a post-processing standpoint...we all use software to clean up noise after we've imported our photos from our camera. But any side effect in terms of improved DR or color fidelity or anything else that you might get, at least according to the log(base2)(maxSaturation-stdevReadNoise) formula, is not reflecting a hardware capability in any way. Actually, the improvement in noise achieved by downsampling is also not reflecting a hardware capability in any way. None of the results gleaned from a software-normalized 8mp image will tell you anything about what the hardware itself is physically capable of...all it will tell you is what the software your using to perform the image normalization is capable of. DxO Analyze is apparently capable of doing amazing things with Nikon RAW files...but the fact that DxO Analyze is capable of doing amazing things with Nikon RAW files doesn't tell me anything about the Nikon cameras itself...its just telling me that DxO Analyze is amazing for processing Nikon RAW files.
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ISO is ISO...it shouldn't be changed in any way as part of computing a "score" or "rating".