Extracting Wintersteel Secrets with the Dark Arts

This is great, thanks.

   502.56       486.56       452.89
   509.51       493.29       459.16
   516.46       500.02       465.43

This is an estimated page-count matrix from taking your data and doing a bit of my own crunching, using the incredibly correlated thickness to page-count data as an inbetween, once accounting for the thickness offset produced by the presence of the covers.

From left to right the columns are Wintersteel pixel widths of 73, 74, and 75, to show how much variance human error causes. Being off by a pixel in measurement is about 6 or 7 pages of error. Not a big deal.

From top to bottom the rows denote a pixel count to thickness ratio of 64.5, 66.6, and 70.9 pixels per inch.

The main thing I wanted to explore was if the angle of the camera vs the books produced a systemic error in how pixels correspond to thickness.
pixel-width / thickness =
1 - 65.152
2 - 65.625
3 - 66.265
4 - 65.152
5 - 68.571
6 - 70.886
7 - 64.474
8 - ???

This data is a bit confusing. If we take the straight average (no distortion) we get pixel width / thickness equal to 66.6. If we assume a trend is present, we can see that it takes more pixels to span an inch as we move from left to right (as though the camera was slightly to the right of center, and pointing to the left, so that books on the right appear closer and larger). So Wintersteel could be in a location that takes at least 70.9 pixels to make an inch. That trend is pretty pronounced, though the most-adjacent book, Uncrowned, runs directly counter to it.

My guess would be that Uncrowned is at an angle less aligned with the camera than the other books, causing it to take up fewer pixels than it ought to. But then that raises the question - since Wintersteel is in contact with it, is Wintersteel more aligned with the angle of the other books, or with Uncrowned? It's difficult to say, since we can't see the tops of the books well enough to guess at their relative angles, so I'm forced to just evaluate Wintersteel's thickness (and thus page length) with the ratios of Underlord (70.9) and Uncrowned (64.5) to see what range that spans.

So... if Wintersteel is aligned the same as the other books, then based on my estimate of camera distortion, it will have 459 pages - pretty much identical to your linear regression. If it is misaligned in a way similar to Uncrowned, then we're actually in for a book with 509 pages. And if the camera isn't causing a distortion and that trend is coincidence, then just based on the average pixel:thickness ratio, we're looking at 493 pages.

In conclusion, Worst-case I expect your estimate of 460 to be accurate. But we could get as many as 509ish pages. Personally I'm putting my money on 480 pages, because I think that trend is significant but that Wintersteel also looks like its at a slight angle, and thus is hiding a bit of its true width.

/r/Iteration110Cradle Thread Link - i.redd.it