Results for different bin ranges

The fits for 2x2 to 20x20 bins are done, pull means and sigmas are show below.

Fitting two separately poisson generated samples together:
r_bb
r_cc
r_gg

Fitting a poisson generated sample to its source:
r_bb
r_cc
r_gg

The chi2 works well for the first step, but then overestimates the error in step 2. That's not surprising since it's still using the errors from the templates, but if you don't (red line) the mean has an increasing bias as the binning increases.
The likelihood on the other hand under estimates the errors for step 1 but works well for step 2.