Fits_FixedBins.pdf shows how the histograms are fitted with equal width bins (0.5 GeV bins from 1.5 - 4.5 GeV for JP, and 1.5 - 3 GeV for HT).
The value of 4.5 GeV was chosen for JP because some rings run out of statistics above that point (~17-20)
The value of 3.0 GeV for HT is the same value used in previous calculations (sufficiently below trigger threshold).

DifferenceInGains_VariableAndFixed.png shows a comparison when the gains are compared tower-by-tower for the extraction that uses equal width bins compared to the extraction that uses bins of roughly equal statistics. (NOTE: the outer rings are not included in the comparison because I did not recalculate the extrapolation values using the new extraction method. The only rings that are compared are 3-38).

You will notice that the gains go down slightly (0.3% on average). This is because there are more bins at higher momentum which are given equal weight. E/p rises slightly with momentum, and therefore the gains are systematically lower compared to the extraction where bins are determined using equal statistics (that extraction biases towards low p bins where there are a lot more statistics).

The rise in E/p as a function of p can be seen in slide 5 of: https://drupal.star.bnl.gov/STAR/system/files/NewLooseVeto.pdf

UPDATE:
I have added two new files showing the fits for when I use the fixed bin width approach, but use the last bin as an overflow bin.
Fits_MostlyFixedBins.pdf shows the fits using this new approach.
DifferenceInGains_FixedAndMostlyFixed.png shows the tower-by-tower difference distribution for when I use the fixed bin width approach, but change the last bin to be an overflow bin.