With matplotlib 2.0, I had weird behavior when I use both the index and superscript of the same character. When they are combined, the index drops completely below the baseline. This did not happen with MPL 1.5. Here is a complete example:
import matplotlib as mpl
import matplotlib.pyplot as plt
mpl.rc("font", family="Times New Roman",weight='normal')
plt.rcParams.update({'mathtext.default': 'regular' })
plt.plot(1,1, label='$A_x^{b}$')
plt.plot(2,2,label='$A_x$')
plt.plot(3,3,label='$A^b$')
plt.plot(4,4,label='$A_x^{*}$')
plt.plot(5,5,label='$A^*$')
plt.legend(fontsize='xx-large')
plt.show()
I took this plot and approached the legend and drew some horizontal lines to show the relative positions of super and indexes.

I found these parameters in the mathtext.py file in the FontConstantBase class:
script_space = 0.05
subdrop = 0.4
sup1 = 0.7
sub1 = 0.3
sub2 = 0.5
delta = 0.025
delta_slanted = 0.2
delta_integral = 0.1
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