Note: that relies on doing proper sRGB -> linear instead of naive gamma conversion, unless I'm completely mistaken:

    In [16]: math.log2(1./colour.models.oetf_reverse_sRGB(1.0/256.0))
    Out[16]: 11.6915341649192

    In [17]: math.log2(1./((1.0/256.0)**2.2))
    Out[17]: 17.6

    In [18]: math.log2(1./((1.0/256.0)**1.8))
    Out[18]: 14.4

Although the stuff you will be losing even if you use 2.2 gamma with 12 bit depth should be fairly minimal if I'm interpreting the numbers correctly