Comparison of 2009 BSMDE Slopes Eta Dependence to Database Absolute Gains

Because there is no 2009 absolute BSMD calibration yet, we have to be careful about making comparisons between the results of the 2009 BSMD relative gains analysis and the current default gains in the database.  However, looking at the gain equation, Gi=A*(Avgi/Slope)alpha, suggests that (if we assume alpha=1, as we do) the ratio of the gain in each bin to the gain in a given bin b should follow the ratio of the average slope in each bin to the average slope in bin b.  These ratios are plotted in the figure below, with absolute gain ratios in red and average slope ratios in black.  I should emphasize that this figure should not be taken as the last word on this subject (and certainly should not be used to calculate percentage deviations, for instance), as it is not a direct apples to apples comparison and the calculation of the average slopes was done in a somewhat ad hoc manner: however, it does give some information about the differences in the eta dependence between the current gains in the database and the slopes calculated from run 9 data.

Figure 1: the red line is the absolute BSMDE gain for each eta bin divided by the absolute BSMDE gain for the 0-.1 eta bin, while the black line is the average slope for each eta bin divided by the average slope for the 0-.1 eta bin.