The statistics are for IDB's, not VDB's, but for 2016-Q3:

DL 0.10 per 10,000 pax
AS 0.35
UA 0.40
AA 0.54
B6 1.19

Raw numbers are generally meaningless because carriers have different passenger headcounts. But, it is telling that B6 had a total of 1,475 denied boardings, but only 439 of those were voluntary. On the other hand, AS had 1,797, but 1,600 of those were voluntary. The suggestion is that B6 seeks volunteers but does not try that hard.

The larger issue is that once it is an IDB situation, DOT rules require that the carrier use a predetermined order. It is not up to the GA or crew to change the order "just because". The order may take into account all sorts of things, but it can't change. Thus, once the doc was the next IDB, he was the next IDB.