I'll 'splain. Is no time, I'll sum up:
a) 99.21% of people stopped by BDOs are not found to be doing anything wrong. (The "falsely suspected" factor.)
b) 0.79% of the people stopped by BDOs have been found to be doing something illegal. (The "sheer dumb luck" factor.)
c) 0.00000% of the people stopped by BDOs have been found to be terrorists. (The "needle-in-a-haystack" factor.)
d) 0.01% of all the people in airports were stopped by BDOs but were not doing anything illegal. (The "hassle" factor.)
e) there is no way of knowing how many people who were not stopped were doing something illegal (terrorist-related or otherwise).
f) If about 0.79% of the people who go through airports are doing something illegal, then the BDOs "secret powers" are no better than just randomly picking people out of the crowd.
But while we can play statistics all day long, I keep remembering this is an organization that agonizes over whether 3 is, or is not, 3.4, and struggles with fluid ounces versus ounces (weight).
When TSA says "BDOs are effective" they mean "it impresses the Kettles to have people asking questions in the airport."