Crunching the numbers on Caballes

Julian Sanchez at Hit and Run has further thoughts on Caballes…

A few fairly obvious problems occur to me belatedly. The first is that to the extent that law enforcement officers now feel increased license to do indiscriminate sweeps, the conditions under which prior accuracy rates were ascertained in the field no longer apply. …

Let’s grant that the dog is 95 percent accurate. Now, you might think that sounds pretty good — 95 percent certainty would surely count as probable cause, right? The problem is making the error — and I wonder whether maybe the justices did this — of inferring from a 95 percent accuracy rate that you’re only going to end up physically searching one innocent person for every 19 who really do have drugs. But if searches are indiscriminate, that’s wrong, because the vast majority of motorists won’t have drugs.

This concept starts generating some scary numbers. For example, if you posit that the dog is 90% accurate (and from what I’ve read that’s not bad) and that 2% of all cars are carrying drugs (surely that’s a high number), then this is what you’ll get:
Out of 1,000 suspicionless sniffs, 2% (20) will have drugs. Of these, 18 will be caught. 980 will not have drugs; of these innocent drivers, 98 will will have their cars torn up. So out of 116 alerts by the dogs, 18 will actually have drugs, or 15.5% of those searched.
Not very good. Those 98 innocent drivers who have their cars searched — will that be considered a “reasonable” 4th amendment search?
Try your own numbers at the linked applet.