In most papers we at Ars cover, we'll be pleasantly surprised to find a single clever turn of phrase that has survived multiple rounds of editing and peer review. So it was an unexpected surprise to come across a paper where the authors, all professors of economics, have spent the entire text with tongues so firmly planted in their cheeks that they threatened to burst out, alien-style. It surprised me even more to find it in a journal that is produced on behalf of the Royal Statistical Society and American Statistical Association. Credit to the statisticians, though, for the journal's clever name: Significance.

What topic allowed the economists to cut loose? Bank robberies—or more specifically, the finances thereof. The UK's banking trade organization decided it wanted an analysis of the economic effectiveness of adding security measures to bank branches. The professors did that, but in the process, they also did an analysis that looked at the economics of bank robbery from the thieves' perspective.

The results were not pretty. For guidance on the appropriateness of knocking over a bank, the authors first suggest that a would-be robber might check with a vicar or police officer, but "[f]or the statistics, look no further. We can help. We can tell you exactly why robbing banks is a bad idea."

The basic problem is the average haul from a bank job: for the three-year period, it was only £20,330.50 (~$31,613). And it gets worse, as the average robbery involved 1.6 thieves. So the authors conclude, "The return on an average bank robbery is, frankly, rubbish. It is not unimaginable wealth. It is a very modest £12,706.60 per person per raid."

"Given that the average UK wage for those in full-time employment is around £26,000, it will give him a modest life-style for no more than 6 months," the authors note. If a robber keeps hitting banks at a rate sufficient to maintain that modest lifestyle, by a year and a half into their career, odds are better than not they'll have been caught. "As a profitable occupation, bank robbery leaves a lot to be desired."

Worse still, the success of a robbery was a bit like winning the lottery, as the standard deviation on the £20,330.50 was £53,510.20. That means some robbers did far better than average, but it also means that fully a third of robberies failed entirely.

(If, at this point, you're thinking that the UK is just a poor location for the bank robbery industry, think again, as the authors use FBI figures to determine that the average heist in the States only nets $4,330.00.)

There are ways to increase your chance of getting a larger haul. "Every extra member of the gang raises the expected value of the robbery proceeds by £9,033.20, on average and other things being equal," the authors note. Brandishing some sort of firearm adds another £10 300.50, "again on average and other things being equal."

What do the numbers mean to the group that actually asked for the study, the bankers? For one, the pattern of branches targeted for robberies appeared more or less random, with branch size, distance to the nearest police station, etc. all failing to influence the frequency of robberies. So the banks probably can't focus their security costs on any subset of their branches that are more likely to be victimized.

One security measure that has been adopted in the UK—bank tellers can trigger compressed air to rocket a security screen up, separating them from the robbers—is remarkably effective: "A fast-rising screen in a banking outlet relative to other counter-security arrangements reduces the expected value of a robbery by £24,463.30, on average and other things being equal." You may be confused by the fact that this is more than the average haul, but the authors are prepared for your conclusion, noting parenthetically, "Those last seven words take care of the fact that the expected reduction in haul is £4,000 greater than the expected average haul. A screen in no case has actually resulted in raiders handing over £4,000 of their own money to the bank cashiers before fleeing the premises."

Despite the effectiveness of these screens, however, the low rate of robberies and their general failure to remove much in the way of cash from the banks means that it's probably not worth the cost of installing them.

So, there you have it: a clear case where crime, economically, doesn't pay. The authors suspect this may be behind the gradual decrease of bank robberies in the UK. "It is worth noting that the criminals themselves seem to have learnt this," they conclude. "Robbing banks is no longer what you could call the crime of choice."

Possibly so, but it's probably a stretch to go from that to their final conclusion: "The lesson of which would seem to be: successful criminals study econometrics. Statistics can help in all walks of life."

Significance, 2012. DOI: 10.1111/j.1740-9713.2012.00570.x (About DOIs).