Over on sursumcorda’s blog, there’s a post about noticing the numbers we read. I’ve recently noticed wrong numbers in two otherwise excellent books – errors that I think are frequent enough that mentioning them here won’t hurt.

The first instance comes in “Switch,” the Heath brothers’ fascinating examination of what helps and what hinders change both in personal and organizational practice. In their tenth chapter, “Rally the Herd,” they discuss how apt reporting of peer behavior can be used to spread proper behavior. They tell the story of a review time turnaround at a peer-reviewed journal called MSOM:

When Gerard Cachon took over MSOM, most peer reviews were taking from seven to eight months… …Cachon announced that MSOM would review papers within sixty-five days – that was 72 percent faster than its previous average!

Now, the 72 percent don’t appear out of nowhere: 65 days are roughly 28 percent of seven to eight months, so it’s correct (albeit oddly accurate) to say Cachon wanted to reduce the average review period by 72%. However, “faster” implies speed, not duration: and then the Heath brothers understate their case. The original review cycle ran at a speed of about 1.6 reviews per year; Cachon wanted to raise the speed to 5.6 reviews per year. The difference – 4.0 reviews per year – is a whopping 250%!

The second instance comes in “Built to Last,” the business book by Jim Collins and Jerry I. Porras which investigates what attributes determine the long-term fate of a company.  In their eighth chapter, “Home-Grown Management,” they write:

Of 113 chief executives for which we have data in the visionary companies, only 3.5 percent came directly from outside the company, versus 22.1 percent of 140 CEOs at the comparison companies.  In other words, the visionary companies were six times more likely to promote insiders to chief executive than the comparison companies [emphasis theirs].

While it is true that 22.1 is roughly six times 3.5, that factor represents the relative likelihood of hiring an outsider, not of promoting an insider.  For insider promoting, the factor is far less majestic: 96.5 percent is only 1.2 times more than 77.9 percent, making the visionary companies only a good fifth more visionary than their peers…