The Mathematics of Management

The Mathematics of Management

Why averages miss the point.

By Sydney Finkelstein



“Average same-store sales have gone up every year I’ve been regional sales manager.”

“We keep cutting the number of days that patients have to wait for an appointment with a doctor.”

“We have a laser focus on one goal: maximizing market share.”

These surely seem like eminently sensible, strong metrics, praiseworthy accomplishments. Or are they? In our quest for simple solutions to complex problems—or maybe because nuance and subtlety take too much hard work—many of the seemingly logical equations that govern management thought are just plain wrong.

Relying on averages, for anything, is a sure-fire method to cover up little differences that might have big meaning. An average removes the most interesting data from the discussion.

Don’t you want to know who is best, and who is worst, at something? Averages disguise this.

Don’t you want to know what accounts for outlier performance, on either end? Averages cover this up.

In baseball, sabermetricians (as they’re called) split a player’s batting average into all sorts of more fine-grained statistics that can dull the senses of the uninitiated: batting average against left-handed vs. right-handed pitchers, strike count, men on base, and month of season, among others. This is one place where Big Data can help by dissecting average performance into its constituent parts that enables tactical responses.

Restaurant, hotel, and location ratings from companies such as Yelp, TripAdvisor, and Google suffer from a related problem. If you tell me that a restaurant has an average 3.5 rating on a 4-point scale, I want to know who is doing the rating. If raters are not much like me, then why is that average score meaningful?

Averages also bypass potentially vital distinctions and insights with huge public-policy import. For example, it is well known that the average test scores of American high-school students are abysmal relative to the students in places such as Hong Kong and Taiwan. But it turns out that if you look only at students in high schools in wealthy U.S. communities, you find they are often performing at an even higher level than their peers in other countries, Hong Kong and Taiwan included.

With this insight, we can begin to understand that the problem of American schools may be less about instruction, spending, and those videogame-addicted kids who can’t read, and more about poverty and family support.

Misleading Goals

OK, so averages can be misleading, but surely a focus on getting absolutely better at whatever goal you’ve got is smart management, right?

Think again.

You don’t have to go any further than the recent scandal at Veterans Administration hospitals to see what can go wrong when you create a stretch goal in an organization that hasn’t been primed for efficiency. Faced with a target that is beyond the ability of historically weak management to meet, what happened?

With patient wait times for medical appointments consistently longer than promised, some managers came up with the idea of creating a second ledger that miraculously showed a perfect record of hitting performance targets. Except none of it was true.

The same thing has happened at schools under tremendous pressure to boost student test scores. Unable to accomplish that goal in a conventional manner—via leadership, hard work, and innovation—some teachers began altering student exams to make it look as if they were doing better, when in fact they weren’t.

I don’t think we can chalk up these appallingly unethical, and likely illegal, incidents to just some bad apples. They’re much more about bad management. Setting a goal that can’t be met by the team in place, or in a culture that hasn’t been fine-tuned for success, is a waste of time. And worse.

Culture and management ability are prerequisites for any type of challenging goal. Even when we can check those boxes, we’re not out of the danger zone.

The endless quest for market share is a perfect example. The problem with market share is that the best way to get there is by lowering price, and that doesn’t always lead to bottom-line success. See Amazon if you’re not sure what I’m talking about.

The other problem with market share is that there comes a point when the law of diminishing returns starts to kick in. It’s one thing to go from 10 percent share to 15 percent but quite another to top off share once the numbers get much higher. Not only does the cost of adding that point of share increase—the likelihood of picking it up goes down.

Logic Warning Labels

Unfortunately, many executives are afflicted with the curse of linear thinking. The truth is that more isn’t always better, and not only for the reasons just noted.

Linear thinking also pushes people to hyper-focus on just one thing. We keep striving for more market share, or shorter wait time for patients, but we don’t consider whether there’s something else we should be doing.

Instead of pushing for that one additional point of share, maybe we should be targeting a different customer group where the upside is much greater. Rather than just try to mindlessly cut wait times for patients, why not consider different ways to provide medical service to war veterans that don’t require doctor office visits? Instead of pushing incremental product improvements, what about creating entirely new products?

Seemingly logical targets—higher average sales, shorter wait times, greater market share—should come with a warning label: May become toxic when applied incorrectly.

Sometimes the mathematics of management just doesn’t add up.

The Conference Board Review is the quarterly magazine of The Conference Board, the world's preeminent business membership and research organization. Founded in 1976, TCB Review is a magazine of ideas and opinion that raises tough questions about leading-edge issues at the intersection of business and society.