I know that a lot of people like to talk about Dunbar's number (and Scoble's number), but in business a much more important number is represented by the concept of span of control. A November 1993 article by George Hattrup defined the concept as follows:
The span of control, or span of management, refers to the number of persons who report to one superior and includes the functions of planning, organizing and leading.
One way to illustrate span of control is by looking at the organization of a football team. For simplicity's sake, let's concentrate on the players and the coaching staff. According to current NFL rules (again, made in 1993), an NFL roster consists of 53 players during the regular season - with fewer on game day, but for most of the week there are 53 players that need to be managed.
These are managed by a coaching staff. As I write this, the head coach of the Washington Redskins is Jim Zorn. But he's not entirely responsible for all 53 players; he has an offensive coordinator (Sherman Smith) and a defensive coordinator (Greg Blache). But that's not the entire coaching staff:
Jim Zorn Head Coach
Greg Blache Defensive Coordinator
Sherman Smith Offensive Coordinator
Joe Bugel Offensive Line
Stump Mitchell Assistant Head Coach / Running Backs
Stan Hixon Wide Receivers
Scott Wachenheim Tight Ends
Chris Meidt Offensive Assistant
John Palermo Defensive Line
Kirk Olivadotti Linebackers
Jerry Gray Secondary-Cornerbacks
Steve Jackson Safeties
Danny Smith Special Teams Coordinator
Bill Khayat Quality Control-Offense
Chip Garber Quality Control-Defense
John Hastings Head Strength/Conditioning
Bobby Crumpler Assistant Strength/Conditioning
Harrison Bernstein Assistant Strength/Conditioning
Now I don't have access to the Redskins' organizational chart, but I'm pretty sure that only some of these people report directly to Zorn - probably the offensive and defensive coordinators, the special teams coordinator, and the head of strength and conditioning. If my assumption is right (and it probably isn't), Zorn directly manages four people. At the same time Smith probably manages Bugel, Mitchell, Hixon, Wachenheim, Meidt, and possibly Khayat.
Is this the right number for a football head coach, or football offensive coordinator, to manage? People have thought about this in the general business environment, according to Hattrup:
Historically, the concern over span of control was based on the idea that some optimal number of manageable subordinates should exist. Researchers in the past, such as Col. Urwick, stated that the optimal span of control was five or six. This as based on the assumption that managers have a limited span of attention, energy and time. If a manager was responsible for more than five or six subordinates, it was felt that the manager would loose track of what was happening. This was illustrated mathematically by A. V. Graicumas, whose work indicated that the number of potential interactions with subordinates will increase geometrically with respect to the manager's increasing span of control. For example, the addition of a fifth subordinate raises potential interactions from 44 to 100. Likewise, the addition of an eighth subordinate moves the potential from 490 to 1,080.
But there have been other studies:
The results of a 1952 study done by the American Management Association indicate that the median span of control for presidents of large companies (over 5,000 employees) is eight to nine with a range of up to 24. Presidents of medium-sized firms (500 to 5,000 employees) were found to have a median span of control of about seven and the range varied from three to 17. However, another recent analysis discloses a much narrower span of control in the middle levels of management than at the top. The president of the United States has more than 100 people who supposedly report directly to him. Since history suggests that he does not always know what White House personnel are doing, this number appears to be too large.
Hattrup ends up questioning the idea of a single number, noting that effective spans of control can vary according to different situations (e.g. stable vs. dynamic environments, issues regarding certain professionals such as doctors and engineers, etc.). In addition, Hattrup noted that span of control choices also affect the overall organization (e.g. small spans of control lead to more management levels between the top and the bottom). And if you believe one study, it may also affect profitability (other than the increased costs from smaller spans of control):
A study done by Sears, Roebuck and Co. provides evidence to support [large spans of control]....At one group of stores, managers were assigned a relatively large number of subordinates by decreasing one level of middle management. Because of the large spans of control, detailed supervision was impossible. Analyses of sales volume, management competence, profit and morale all indicated that the stores with the wide span of control were superior in every way to those stores that were more conventionally organized.
It's clear that Harttrup is a fan of larger spans of control, and from his perspective in 1993, he predicted "[s]pans of control reaching 50 to 70 will not be uncommon." Well, that was 1993. I haven't seen such spans of control in practice (granted, I've worked for somewhat traditional companies), and we've already seen that the Washington Redskins team doesn't have such a span of control. Then again, I'm forced to admit that the Redskins have not ben excelling as of late...
