The 3/2 rule of employee productivity

The more employees your company has, the less productive each of these employees are. It is a generalization, of course, but a useful one and one that is confirmed by most people who have worked for growing organizations. As the company grows, so does the internal processes and the layers of bureaucracy, and the time spent on communications grows rapidly.

It is, however, useful to look at the actual numbers. How much does productivity decrease as the organization grows? The answers are frankly frighting.

To look at the effect in large organizations, we considered the constituents of the Standard & Poor’s S&P 500 index of leading companies in leading industries of the U.S. economy.

For each company we collected information on revenues, gross profit, EBITDA, and the number of employees. After removing some companies with missing or hard-to-use data (e.g. negative profits), we ended up with 475 large, publicly quoted American companies.

As a metric for employee productivity we chose profits per employee. You can re-run the analysis with EBITDA or some other metric and the basic results do not change. See below for how to get the files.

We then plotted in a log-log plot the profits per employee against the number of employees for the 475 companies in nine different industry sectors.

[Profit per Employee (S&P500)]
The profit per employee versus the number of employees for 475 of the companies in the S&P 500 index.

Naturally there is enormous variation in employee productivity in such a diverse set of companies and industry sectors. The largest employer is Wal-Mart with $75 billion profit and 1.8 million employees ($41,800/employee). The three top slots in terms of employee productivity are all in the financial sector, with Ambac Financial Group’s 354 employees generating $1.66 billion profits ($4.7M per employee). At the bottom we find Darden Restaurants whose 157,300 employees each contribute $8,201 to the company’s profits.

Distribution of profit per employee
Min. 8,201
1st Qu.88,961
Median 167,089
Mean 298,578
3rd Qu.311,342
Max. 4,689,266

However, the trend is clearly downwards. Fitting a power law give a slope of -0.68. This is scary. Three raised to the power of -0.68 is 0.47. This means that when you triple the number of employees, you halve their productivity. Or: When you add 10% employees the productivity of each drops by 6.3%. Of course, since 3 times half is greater than one, your total profits are typically growing.

What causes it? Clearly, there is some element of self-selection: companies sometimes rationally choose to be in high-volume, low-margin markets. But I suspect that is also used as an excuse. There are more possibilities to encounter expensive relationship friction, but also more opportunities to resolve them.

I think it is largely down to communications: the degree to which a vision is shared and the effective dissemination of new ideas ideas and working practices. Innovation velocity is dependent on collaboration; and collaboration among larger groups and creation networks require different skills and tools than what most executives are used to from smaller situations and is therefore often underestimated.

Productivity in large enterprise is clearly a subject that deserves attention. If the S&P companies all achieved their average productivity, then they would between them generate an additional $2.9 trillion profit between them (with both winners and losers, of course).

Update

There is some selection bias in the companies we have chosen; see The 3/2 rule revisited for additional analysis.

Data files

The data and analysis scripts are available in the file sp500.tar.gz. If you wish to run the analysis, then you must install R, a wonderful software environment for statistical computing and graphics. On many modern systems you can simply type

% pkcon install R

as root and then unpack the files and run the analysis as

$ tar zxvf sp500.tar.gz
$ cd sp500
$ ./analysis               # Creates sp500.png, sp500.RData, and analysis.Rout
$ cat analysis.Rout        # View output from analysis command

On legacy systems you can download R from the project site and install it. Then you must either run it and open the analysis.R file in the application, or you can double-click on the sp500.RData file which should launch R with the data and command history loaded (try summary(sp) and summary(fm) to get started). You may also need to pay for a program to unpack the archive.