The 3/2 rule of employee productivity

2006-10-16 18:07:00 Allan Engelhardt wrote in CYBAEA Journal:

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.

[Analysis graph]

The profit per employee versus the number of employees for 475 of the companies in the S&P 500 index.
(Click on the image for a larger version.)

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

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.

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.

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    We revisited the 3/2 rule of employee productivity using a larger data set and showing each sector independently. As before, we chose profits per employee as our metric for employee productivity and show it against the number of employees. The resulting per-sector graphs are shown below (click through for a larger version). The data clearly debunk any myths that large companies are more efficient , an oft-quoted statement in merger situations, at least as far as HR is concerned. In total, there is probably a downward trend with size but with a slope of perhaps -0.1 or thereabouts. That still means that when you add 10% employees you lose 1% productivity per employee, which is clearly problematic.

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Follow-up analysis posted

2010-06-22 13:54:00 Allan Engelhardt said:

<p>We posted a follow-up analysis several years later and using British listed companies with the same results. See http://www.cybaea.net/Blogs/Journal/Employee-productivity-revisited.html

law of diminishing returns

2011-02-10 22:30:00 andarr said:

I disagree with your use of profit to measure employee productivity. When you use profit as a metric to measure productivity, then what you are really saying is that profit = employees * productivity.

Therefore productivity = profit / employees. That last statement is not true in that you can not measure productivity by how much profit is produced.

What you are in fact describing in this article is the law in economics called the law of diminishing returns. The law of diminishing returns states that you will increase your return for each employee you add up to a point. After that point, your return on each additional employee will be less and less and less until eventually they are producing negative returns.

So the employees productivity does not change, but the fruits of the productivity diminish with each employee added.

I agree with your thesis and the conclusions you reach. I just disagree with how you arrived at your conclusion.

incorrect analysis

2011-02-10 23:39:00 Jenya said:

I would fit the trend line separately for each of those 9 industries. What happens usually is that highly capital intensive companies tend to have high profit margins and their industries are not labor intensive. So, what you see in that graph is misleading. It may not tell you the productivity story.

Another explanation

2011-02-11 05:49:00 KW said:

Your data does not support your conclusions.

You ignore realities like the fact that high head counts are usually present in large organizations in highly competitive markets where high margins are rare. Also, when building your company, which would you rather build: a 100 employee company that makes $250,000 per employee, or a 100,000 employee company that makes $50,000 per employee.

There is no 3/2 rule of employee productivity. please don't use shoddy data analysis to start a non-factual meme.

problem with log-log here

2011-02-11 06:02:00 fooburger said:

I can see a reason for plotting # of employees in log scale.
Profit-per-employee though, does not belong on a log scale, as we are trying to establish that the naively intuitive answer (linear) is incorrect.
This makes me suspicious that log-log is being used here to 'trend up' the data.

re: log-log

2011-02-11 06:45:00 Andy said:

The log-log scatter doesn't look convincing. If you take away say the 5% most outlier points, you will just have a blob.

Partially true

2011-02-11 10:17:00 Vivek said:

This is basic. As the firm size increases, wouldn't coordination problems cause marginal productivity to decrease.
Also, wouldn't the productivity actually increase, or at least theoretically should do so, when the size is very small and increasing i.e. company of size 1 expanding to one of size 2 and then 3 and so on because of efficiencies due to specialization. How much sales (ebitda, net income, free cash flow, owner earnings or what not ) per capita can you generate when you perform all of these activities: book keeping, software development, marketing and sales (and janitorial services :) ). Would you perform each of these activities perfectly or nearly as well as a person specializing in it would? Wouldn't a team of say 4 people be able to generate 4x the metric? I think so. It would be interesting if you ran these numbers for small firms -- obviously data collection would be the biggest problem.

Just shows data selection method

2011-02-11 10:58:00 Paul Johnson said:

The correlation is probably caused by the data selection method. A company is presumably considered "leading" if it has an important position in the market, which means that small companies only get on the list if they are particularly impressive. Thus the selection criteria filter out small companies with average performance but lets in big companies with average performance, and hey presto, correlation!

loose

2011-02-11 11:09:00 multilind said:

Say you've got a craftsman making furniture, and you got 10 craftsmen making furniture together. Then by your logic the lonely craftsman makes more furniture than the team of craftsmen, because the lonely guy has a stronger connection between product and originator, and the 10 guys never complete their furniture because you don't see them as team! While one single craftsman in this team made 20 armrests, by your logic he made less furniture than the lonely craftsman who made one whole armchair, although the team together made 20 armchairs in the same time ..

You need to learn what an emergent system is before you analyse this kind of stuff ..

labor arbitrage

2011-02-11 16:51:00 Red pen said:

Revenue per employee is a dated metric that should have already gone the way of the dinosaur.

Labor arbitrage (the shifting of budget dollars overseas to lower cost GEOs) is in wider use at global MNCs and increases in use with company size.

To do a meaningful analysis, you would need to look at revenue per 'funds spent on employees as a whole'.

If a person in Egypt costs 10x per year less, than a person in California, an employer is not 'less productive' if they spend the same amount of money on 10x the people in Egypt.

similar analysis for size of software development team

2011-02-19 17:59:00 Denny said:

There is a post by Dr. Neil Gunther about the communication overhead vs. number of people, in a software development team, which is another analysis that may be of interest.

http://perfdynamics.blogspot.com/2007/11/modeling-mythical-man-month.html

Other Variable

2011-02-21 17:24:00 Basil said:

One thing that a company also needs to take into strong consideration is quality. Production margins will increase with less employees; however, quality will likely decrease. There is a threshold that the company needs to find to where quality is not being jeopardized. There are also other long term effects for the company to consider as far as job satisfaction, public opinion, etc when trying to increase productivity. I believe it would be interesting to see a 3-d plot with the inclusion of a quality variable for this same data set. I worked at Wal-mart distribution center during my undergraduate degree and know they have loads of quality data paired with productivity data.

Makes Sense

2011-08-26 20:58:00 David K Waltz said:

Given the higher coordination costs in larger organizations, it makes sense that productivity goes down, but not enough that a marginal addition still creates value.

In reading business literature, almost all the problems have a "somebody was not communicating with somebody" component. It semms somewhat like squeezing a balloon, as soon as we finally get some areas talking with each other (i.e. coordination), two or more other areas have stopped.