The team averages thirty hours. The dashboard looks comfortable. Two people are carrying most of the recorded work.
An average can describe the team accurately and still conceal the problem that matters. Put five people behind one number and the distribution disappears. So does the question of who keeps absorbing the next assignment.
If management wants to understand the workload, it has to look inside the average.
Thirty hours each. Except they did not.
Consider two illustrative teams of five people. Both record 150 hours over the same period.
In the first team, everyone records thirty hours. In the second, the hours are sixty, sixty, ten, ten and ten. The average is thirty in both teams. In the second, two people account for 80% of the recorded hours.
That difference deserves attention. It does not yet tell us whether the allocation is wrong. Perhaps three people work shorter contracts. Perhaps the two longest records include unattended timers. Perhaps the work genuinely depends on two specialists while others wait for permission to help.
Those explanations lead to different decisions. None is visible in the average.
Measure the concentration
Theil T measures how unequally a non-negative quantity is distributed across a defined population. It is an established inequality measure, with a mathematical literature extending well beyond work analytics. A recent statistical study of Theil estimation examines its properties and uncertainty in income surveys. That research does not turn it into a test for employee burnout.
For our equal team, Theil T is zero. For the sixty, sixty, ten, ten, ten example, it is approximately 0.334795, using natural logarithms. The calculation is set out in our Theil reference.
That number is not “33% unfairness.” It describes concentration. There is no universal boundary at which a distribution becomes unacceptable. The next step is to inspect the values and the population behind it.
Known zeros matter too. If two people have values of zero and ten, dropping the zero makes the remaining person look perfectly equal to themselves. Keeping both people gives Theil T of approximately 0.693147. Removing an inconvenient observation changes the question being answered.
Missing records require a different response. Someone whose work was not captured cannot simply be assigned zero.
Where does the imbalance sit?
Theil T can be decomposed into differences within groups and differences between their means. This helps distinguish a concentration spread across departments from one concentrated inside a particular team. The PySAL technical guide explains that decomposition.
But grouping is a choice. Comparing unlike roles can manufacture a dramatic story from ordinary differences. A support queue, a research project and an approval function do not necessarily produce comparable records or require equal time.
Use the breakdown to locate questions. Check staffing, responsibilities, coverage and allocation rules before deciding what the answers mean. A statistic can expose a pattern without explaining who created it.
What Observatory actually measures
The Ghost Observatory development snapshot described in our documentation applies Theil T to recorded process-event counts, not to the illustrative hours above. Each included event receives the same weight. The result therefore describes the concentration of those events; it cannot establish the difficulty, duration or quality of the work.
The Engine also calculates an expected index under equal random allocation. Small numbers of events can produce unequal counts even when everyone has the same chance of receiving an event. That comparison adds context, rather than a verdict that anything above expectation is unfair.
The documented snapshot does not publish the within-group and between-group decomposition described earlier. The publication and population rules distinguish the available product outputs from the general mathematics.
Give the people behind the average a hearing
A concentrated workload is a reason to investigate. Ask whether assignments can be shared, whether knowledge is trapped with a few people, whether records are incomplete and whether the people doing the work recognise the picture.
Do not replace an average with a more intimidating number and call the problem solved. Theil cannot read exhaustion, establish effort or predict a resignation. Its value is that it makes a distribution harder to ignore.
The average can keep the meeting quiet. Understanding what sits behind it is where management starts.