Types and Programming Languages Part 20 – Measuring how hard your work is

This is the twentieth part of the Types and Programming Languages series. For your convenience you can find other parts in the table of contents in Part 1 — Do not return in finally

Sometimes you may ask yourself how hard you work. You could count the hours of work but we all know that some things are harder and some others are easier. One hour isn’t the same effort in different activities. Similarly, it’s easier to work when you’re not supervised and there is no time pressure. With deadlines ahead of you, the same amount of work now becomes harder and more stressful. Another factor is when you can do your work. Maybe you can work 24/7 and do it when you just feel like it, or maybe you need to stick to a strict schedule.

Being that said, there are many factors that affect “how hard” the work is. I was considering that recently and this is the formula I think works in my case. Let’s call this “Work Complexity Model”:

$\begin{gather*} C - \text{Cost of single context switch between activities} \\ A - \text{Set of activities} \\ S - \text{The size of particular increment} \\ I - \text{Number of increments in a given timeframe}\\ T - \text{Timeframe length} \\ E - \text{Final effort} \\ E = C^{card(A)} \sum_{a \in A} \frac{S \cdot I ^2} {T} \end{gather*}$

Let’s say that at your work you need to do coding, doc writing, and mentoring. Therefore, your set of activities would have these three elements. You then need to asses the cost of context switch which is your personal coefficient. It doesn’t matter per se and do not compare it with others. You can use it to compare your effort in different months when you move between projects or tasks.

Next, you need to decide on the period, for instance a single quarter.

Next, for each activity you need to measure how many increments you have. If you need to deliver your work at the end of the sprint, then you would have six increments (two increments each month). If you need to deliver something every day, then you would have ninety increments.

You then need to measure the size of the increment. Obviously, this is very subjective and it’s up to you to define how hard a particular piece of work is. Technically, this should be the amount of energy (physical and mental) you spent on the task. Since it’s hard to measure, you can just count the number of hours dedicated to the task and then multiply that by how intense and frustrating the work was.

Finally, you need to include the length of the timeframe to do the work. If you can work asynchronously 24/7, then your timeframe would be the whole period. If you can do your work during work days 9-5, then it’s just these working hours.

Let’s say that you can do coding 24/7, same for doc writing, but the mentoring you can do only on Mondays 9-5. You need to deliver your coding artifacts every other week, your doc writing twice a week, and your mentoring every Monday. Therefore, this would be your complexity over 3 months.

$\begin{gather*} E = C^3 \cdot \left(\frac{S_1 \cdot 6^2} {2160} + \frac{S_2 \cdot 24^2} {2160} + \frac{S_3 \cdot 12^2} {48} \right) \end{gather*}$

See that the formula has the following features:

It shows that context switching has some cost that scales non-linearly with the number of activities
Number of increments affects the result much more than the size of the increments. That’s because supervision tends to slow us much more
The length of the timeframe is also included in the formula

It’s up to you what your values for C and S are. The goal of this formula is not to give you some absolute scale. It’s much more to compare your different projects to have some numbers showing you how hard it was, as we know that our memory misleads us often.