Daniel Vacanti

# When an Equation Isn't Equal

Updated: May 27

This is post 1 of 9 in our Little's Law series.

Try an experiment for me. Assuming you are tracking flow metrics for your process -- *which if you are reading this blog, you probably are* -- and calculate your average Cycle Time, your average Work in Progress (WIP), and your average Throughput for the past 60-ish days. [*Note: what data to collect and how to turn that data into the four basic metrics of flow is covered in a ** previous blog post*]. The exact number of days doesn't really matter as long as it is arbitrarily long enough for your context. That is, if you have the data, you could even try this experiment for longer or shorter periods of time. Now take your historical average WIP and divide it by your historical average Throughput. When you do that, do you get your historical average Cycle Time

*?*

**exactly***Another quick disclaimer, for the purposes of this experiment, it is best if you don't pick a time period that starts with zero WIP and ends with zero WIP. For example, if you are one of the very few lucky Scrum teams that starts all of your Sprints with no PBIs already in progress, and all PBIs that you start within a Sprint finish by the end of the Sprint, then please don't choose the first day of the Sprint and the last day of the Sprint as the start and endpoint for your calculation. That's technically cheating, and we'll explain why in a later post.*

You've probably realized by now that we are testing the equation commonly referred to as Little's Law (LL):

CT = WIP / TH

where

CT is the

**average**CT of your process over a given time period,WIP is the

**average**Work In Progress of your process for the same time period,and TH is the

**average**Throughput of your process for the same time period.

It may seem obvious, but LL is an equation that relates three basic metrics of flow. Yes, you read that right. LL is an *equation*. As in equal. Not approximate. Equal. In your above experiment, was your calculation equal? My guess is not.

Here's an example of metrics from a team that I worked with recently (60 days of historical data):

WIP: 19.54, TH: 1.15, CT: 10.3

In this example, WIP / TH is 16.99, not 10.3. For a different 60-day period, the numbers are:

WIP: 13.18, TH: 1.03, CT: 9.1

This time, WIP / TH is 12.80, not 9.1. And one last example:

WIP: 27.10, TH: 3.55, CT: 8.83,

WIP / TH is 7.63, not 8.83. Better, but still not ** equal**.

If you are currently using the ActionableAgile tool, then doing these calculations is relatively easy. Simply load your data, bring up the Cumulative Flow Diagram (not that I normally recommend you use the CFD), and select "Summary Statistics" from the right sidebar. Here is a screenshot from an arbitrary date range I chose using AA's preloaded example data:

From the above image, you'll see that:

WIP: 15.04, TH: 1.22, CT: 9.45

However, 15.04 / 1.22 is 12.33, not 9.45. As evidence that I didn't purposefully select a date range that proved my point, here's another screenshot:

Where 27.09 / 3.47 equals 7.81, not 8.86. In fact, I'd be willing to bet that in this example data -- *which is from a real team, by the way* -- it would be difficult to find an arbitrarily long time period where Average Cycle Time actually equals Average WIP divided by Average Throughput. Just look at the summary stats for the whole date range of pre-loaded data to see what I'm talking about:

21.62 / 2.24 equals 9.65, not 9.37 -- still close, but no cigars.

I'd be willing to bet that you had (or will have) similar results with your own data. If you tried even shorter historical time periods, then the results might even be more dramatic.

So what's going on here? How can something that professes to be an equation be anything but equal? We'll explore the exact reason why LL doesn't "work" with your data in an upcoming blog post, but for now, we'll actually need to take a step back and explore how we got into this mess, to begin with. After all, it is very difficult to know where we are going if we don't even know where we came from...

**Explore all entries in this series**

__When an Equation Isn't Equal__(this article)__The Most Important Metric of Little's Law Isn't In the Equation__

**About Daniel Vacanti, ***Guest Writer*

__Daniel Vacanti__* is the author of the highly-praised books "*__When will it be done?__*" and "*__Actionable Agile Metrics for Predictability__*" and the original mind behind the ActionableAgile**™️** Analytics Tool. Recently, he co-founded ProKanban.org, an inclusive community where everyone can learn about Professional Kanban, and he co-authored their Kanban Guide. *

*When he is not playing tennis in the Florida sunshine or whisky tasting in Scotland, Daniel can be found speaking on the international conference circuit, teaching classes, and creating amazing content for people like us. *