39 916 800 Ways to Prioritize Eleven Backlog Items

What is Most Important?

We need to prioritize our efforts in order to use time and other limited resources wisely. The activity can be challenging, and in some contexts, e.g., triage in care situations, it may have life-changing consequences. In most cases, when concerned with business development, the effects of prioritization are not causing such effects, but may affect the future of the organization and its people. In businesses working with development of products, e.g., software-intensive systems, many have adopted methodologies using backlogs of items to be addressed. Having a backlog in a perfectly prioritized state is challenging. Often you still have a nudging feeling and ask yourself, is this actually the right prioritization?

It may not just be because of indecisiveness or disagreements between you and your colleagues. Mathematically, we can arrange a backlog with eleven features in almost 40 million ways. A meeting with the goal of arranging eleven items in all orders, where each order takes one minute to arrange and assess, will last over 75 years.

How Seemingly Small Numbers Results in Complexity

The large numbers may seem intuitively unsound, but the way we can calculate the number of unique orderings, called permutations (Balakrishnan, 1996), of the backlog, is by calculating the factorial of 11, denoted as 11! (Balakrishnan, 1996). The exclamation mark is shorthand for: 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1. Depending on the backlog size to prioritize, the relation between items and combinations is:

From a mathematical standpoint, it is almost impossible to agree on a common list of priorities. But most prioritization discussions won’t last for years. We have strategies and ideas to reach a common ground on how to proceed. We will often have a good-enough backlog, but looking at the table above, it is not surprising that there may be different opinions on what is the best possible prioritization of a backlog.

Backlog Size Matters

Those arguing for smaller batch sizes, work in process/progress (WIP) limits, and queue limitations, are on to something beneficial from a prioritization perspective. Backlogs are in some sense a queue and those are costing organizations more effort and costs than we realize (Reinertsen, 2009). By reducing the scope from eleven to five items would cause the hypothetical eleven-item 75-year meeting to end in two hours. A backlog of 15 features will make our meeting considerably longer. It would last over 2,4 million years, making it challenging to find a suitable venue with proper catering for such a lengthy event.

Prioritization isn’t just about math. Besides possible orderings, other factors are contributing to the actual prioritization (and execution) of a backlog, reducing the number of feasible orderings. This reduces the complexity of the prioritization problem. Here are some examples:

• Resource considerations. Resources that aren’t available and don’t have time, the need to wait on item X in order to do Y etc. give us constraints for what can be done and when.
• Company vision and important goals assist us in what is more important than other items.
• A shared understanding of the backlog subject. If we understand the subject, we may reach consensus faster. A lack of shared understanding may make consensus harder.
• Internal politics and power relationships. Sometimes a leader or person with authority will steer the backlog towards their priorities. Both formal and informal leaders may do this.
• Ideas of what contributes with the most valuable outcomes.
• Various prioritization techniques can contribute to better prioritizations and more objective discussions on what is a better priority.

Not all aspects reducing the prioritization complexity are positive. For instance, people with strong opinions may push their agenda, and make the prioritization effort easier, but for the wrong reason.

Improvement is Possible, Focus on Value

The next time you are stuck in prioritization discussions, see it from the bright side. Most of the time you will find a good enough prioritization within a timely manner, even if the mathematical odds are against you. There are challenges and hidden forces that may cause us not to prioritize the best way. We need to fine-tune and research better practices, tools, and mindsets to deliver the best possible value to customers and other stakeholders. There are room for improvement and new practices supporting an increased value focus. I will retrun to this in future posts.

List of References

• Balakrishnan, V. K. (1996). Introductory discrete mathematics (Dover ed). Dover Publications.
• Reinertsen, D. G. (2009). The principles of product development flow: Second generation lean product development. Celeritas Publishing.