Estimating Projects using PERT and Fermi Tests

I once inherited a project that was 2 years late. The project had languished for so long that can be a challenge to breathe new life into a project that everyone has given up on and tossed into the corner of their "other duties as assigned" pile.

It quickly became obvious that there were many reasons the project's unhealthy status. One key problem is that no one had ever created a true task list (or Work Breakdown Structure or WBS as it is called in project management), or validated that list with the team members who were supposed to complete it. Calling the team together, we began this process. "What needs to happen first?" I asked. Team members volunteered task steps. "Who is the best person to do task 1?" I asked next. People looked around the room at each other, mentally trying to determine who should get the short straw. I knew who would be the appropriate person but I wanted to see if that person would volunteer. Reluctantly a hand lifted off the table. "Thanks, John1," I said.

Then the really hard work began. "John, how long will this task take you?"

"Hard to say," John replied. "It all depends on whether other emergencies come up. On whether my manager gives more higher priority work. Maybe I'll need some extra help. Maybe it won't work the first time and I'll have to figure out a different way to do it. Maybe the server won't be ready in time for me to start my work." The list just went on.

"OK," I said. "What's the worst case scenario for this task? Let's say all those things happen as you describe. What is the longest amount of time it will reasonably take you to complete the task?" John was still unwilling to put a number down. Finally I offered two months. John assured me it wouldn't take that long. We agreed that a month would be the worst case. Next we turned to the best case. "Let's say that I get your manager to agree that this task is the most important work you will be working on. If there are any emergencies, someone else will look after them, and your first hunch will work out." After some more minutes hemming and hawing and negotiating, we agreed the best case was 3 days. Finally, we agreed on the "average" case. Some things go wrong--as they inevitably do--but not everything and John's manager still agrees that the project needs to be completed. We agreed on 5 days as the average time to complete the task.

Project managers will recognize this as a PERT estimate. The PERT estimate for the first task took probably about 10 minutes. Estimating the rest of the tasks did not go much faster and after fourteen hours of meetings, we had our full WBS estimated.

And then a funny thing happened: we executed and delivered the project on track with the new estimates about 3 months later. Why is this? A project is two years later, and then after 14 hours of meetings, we can suddenly deliver a new project pretty much right on schedule.

I attribute a big part of the reason to the fact that the second time around, the team was empowered to estimate their own effort.. Once John and the others described the work that needed to be done and said in their own words how long each task should take them, they wanted to be accountable for their own estimates and promises. That's not to say that the problem hummed along from then on; but after a contingency reserve was plotted into the schedule, the amount of time by which some tasks were underestimated balanced out with the amount of time by which other tasks were overestimated.

In my career as a project manager, I firmly believe in the value of good estimating, in getting teams to do their own estimating, and in validating and revising those estimates through the life of the project. I have been known to say on many occasions that, "Anything can be estimated."

But getting teams to come up with estimates isn't always easy. People hate estimating because it holds them accountable for their performance.

I was recently exposed to Fermi Problems. Named after Enrico Fermi, an American professor and researcher who created the world's first nuclear reaction, Fermi would often ask his students to answer ridiculous questions like, "How many piano tuners are there in Chicago?"

This is a hard number to estimate. There is not accurate count of this number. The Yellow Pages would list some piano tuners but not all of them. Some tuners are employed by universities and music conservatories and don't advertise their own services. Some companies are listed in the Yellow Pages but employ more than one piano tuner so there isn't an easy way to count them directly.

To solve a Fermi Problem, we first of all need to identify the facts of the problem that we know from the facts that we can estimate. For example, if we can "know" how many pianos there are in Chicago, how often a piano gets tuned and how long it takes to tune a piano, we can estimate how many full-time positions there would be in piano tuning. To know how many pianos there are, we could estimate that piano has an average 50 year lifespan. If we can then find how many pianos were sold in the United States over the past 50 years, we can then prorate this total number to the ratio of the American population living in Chicago. In summary:

  1. Facts we can easily know: the total population of the United States, the population of Chicago, the number of pianos sold in the past fifty years.
  2. Facts that we might need to estimate: The lifespan of an average piano, the amount of time required to tune a piano, the amount of travel time for the tuner to go to the next appointment, an assumption that all tuners work full-time.

Working out these numbers, I estimate the number to be 62 full-time piano tuners.2 So for even difficult problems, estimation is still possible. Of course, my estimate differs considerably from other on-line estimates of this same problem (Wikipedia estimates 290 tuners) but by using a Fermi Test, anyone (including members of my project team) who wants to challenge my estimate has to come up with a criticism or refinement of my method (for example, they might argue that Chicago has a much more active arts and music scene than other parts of the country and therefore has a higher concentration of pianos than the national average). But these challenges do not undermine my estimate; they only refine it.

For managers and project managers, the work involved in estimating the effort and time to complete a project's tasks will be a bonus as the entire organization will have a clearer idea of how much capacity they have to undertake their chosen projects and when those projects will be completed.


1 All names have been fictionalized to protect the innocent.

2 Crunching the numbers (I found internet sources to confirm each of my estimates but since this is just an estimation exercise and not an attempt to prove or validate the estimate, I'm not going to bother to list there here), there are about 2.8 million people in Chicago out of a national population of 318.9 million people. Roughly 0.87% of the nation lives in Chicago. Some estimates have put the total number of pianos sold each year at 90,000 - 100,000 nationwide. This means that there are likely 1 million pianos sold per decade and if we assume a lifespan of 50 years, a current inventory of 5 million pianos. 5 million pianos multiplied by 0.87% leaves about 44,000 pianos in Chicago. Websites recommend tuning a piano every six months but let's estimate pianos are tuned on average once a year (institutional pianos are likely tuned more often and many people will never tune their home pianos so this might balance out). Other websites suggest that it takes about 2 hours to tune a piano. Let's also estimate a 30 minute travel time between appointments. Assuming a 7.5 hour work day, the average piano tuner can tune 3 pianos a day. With 44,000 pianos in use, this means 44,000/3 = 14,666 person days per year to tune pianos in Chicago. Accounting for statutory holidays and vacations, the average worker works about 47 5-day weeks per year, or about 235 working days. 14,666 person days/235 days per person = 62 piano tuners working full-time in  Chicago.