Mastering Fermi Estimations

Making Informed Decisions in an Uncertain World 

Combat cognitive biases, improve decision-making, and find practical applications in various fields. 

I was working with a program that had a mid-sized annual event – a Thanksgiving run.  

There was a debate about how short to cut the grass in the field they planned to use for parking. Do they cut it short and risk damage to the field if it rains, or do they leave it long and risk people getting wet feet from the morning dew? 

The discussion that ensued was illustrative for several reasons. It is the perfect example of the trivial matters that weigh us down daily and burgle time. This isn't something that should take more than 30 seconds of our time, and it certainly did not require a meeting, especially not one with me present, but this camp allowed it. It also shows how emotionally attached we are to our jobs, that we often make decisions based on irrationality rather than a data-driven understanding. But for our purposes here, it's about identifying misinformation and training ourselves in a method for making more educated forecasts for the future. 

The facility director wanted to cut the grass short, to keep feet dry – but really it was because it looked better, and he likes cutting grass. The Executive Director was worried about a forecast of rain and didn't want cars to get stuck and the field to get dug up as they tried to free themselves, he also had more pressing maintenance tasks. His answer, which I also believe was the correct one, was to leave the grass as it is. But the Facilities director insisted we cut the grass because we get so many complaints about wet feet. 

 "How many?" I asked. "A lot." 

 "Like 10?" I inquired. 

 "No, more," he responded. 

 "A hundred?" I continued. 

 "Maybe more like 200," he replied. 

 “200 hundred complaints during a 2-hour, 1000-person event seems like a lot.”  He was insistent despite our now joint push back. 

 "So, 200 people complained, to who? To you?" I questioned. 

 "Yes," he replied. 

 Right away, I knew this was questionable because I performed a quick Fermi Estimation. 

A Fermi estimation, named after the renowned physicist Enrico Fermi, is a problem-solving technique used to make rough but reasonable estimates of quantities or values, often in situations where precise data is unavailable or impractical to obtain. Enrico Fermi was an Italian American physicist who made significant contributions to various fields of science, including nuclear physics and quantum mechanics. He was known for his ability to make quick and accurate estimations, which is why this method bears his name. 

The Fermi estimation process typically involves breaking down a complex problem into simpler, more manageable parts and making educated guesses or assumptions about the various factors involved. By making reasonable approximations and simplifications, you can arrive at a rough estimate that is often surprisingly close to the actual answer. 

 You might have heard of early Google and PayPal interviews where these types of questions were common. For example, questions like "How many piano tuners are there in New York City?" or "How much would you charge to clean all the windows in Chicago?" are common examples. 

 In this situation, I asked myself - How long would it take one person to hear 200 complaints? 

 Let's say that every person takes 30 seconds to make their complaint. It would then take the facility guy 20 seconds to respond, and then an additional 10 seconds for the complainer to thank him and move along. That would be 1 minute. And assuming that there is no gap between complainers, it would be 200 minutes (about 3 and a half hours) of complaining. 

 That seems like a very quick resolution, so let's make it more realistic and say that it took 3 minutes per person, or 900 minutes (about 15 hours) of complaints. We have a range of between 3.5 and 15 hours of complaining. Remember, this was a 2-hour event. There is no way this could be true. 

 So, the conversation was brief, and the grass stayed long. 

So, how could Fermi estimations help us at Camp? 

We often tend to overestimate the time something will take and underestimate the costs of a project due to a combination of psychological factors. One key factor is what psychologists call the Planning Fallacy. This cognitive bias causes us to be overly optimistic when assessing our abilities and the time required for tasks. We tend to focus on our best-case scenarios and past successes while overlooking potential obstacles and delays. Additionally, there's a psychological phenomenon known as optimism bias, which leads us to believe that we are less likely to encounter problems than others, leading to underestimations in costs and overconfidence in our planning. Moreover, we often fail to account for hidden or unexpected expenses due to what's called the Anchoring effect. We anchor our estimates to initial, overly optimistic figures and then struggle to adjust them upward as we gather more information. These psychological biases can significantly impact project planning and management, leading to delays and budget overruns if not recognized and addressed effectively. 

We see this all the time at Camps. All the time. Camps want to have the latest and shiniest things, especially when there is a new director who wants to have the things they've had before. "If we had this [Enter cool thing here], then we would have [enter a large number] more [normally campers or revenue]." The two most common ones I hear are new ropes courses and bigger dining halls. 

We can use Fermi estimations to get a rough approximation of the actual value of change. 

Here's a simple step-by-step guide to performing a Fermi estimation: 

1. Identify the Problem: Clearly define the problem or question you want to estimate. It could be anything from "How many piano tuners are there in New York City?"  to "What would be the ROI on a new Ropes Course or Dining Hall [Hint: they won't pay for themselves in a couple of years like you think]." 

2. Break It Down: Divide the problem into smaller, more understandable components. For example, in estimating the number of piano tuners in NYC, you might consider factors like the population of the city, the percentage of people who own pianos, how often pianos need tuning, and how many pianos a tuner can service in a day. 

For your ropes course, you would ask: How many programming days can it be used? How many hours a day can we use it? How many groups do we currently have? How many of them would be able to use the ropes course? 

3. Make Assumptions: Make reasonable assumptions about each component. These assumptions should be based on your knowledge and common sense. For instance, you might assume that approximately 1 in 100 households owns a piano and that a piano tuner can service about 5 pianos in a day. 

You currently have 50 groups a year, with an average of 25 people per group, totaling 1,875 people per year. Prehaps Sixty percent of those users are between 12 and 50 and in good health, so you have 1,125 potential users ropes course users.  

4. Perform Calculations: Calculate the intermediate results for each component based on your assumptions. In our example, you would calculate the number of piano-owning households, the frequency of tuning, and the number of tuners required. 

Let's say 16 people can use the ropes course in 2 hours. With lunch, you can have 4 groups use the ropes course in 1 day, or 64 people. The market rate is $250 per 2-hour group. 

Given that you currently have 50 programming days, that's $12,500 of revenue per year. This does not include expenses. 

5. Combine and Adjust: Combine the intermediate results to get an estimate of the final answer. Be sure to adjust your estimate if some components have a significant impact on others. 

We can now play with the numbers. Of course, you need staff on the ropes course, and to make it cost-effective, you need to fill all 64 slots. That would mean you need 3,200 users over the 50 typical programming schedule or 2,075 new program participants. 

But remember, only 60% of your users are in ropes course-using condition, so 2,075 is approximately 60% of 3,460. 

6. Express the Estimate: Present your estimate with an appropriate level of precision, often using scientific notation or a range to account for uncertainties. 

To make $12,500 per year of off-season revenue, you would need to double the number of program participants. Off-season use of your ropes course would take 10 years to see a ROI on a $125,000 course. (I just made these numbers up, so don't take it as meaning you can or can't get a ropes course.) 

 7. Check Your Estimate: Compare your Fermi estimate to any available data or known values if possible. This can help you refine your estimation skills over time. 

We can then repeat stages 4 through 7 as many times as you need to refine your estimate, adding expenses, and other variables like the cost.  But you now have a close estimate, if we keep our numbers at their current level, we will see a $X increase in revenue, if we double our current numbers #a to #b, we could see a $Y increase in revenue.  Now you can make a more educated decision does not build, but as to whether it's even worth presuming the opportunity and doing more detailed due diligence. 

Fermi estimations are useful in a wide range of fields, from science and engineering to camp, and everyday problem-solving, as they encourage creative thinking and the development of intuition for making reasonable approximations quickly when exact information is lacking. 

TL: DR 

Prioritize Open and Data-Driven Decision-Making: Foster a culture of openness and rely on data and evidence to guide our choices, facilitating continuous improvement and achieving success.