# Improving Back-of-the-Envelope Calculations By:: [[Brian Heath]] 2022-09-14 Back-of-the-envelope calculations are a common exercise in business. The hallmark of these models is many assumptions with single value estimates that all lead to one key metric. Often these single value estimates are called point estimates because they only capture what a value might be versus a range of possibilities. For example, is the average age of customers 35 or somewhere between 30 and 40? These types of calculations exist because data is missing, time is short, and/or the system isn't well understood. However, despite shortcomings, these types of calculations can also be insightful in identifying the core dynamics of the system. To capture these [[insights]], the analyst must identify which factors have the greatest impact on the final metric. This means challenging the assumptions and transforming the point estimates into range estimates. Using a range estimate for each assumption introduces uncertainty into the model, which immediately positions the model into a new realm of consideration. Instead of one value, we see a range of possible outcomes. When we see a range of possible outcomes we will immediately ask ourselves what causes that range to exist. This pivot switches our mindset from what the model says to how the model behaves. [[Understanding]] behavior is the first step toward attempting to predict and control future outcomes. There are easy and hard ways to transform a point estimate in a calculation into a range estimate. Easy ways typically use some software to automatically generate random values for each range estimate, calculate the outputs, and compile the distribution of outcomes many times over. Look for [[tools]] that do Monte Carlo Simulation, Sensitivity Analysis, or Risk Analysis and there are many options available including [[The Spreadsheet Language|spreadsheet]] plug-ins. The harder way is to do it yourself, one random draw (pick a number on the range) and one calculation at a time. However, both approaches will both generate the desired transformation. Selecting the distribution of the range estimate can be challenging, but that is for another day. For now, just assume the distribution is uniform from the minimum value to the maximum. Once you have generated a whole range of results, the next step is to figure out which assumptions are critical. Many times assumptions will seem important but have little impact on the final results. For example, the price of diapers may seem like an important factor in revenue for a grocery store but it may be the price of milk that is the most important. When the outcome does not change when one assumption changes a lot, this outcome is said to be insensitive to that assumption. So, when you find one of these assumptions, do not worry about validating that assumption. Instead, focus on validating the assumptions that have the most impact on the outcome. This is the best use of your limited time and resources. Taking a simple back-of-the-envelope calculation and transforming it into something meaningful and believable is a classic and effective way for an analyst to win over decision-makers. It starts with their rough calculation that they already believe in and transforms into something greater. #### Related Items [[Analytics]] [[Business]] [[Statistics]] [[Monte Carlo Simulation]] [[Sensitivity Analysis]] [[Risk Analysis]] [[Decision-making]] [[Models]]