I first read The Flaw of Averages by Sam Savage about 15 years ago, back when I worked in the finance industry. I don’t remember every chapter, but I do remember the central idea—and it has shaped how I think about estimates and projections ever since.
The short version: using “average” inputs to produce a single “expected” output is a great way to feel confident and still be wrong.
The flaw isn’t that averages are “bad.” It’s that an average by itself doesn’t communicate uncertainty. It tells you nothing about how wide the range is, how lopsided the outcomes might be, or how often you’ll land in the uncomfortable tail.
One of the book’s most practical recommendations is to use Monte Carlo simulation to turn uncertain inputs into a histogram. That histogram is the whole point: it makes the possibility space visible, and it gives you an immediate visual read on what looks likely versus what’s merely possible.
Below is a simple Monte Carlo simulator for estimating cloud infrastructure costs.
The Problem with Averages
When planning a startup or a new project, cloud cost estimates often end up as a single number produced by one of these approaches:
- “Average customers” × “average usage” × unit price
- A best-case / expected / worst-case trio, followed by “expected” being treated as the plan
- Last month’s bill plus a growth factor (sometimes optimistic, sometimes panic-driven)
- A spreadsheet with a handful of line items and no model for variability
Those can look reassuringly precise and still go horribly wrong. A small miss on two or three assumptions can stack up, and the surprise usually shows up at the worst possible time (right when you’re scaling, hiring, or committing to a roadmap).
The problem is that this style of estimating quietly assumes the world is linear and well-behaved. In practice, costs often have thresholds, step functions, and nonlinearities (tier changes, headroom requirements, on-call coverage, scaling inflection points). On top of that, your inputs aren’t known—they’re guesses with uncertainty.
So the question isn’t “what’s the cost for the average customer?” It’s “what costs are plausible, and how bad can it get if a few assumptions break in the same direction?”
Monte Carlo simulation helps by running thousands of scenarios, each with randomized values drawn from your estimated ranges, and then plotting the results as a histogram. Instead of a single number, you get a visual map of the possibility space—including which outcomes cluster as “likely” and which live out in the tail.
Cloud Cost Estimation Example
Let's model the monthly cost of a cloud-based startup. We'll consider three main cost drivers:
- Customers: How many active users will we have?
- Stored Data per Customer (GB-month): How much data will you keep per customer?
- Requests per Customer: How many API requests will each customer make?
To keep this concrete and readable, we’re going to use a deliberately simplified model. Real cloud bills have a lot more knobs (tiers, free grants, regional pricing, reservations/commitments, data transfer nuances, and service-specific oddities). The goal here isn’t billing accuracy; it’s to show how uncertainty turns into a range of outcomes.
With that in mind, we'll make a few explicit assumptions:
- Pricing varies: We'll treat unit pricing as inputs so you can explore sensitivity.
- Not all stored data is transferred: We'll model egress as a fraction of stored data each month (for example, if 20% of stored data is downloaded/served externally).
For each variable, you provide a low and high estimate. The simulation then:
- Runs 10,000 iterations (you can often get a decent picture with as few as 1,000)
- For each iteration, picks random values for each variable within your ranges (uniformly, for simplicity)
- Calculates the total cost for that combination
- Builds a histogram showing the distribution of possible costs
Try adjusting the values below to see how uncertainty in your inputs changes the projected range of outcomes.
What the Results Tell You
After running the simulation, look at the histogram. The shape reveals important insights:
- Peak: The most likely outcome (the mode of the distribution)
- Spread: How much uncertainty there is in your estimate
- Tail: Worst-case scenarios that might require contingency planning
The statistics panel shows percentiles, which are especially useful for planning:
- 50th percentile (median): Half of scenarios cost more, half cost less
- 90th percentile: Only 10% of scenarios cost more than this (useful for conservative budgeting)
Beyond Cloud Costs
This technique isn't limited to cloud costs. You can use Monte Carlo simulation for:
- Project timeline estimation: Account for uncertainty in each task's duration
- Sales forecasting: Model variability in conversion rates and deal sizes
- Capacity planning: Understand the range of infrastructure needs
- Risk assessment: Quantify the probability of different outcomes
The key insight from "The Flaw of Averages" is that uncertainty compounds. When you have multiple uncertain variables, the range of possible outcomes is wider than you might think. Monte Carlo simulation makes this uncertainty visible and quantifiable.
Try It Yourself
Go back to the simulator above and experiment with different scenarios:
- Conservative estimate: Set narrow ranges (low and high close together) to see minimal uncertainty
- Wide uncertainty: Set wide ranges to see how uncertainty compounds across variables
- Extreme scenarios: Set very high or low values to understand edge cases
The beauty of Monte Carlo simulation is that it nudges you toward probabilistic thinking. It shifts the conversation from “what will it cost?” to “what range of costs is plausible, and how much risk are we taking on?”
This is the part that stuck with me from that first read in finance. Every forecast carries an implied risk tolerance, even if nobody says it out loud. A single point estimate tends to hide it. Percentiles force it into the open.
If you need a single number for a spreadsheet or a budget, pick it on purpose (for example, P50 for “most likely” or P90 when missing budget is expensive), and be clear about what it means.
One of the biggest challenges with this approach isn’t the math—it’s the conversation. Leadership and stakeholders often want a single “average” projection (date, cost, headcount, revenue) because it feels decisive and easy to plan around. But the real world is rarely that predictable. The sooner you can get comfortable discussing ranges and probabilities, the fewer “surprises” you’ll have later.