> ## Documentation Index
> Fetch the complete documentation index at: https://docs.meerietechnology.com/llms.txt
> Use this file to discover all available pages before exploring further.

# Why ranges, not single numbers

> The future is uncertain. A single number hides the risk, and plans built on averages are usually wrong.

Nobody knows what will happen next year. Demand, costs, delays and prices are all uncertain. A single number such as "\$2M return" or "1,000 customers" pretends otherwise. It looks precise, but it only hides how unsure everyone is.

Meerie asks for an **honest range** instead, for example "somewhere between $1M and $3M, most likely \$1.8M".

## A single number hides the risk

Two options can have the same average and very different risk:

* **Option A:** between $1.8M and $2.2M. You will almost certainly get about \$2M.
* **Option B:** between a $1M loss and a $5M gain. It also averages about \$2M, but you could lose money.

On a slide, both read "\$2M". Only the range shows that B can lose money. If you decide on the average alone, you cannot tell them apart.

## The flaw of averages

The average of the inputs is **not** the average of the outcome. Plans built on average inputs are usually wrong, and often wrong in the same direction.

> [accordion] A worked example
>
> A shop can serve at most **1,000 customers** a month. Each sale earns \$10, and fixed costs are \$6,000 a month.
>
> Demand is uncertain. Say next month it is equally likely to be **600** or **1,400**. The average is exactly 1,000.
>
> **The plan built on the average:** 1,000 customers × \$10 − \$6,000 = \$4,000 profit.
>
> **What can actually happen:**
>
> | Demand | Customers served | Profit |
> | - | - | - |
> | 600 | 600 | 600 × \$10 − \$6,000 = \$0 |
> | 1,400 | 1,000 (capacity is full) | 1,000 × \$10 − \$6,000 = \$4,000 |
>
> The real average profit is (\$0 + \$4,000) ÷ 2 = \$2,000, half of what the plan promised, and half of the time you make nothing.
>
> The good months cannot make up for the bad ones, because capacity caps the upside while the downside is open. Whenever something caps, floors or multiplies your numbers, such as capacity, deadlines, budgets, or a price times a volume, the average of the inputs gives the wrong answer.

Meerie avoids the flaw by never calculating with the averages. It plays out thousands of possible futures, each with its own values, and then looks at the whole spread of results. See [Monte Carlo simulation](https://docs.meerietechnology.com/simulate/monte-carlo.md).

## What a range shows that a number hides

* **How bad it could get.** The low end of the range is the risk you are accepting.
* **How good it could get.** The high end is the upside you may be giving up if you play safe.
* **Which numbers matter.** A wide range on an input that drives the result is where more research pays off. See [Sensitivity and value of information](https://docs.meerietechnology.com/revise/sensitivity-voi.md).
* **Where people disagree.** Two experts who both say "about 10" may mean "8 to 12" and "2 to 40". Ranges make that visible.

## P10, P50, P90

A range is described by three points called **percentiles**:

| Name | Meaning |
| - | - |
| **P10** | A 1 in 10 chance the true value is below this |
| **P50** | The middle: half the time the true value is below, half above (the median) |
| **P90** | A 1 in 10 chance the true value is above this |

So P10 to P90 is the **likely range**: about 8 times in 10 the true value lands inside it. Values outside it are still possible, just less likely.

## The mistake to avoid: overconfidence

People nearly always set ranges too narrow. They anchor on a best guess and add a little either side. A well-calibrated range feels uncomfortably wide.

A quick test: **would you be surprised if the true value fell outside your range?** If not, the range is probably too narrow. If you would be shocked, it is probably about right.

> [!TIP]
>
> Write the low end first. Then ask "what would have to be true for it to be even lower?" before writing the middle and high values.

Too wide is a mistake too: if every range is huge, all options look the same and nothing can be decided. Use [Calibration & Training](https://docs.meerietechnology.com/advanced/calibration-specialist.md) to see how your own ranges have performed.

## Two kinds of uncertainty

* **What we do not know yet**, such as the true average effect of a new tool. Research can reduce this.
* **What will vary anyway**, such as how a particular year turns out even if we knew the average perfectly. No research can remove this.

Meerie keeps these apart so it never overstates what research is worth.

**Next:** [Choosing how to describe an estimate](https://docs.meerietechnology.com/estimate/describe-estimates.md)


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