Inventory entropy: measuring variety in your store

Every retailer has an instinct about their own assortment. Some feel too concentrated in a handful of references; others feel they have spread capital across variety that does not move. The trouble with instinct is that it does not go in a report, and you cannot compare one store against another with it.

There is a measure borrowed from information theory that handles this well: entropy.

What entropy measures

Entropy measures how spread out a distribution is. Applied to inventory, it answers a simple question: how concentrated are your sales across a few products?

Low entropy means concentration. A few references account for nearly all sales.
High entropy means dispersion. Sales are spread across many references.

Neither is good or bad on its own. What matters is whether the number sits where it should for your kind of operation.

How to calculate it

For each product i, take the fraction p it represents of total sales for the period. Entropy is:

H = -Σ (pᵢ × log₂ pᵢ)

A store selling 100 units split evenly across 8 references has exactly 3 bits of entropy. That same store, if 95 of those units come from a single reference, drops below 0.5 bits.

Why it earns its place

The number itself matters less than its movement.

Entropy falling month over month usually means assortment is shrinking in practice, even if the catalogue still looks full. It is normally stockouts: tail items ran out and were not replenished, so sales concentrated on what was left.

Entropy rising without revenue growth usually means fragmentation. New variety came in and split the same sales, which raises trapped capital and complicates operations without adding revenue.

Entropy differing sharply between stores in the same chain is the most actionable signal of all. If two locations with similar customers show distant entropy, there is almost always a stock imbalance between them — and a transfer fixes it more cheaply than a purchase order.

One caveat

Entropy does not replace ABC analysis or margin review. It does not know what is profitable; it only knows how sales distribute. Use it as an assortment thermometer alongside the indicators you already track, not instead of them.