The Foundations of Hick's Law

A forgotten equation that decides your conversions

In 1952, British psychologist William Edmund Hick, working with Ray Hyman, published an experiment that would remain unknown outside of cognitive psychology labs for decades. The two researchers measured, to the millisecond, how long it takes a subject to react when presented with a growing number of light options on a panel. The result was as simple as it was implacable:

The time a human needs to make a decision grows logarithmically with the number of options presented.

This is Hick-Hyman's Law, more commonly known as Hick's Law. It is written as:

T = b · log₂(n + 1)

Where:

• T is the average decision time (in seconds)
• n is the number of options presented
• b is a constant specific to each individual (typically between 0.1 and 0.2 second)

This equation, later embedded by the pioneers of software ergonomics (Card, Moran, Newell, 1983 — The Psychology of Human-Computer Interaction), has become one of the hidden pillars of every interface design, every offer architecture and — as we will see — every serious conversion strategy.

The original experiment: a lab and ten light bulbs

Hick sat his subjects in front of a panel with ten light bulbs, each linked to a key. On every trial he turned on a given number of bulbs, then made just one of them flash brightly. The subject had to press the matching key.

Hick varied the number of active bulbs:

The time does not double when you double the options. It grows by a near-constant increment every time the option count doubles. That is the logarithmic signature.

Hyman replicated the experiment in 1953 with other sensory modalities (sounds, colors) and confirmed the law's robustness.

Why a logarithm and not a linear function?

Intuitively, one would think that scanning 8 options takes 8 times more time than scanning one. The brain does not, however, do a naive sequential sweep. It runs a dichotomous elimination — much like a binary search in algorithmics.

Picture this: faced with 8 products, your brain mentally splits them into two groups of 4, eliminates one group, then splits the remaining 4 into groups of 2, and so on. At each step it halves the decision space. Hence the base-2 logarithm.

graph TD
    A[8 options] --> B[4 options kept]
    A --> C[4 options eliminated]
    B --> D[2 options kept]
    B --> E[2 options eliminated]
    D --> F[Final decision]

This is elegant — but it assumes options are comparable and clearly differentiated. If they are not (for example 8 nearly identical mobile plans), the law breaks down and decision time explodes. We call that saturated Hick effect, the prelude to decision paralysis.

The constant b: expertise changes everything

The constant b depends on the decision-maker's expertise. A seasoned developer navigates their IDE with a very low b (automatic shortcuts, stable mental hierarchy). A beginner facing the same IDE has a b three to ten times higher.

Business implications:

• Technical B2B: your buyer has a low b on tools they know, a high b on what they are discovering. Hence the importance of using their vocabulary.
• Mainstream B2C: b is high on average. Every bit of friction is costly.
• Onboarding: a new user's b peaks during the first 5 minutes. That is precisely the moment when no complex choice should be required.

The scientific limits of the law

Hick's Law is not magical. Several limits frame its application:

1. It assumes homogeneous option complexity

If a single option in the set is markedly more complex (e.g., "custom plan"), it acts as an attention sink and distorts the average.

2. It assumes a conscious, deliberate choice

For habitual or impulsive choices (impulse buying at the till), the law does not apply. The amygdala and orbitofrontal cortex decide — not the slow prefrontal cortex.

3. It does not account for decision quality

Shortening decision time does not mechanically improve post-purchase satisfaction. In some cases the opposite happens — a topic we tackle in chapter 4.

4. The saturation threshold (≈ 7 options)

Past 7 to 9 simultaneous options, working memory (Miller, 1956 — The Magical Number Seven) saturates. Decision time detaches from the logarithmic model and the user simply gives up.

Why this law is worth gold today

Hick's Law was born in a psychology lab — but it has become central to the attention economy:

These are recurring numbers in optimization studies (Baymard Institute, ConversionXL, Nielsen Norman Group). Hick's Law is the law of conversion.

The trap of perceived abundance

Beginner entrepreneurs think that offering "more choice" is generous. It is almost always a mistake. Sheena Iyengar (2000) demonstrated this with her famous jam experiment:

• Stand with 24 jams: 60% of passers-by stopped, 3% bought.
• Stand with 6 jams: 40% of passers-by stopped, 30% bought.

Dividing the choice by 4 multiplied sales by 10. Hick's Law gives the cognitive mechanism behind that effect: too many options blow up T, and beyond a threshold the user cancels the decision altogether.

What you will learn

This course will turn Hick's Law into a concrete business lever:

Summary

Hick's Law (Hick-Hyman, 1952) states that human decision time grows logarithmically with the number of options. It rests on a dichotomous-elimination mechanism specific to the prefrontal cortex, saturates past 7 to 9 options, and provides the quantitative skeleton behind the big laws of conversion. Understanding this law means stopping believing that offering "more" is generous, and starting to design journeys where every extra option must earn its place. The next chapter dives into the underlying psychological mechanisms: cognitive load, decision fatigue and analysis paralysis.