Hick’s law: the most misquoted number in interface design

What it is

W. E. Hick published “On the rate of gain of information” in the Quarterly Journal of Experimental Psychology in 1952. He applied Claude Shannon’s information theory to choice reaction tasks and found that the time to respond rose approximately in proportion to the logarithm of the number of stimulus–response alternatives. Ray Hyman reached a compatible result in the Journal of Experimental Psychology the following year, and — importantly — got there by varying uncertainty three different ways: the number of equally probable alternatives, how often one alternative occurred relative to the others, and how predictable each stimulus was from the one before it. Reaction time tracked the information content in bits, not the raw count of options. The pairing is why the result is properly the Hick–Hyman law.

The experimental situation was deliberately minimal. A small set of stimuli, each mapped to a response the participant had already learned, all alternatives equally likely, and a participant whose only job was to respond. There is no reading, no searching, no scrolling, no deciding which option is the one they actually want. The law describes the cost of resolving uncertainty among known alternatives, and nothing else.

Robert Proctor and Darryl Schneider reviewed the law’s first sixty-five years in the Quarterly Journal of Experimental Psychology in 2018. They document that it is real and durable, and also that it comes with conditions. The slope varies substantially with stimulus–response compatibility. Extensive practice flattens it: in one study they cite, an eight-choice task was close to 500 ms slower than a two-choice task in the first session and a little over 300 ms slower by the fifth. And because the standard method uses one finger per alternative, the law has been studied predominantly between two and ten alternatives; the handful of studies that went further produced mixed results.

That last point deserves to be sat with, because it is the one designers skip. Hick’s law was established on a range of roughly two to ten options. A country dropdown has about two hundred. Nothing in the original work licenses the extrapolation, and the studies that have tried it do not agree.

The level in this game is what a long list feels like when every other cost is turned up to maximum. It is a country selector containing several hundred entries: invented countries, and then a dense cluster of near-miss spellings of the target — “United Sates”, “Untied States”, “United Steaks” — sorted alphabetically so the decoys sit directly around the real entry. It opens scrolled to a random position, and it closes itself after two seconds of inactivity. None of that is choice reaction time. All of it is what actually costs the user their afternoon.

Why it works on people

The logarithm is the whole story, and it is the part that gets dropped. Logarithmic growth means each doubling of the option count adds a constant increment, not a proportional one. Going from 4 options to 8 costs the same additional time as going from 8 to 16, or from 100 to 200. A list ten times longer is not ten times slower to choose from.

This has a consequence that runs directly against the usual design advice. Suppose you split a list of n items into a two-step hierarchy with roughly √n items at each step. Under a strictly logarithmic law the total is log√n + log√n, which is exactly log n — the same as choosing once from the whole list. Wanyu Liu and colleagues made this argument at CHI 2020: Hick’s law “speaks against, not for, the popular principle that ‘less is better’”. Splitting is break-even by the law’s own arithmetic. Any real benefit from a hierarchy has to come from somewhere other than Hick’s law.

It does come from somewhere else, which is why hierarchies are not useless. Real selection involves processes that grow faster than logarithmically — you have to find the item, not merely choose it. Liu and colleagues make exactly this point: many things produce a logarithmic curve, including visual search in a hierarchical menu, and observing a logarithmic relationship in your data is not evidence that Hick’s law caused it. They call the conflation of the formula with the law an unfortunate one.

Thomas Landauer and Dennis Nachbar had shown the practical version at CHI in 1985, testing touch-screen menu trees and finding that broad, shallow structures beat narrow, deep ones. The finding is robust and widely replicated, and it is usually credited to Hick’s law. It is better explained by counting what a deep hierarchy actually costs: more screens, more pointing movements, more opportunities to take a wrong branch and have to come back.

So when a two-hundred-item list is genuinely painful — and it is — the costs to attack are visual search through a list where the target is not visually distinct, the motor cost of scrolling and pointing, the memory cost of holding your intent while you hunt, and the recovery cost when the list closes and dumps you back at the start. Trimming the option count addresses the smallest term in that sum.

There is a real, separate reason to reduce options, and it is worth keeping distinct: a person who does not yet know which option they want is not performing a choice reaction task at all. They are deliberating, and deliberation is genuinely expensive and genuinely sensitive to how many things must be compared. That is an argument about decision-making under uncertainty. It is a good argument. It is not Hick’s law, and citing Hick for it borrows an authority the law does not confer.

Where you meet it

• Country, currency, timezone and language selectors, where the list is long, fixed, and known in advance to be dominated by a handful of values.
• A search or filter field inside a long list that matches on substring anywhere in the entry, so typing three characters returns a hundred rows and the target is not among the first ten.
• Menus that close on blur, on a timer, or on an incidental scroll, discarding the position the user had painstakingly reached.
• Long lists that open scrolled to the top, or to a remembered position, rather than to the current value or the most probable one.
• Navigation reorganised into a deep hierarchy on the stated grounds of “reducing cognitive load”, where every previously one-click destination now takes three.
• Settings screens split into so many categories that finding the right category is harder than scanning the original flat list would have been.
• Option sets padded with near-duplicates that differ in ways the interface never explains, forcing a comparison the user is not equipped to make.
• Autocomplete that ranks by string similarity rather than by likelihood, so the most common answer sits below six things nobody has ever picked.

Designing around it

• Stop citing Hick’s law to justify hierarchy. Under a logarithmic law, splitting a set is break-even. If a hierarchy helps your users, it helps for reasons you can name and measure — shorter visual search, better grouping, fewer irrelevant items on screen — and naming them will lead you to better decisions than invoking a law that does not predict the benefit.
• Optimise for search and pointing, because that is where the time goes. Make entries visually scannable, keep row heights and hit targets generous, and never make the user scroll through a region where every row looks identical.
• Weight by probability rather than treating options as equally likely. Hyman’s result was that response time tracks information content, and an option the user takes eighty per cent of the time carries very little. Put the likely values first, remember the last choice, pre-select the best guess — and make the guess easy to override, which is the line between a helpful default and the kind covered on the pre-selected defaults page.
• Make typing work the way people expect. Match on prefix before substring, rank exact matches above partial ones, tolerate diacritics and common misspellings, and never let a near-miss entry outrank the exact one.
• Never close a long list on a timer or an incidental blur. Discarding a user’s scroll position destroys work that cost real effort, and no amount of option-trimming compensates for making someone start over.
• Open the list at a useful position — the current value, or the most likely one — rather than at the top or somewhere arbitrary. Where the user is starting from determines how much searching is left.
• Reduce options when the reason is deliberation, not reaction. If your users genuinely do not know which one they want, fewer and better-differentiated options help enormously. Say that is the reason. It is a stronger argument than a misapplied law, and it points at the real fix, which is usually better labels rather than fewer items.
• Measure end-to-end task time on the real list, not choice time on a toy one. The difference between a good and a bad two-hundred-item selector is measured in tens of seconds and shows up immediately in a task-completion test; the Hick term is tens of milliseconds and will never be the thing you observe.

Questions

What is Hick’s law?

Hick’s law states that the time taken to choose among equally likely alternatives increases approximately with the base-2 logarithm of the number of alternatives. W. E. Hick published it in 1952 and Ray Hyman produced the companion result in 1953, showing that reaction time tracks the information content of the choice in bits rather than the raw number of options.

Does Hick’s law mean I should give users fewer choices?

Not by itself, and arguably the opposite. Because the relationship is logarithmic, splitting a list of n items into two steps of about √n each costs log√n twice — which equals log n, the cost of the single undivided choice. Liu and colleagues put it directly at CHI 2020: Hick’s law speaks against, not for, the principle that less is better. Any real benefit from splitting comes from processes other than choice reaction time.

Then why do long dropdowns feel so slow?

Because almost none of the cost is choice reaction time. It is visual search through rows that look alike, the motor cost of scrolling and pointing, holding your intent in memory while you hunt, and starting over when the list closes or the filter misfires. Those are the terms worth attacking; the Hick term is tens of milliseconds and is the smallest number in the sum.

Does Hick’s law apply to a list of 200 countries?

There is no good evidence that it does. The standard method assigns one finger per alternative, so the law has been investigated predominantly between two and ten options, and the few studies using much larger sets have produced mixed results. Extrapolating a curve fitted over eight options to a list of two hundred is an assumption, not a finding.

Is there ever a good reason to reduce the number of options?

Yes, but it is a different argument. Hick’s law describes choosing among alternatives you already know how to respond to. A user who does not yet know which option they want is deliberating, and deliberation is genuinely expensive and genuinely sensitive to how many things must be compared. Reduce options for that reason, name that reason, and you will usually find the real fix is clearer labels rather than a shorter list.

Related patterns

• Pre-selected defaults: when the form has already answered for you
• Placeholder text as a label: what breaks and what to do instead
• Signifiers: an affordance nobody can see is not a feature