A simple reaction-time test asks one question: how fast can your finger move when the light turns on? A choice reaction-time test asks a harder one. There are several lights, and each one demands a different finger. Now your brain has to decide before it can act, and the decision is not free. The cost of that decision, measured in milliseconds, is the subject of one of the oldest quantitative laws in psychology.
Choice reaction time (CRT) is the time from stimulus onset to a correct response when multiple stimulus-response mappings exist. Where simple reaction time isolates detection plus motor execution, CRT layers a decision stage on top: identify which stimulus appeared, retrieve the right response, and execute it. Doing that work takes time — and the more alternatives there are, the more time it takes.
The Decision Tax: Simple RT vs Choice RT
Healthy adults, tested on good hardware, produce simple visual reaction times around 220 to 250 ms. The same people, tested on a two-choice version of the same task — two possible stimuli, two possible keys — typically land between 370 and 450 ms. The gap of roughly 130 to 200 ms is the decision tax: the extra cognitive work of identification and selection, layered on top of the sensory and motor minimum.
That gap is not arbitrary. It grows in a predictable way as you add more alternatives, and the shape of the growth has been replicated thousands of times since the early 1950s.
Hick's Law
In 1952, the British psychologist W. E. Hick asked participants to respond to one of n equally likely lights with one of n keys. He found that reaction time increased linearly with the logarithm of the number of alternatives. Ray Hyman, working independently in 1953, showed that the same relationship held when alternatives were unequally probable, with each stimulus weighted by its information content. Together their results are called Hick's Law or the Hick-Hyman Law:
RT = a + b · log₂(n + 1)
Here a is the intercept — sensory plus motor latency, the floor that does not depend on the number of choices. The slope b captures how much each extra bit of information costs, typically around 100 to 150 ms per bit for novice participants. The argument log₂(n + 1), rather than log₂(n), is Hick's correction for guesswork: even with one stimulus, the participant briefly considers "no stimulus" as a possibility.
A worked example with a typical slope of b = 150 ms per bit and a = 220 ms:
| n (choices) | log₂(n + 1) (bits) | Predicted RT | Decision cost vs simple RT |
|---|---|---|---|
| 1 | 1.00 | 370 ms | +150 ms |
| 2 | 1.58 | 458 ms | +238 ms |
| 4 | 2.32 | 568 ms | +348 ms |
| 8 | 3.17 | 696 ms | +476 ms |
Notice how doubling the number of options does not double the reaction time — it adds a roughly constant 150 ms each time, because each doubling adds one bit of information. That logarithmic scaling is the headline result.
Why Logarithmic? An Information-Theoretic Answer
The log₂ in the formula is not a curve-fitting accident. It comes directly from Claude Shannon's information theory, which Hick read in draft before designing his experiments. A binary distinction — "left or right?" — carries exactly one bit of information. Choosing between four equally likely options is two binary distinctions stacked on top of each other, two bits. Eight options, three bits.
Hick's empirical finding is that the brain takes a roughly fixed amount of time per binary distinction, regardless of how those distinctions are packaged. Four options do not feel like four times the work of one option; they feel like two extra yes/no questions, and the timing of the response reflects exactly that.
When Hick's Law Breaks
The law is beautiful, but it has well-known boundary conditions. It applies cleanly when three conditions hold: alternatives are equiprobable, perceptually discriminable, and not deeply over-practiced. Violate any one of those and the formula bends.
Highly Practiced Mappings
Touch typists do not slow down logarithmically as they hit more keys. After enough practice on a fixed stimulus-response mapping, the dependence on log₂(n) flattens dramatically — the slope b approaches zero. The response stops being a deliberate choice and becomes a retrieved association. This is why expert gamers can react to one of a dozen visual cues almost as fast as to one — for their practiced map, the decision stage is nearly free.
Stimulus-Response Compatibility
Even before practice flattens the slope, the intercept depends strongly on how naturally the stimulus maps to the response. A left light controlling a left key is faster than the same left light controlling a right key, even though the information content is identical. The compatible version trims roughly 50 to 100 ms from CRT. Paul Fitts and his colleagues mapped this systematically in the late 1950s, and the lesson — match the spatial geometry of stimuli to responses — became a cornerstone of human-factors design.
The Stroop Wrinkle
Hick's Law assumes that the only competition between responses is the one the experimenter designed. The Stroop task adds a second, uninvited competition. Show the word "RED" printed in green ink and ask the participant to name the ink color. The correct answer is "green", but the highly automatic process of reading shouts "red". The two response candidates race, and the loser tax shows up as a 100 to 200 ms slowdown plus a sharp rise in errors.
The Stroop effect is not a violation of Hick's Law so much as a reminder of what Hick's Law does not cover: it measures the cost of selecting among intended alternatives, not the cost of suppressing an unintended one. The Stroop wrinkle is closer in spirit to a Go/No-Go task than to a choice task — the bottleneck is inhibition of an automatic response, not the information-theoretic selection of one option from many.
Speed and Accuracy: The Drift-Diffusion Intuition
Modern accounts of choice reaction time go beyond Hick's average-RT formula and model the full distribution of responses, both correct and incorrect, using the drift-diffusion model. The idea is that evidence for each response accumulates noisily over time, and the brain commits to a response when accumulated evidence reaches a fixed threshold.
Two parameters dominate. The drift rate describes how quickly evidence accumulates — high for an easy discrimination, low for a hard one. The threshold describes how much evidence the brain demands before committing — high if you want to be sure, low if you want to be fast. Pushing the threshold down makes responses faster but increases the error rate in a lawful way. This is why telling someone to "go faster" predictably hurts accuracy: they are not just hurrying, they are committing on weaker evidence.
Choice Reaction Time Norms by Age
The same age curve that affects simple reaction time also affects choice reaction time, but more steeply — the decision stage is more sensitive to aging than the sensory-motor floor. Rough averages on a four-choice task, with the usual caveat that hardware adds 30 to 50 ms on browser-based tests:
| Age band | Typical CRT (4-choice) | Comment |
|---|---|---|
| Teens, 20s | ~370 ms | Peak; sharpest decision stage |
| 30s | ~395 ms | Slight slowing, mostly motor |
| 40s | ~410 ms | Decision stage starts to lengthen |
| 50s | ~430 ms | Both stages slower; variability up |
| 60s | ~460 ms | Slope b notably steeper than at 20 |
These numbers are population averages for healthy adults under standard test conditions. For a broader breakdown by age and a discussion of variance within bands, see our piece on the average reaction time by age.
Esports, Sprints, and the Real World
Professional Counter-Strike and Valorant players regularly hit choice reaction times under 300 ms on in-game tasks — flick to an enemy peeking from one of several known angles, pick the correct weapon for the situation. The reason they outrun the textbook curve is the same reason touch typists do: extensive practice has collapsed the decision component, leaving mostly sensory plus motor latency.
Formula 1 uses an explicit choice-reaction setup at the start of each race. Five red lights illuminate in sequence; when all five extinguish at a random interval, drivers launch. The randomization defeats anticipation — drivers cannot rehearse a launch keyed to a known delay. Sub-200 ms launches at this level are sometimes flagged for review precisely because they are close to the floor of what a human can plausibly produce reactively rather than by guessing.
UX Implications, and What Hick's Law Doesn't Say
"Fewer options means faster decisions" gets cited in UX design constantly, often with Hick's Law as the justification. The general direction is right, but the specific formula does not carry over cleanly. Real menus are not equiprobable; you click "Settings" much less often than "Search". Real labels are not perfectly discriminable; users have to read and parse, not just recognize. And in many interfaces the user is browsing, not picking from a known set — the choice is part of the task, not a preliminary to it.
The useful core of Hick's Law for UX is that adding alternatives has a real cognitive cost, not that the cost is exactly b · log₂(n + 1). Categorization, grouping, defaults, and progressive disclosure all work by reducing the effective number of options at any one decision point — and that, rather than the precise slope, is what makes them effective.
Can You Train Choice Reaction Time?
Yes, but with caveats. Practice on a fixed stimulus-response mapping reliably lowers the slope b, sometimes nearly to zero, by converting deliberate decision into automatic retrieval. What practice does not do is lower the intercept a, which is set by sensory and motor latencies. For a measurement to be meaningful, repeat the same task on the same hardware on different days — the measurement methodology piece covers the hardware and procedural details that swing browser-based scores by tens of milliseconds.
To run your own choice-reaction sessions and watch your slope come down with practice, try the Choice Reaction Test. It records both average reaction time and accuracy across trials so you can see how your speed-accuracy tradeoff shifts over time.