Choice reaction-time model
Hick-Hyman Law
Choice reaction time often increases approximately linearly with the information uncertainty of the alternatives, not simply with their raw count.
RT = a + b H; H = log2(n)
For n equally likely stimulus-response alternatives, uncertainty H is log2(n) bits. The intercept a and slope b are estimated for a task, device, population, and speed-accuracy regime.
Illustrative parameters are a = 250 ms and b = 120 ms/bit. Real values depend on stimulus quality, response compatibility, practice, errors, and the distinction between searching, deciding, and acting.
(ms)
- CHANGE
- Equally likely alternatives
- WATCH
- reaction time
- MEANING
- Illustrative parameters are a = 250 ms and b = 120 ms/bit. Real values depend on stimulus quality, response compatibility, practice, errors, and the distinction between searching, deciding, and acting.
Choices grow fast; information grows slowly.
Doubling equally likely alternatives adds one bit and roughly one slope increment to reaction time. Grouping and unequal probability change the effective uncertainty.
What it actually says
Hick and Hyman connected choice reaction time to Shannon information. When alternatives are equally likely, moving from 2 to 4 choices adds the same information as moving from 4 to 8: one bit. Reaction time therefore grows roughly with the logarithm of count rather than in direct proportion to count.
Hyman's contribution makes probability central. For unequal alternatives, entropy H = -sum p_i log2 p_i can predict performance better than count because practiced, expected responses carry less surprise than rare ones.
"A useful law compresses a pattern. It does not erase the conditions that make the pattern true."
How the idea developed
The modern form emerged through observation, argument, and later refinement. The timeline separates the first insight from the version now used in textbooks and practice.[1]
Claude Shannon formalizes information entropy and communication uncertainty.
W. E. Hick publishes experiments on the rate of gain of information.
Ray Hyman manipulates stimulus probabilities and links reaction time to transmitted information.
Human factors, neuroscience, and interaction design test when uncertainty predicts response time and when search or motor costs dominate.
How the pattern works
The relation becomes useful only when its mechanism, measurement process, and operating range are visible.
More equiprobable alternatives increase the information needed to identify the correct response.
Expected alternatives become faster, so entropy matters in addition to raw set size.
Compatible and practiced mappings reduce processing demands and change the fitted slope.
Faster responding can increase errors; reaction-time comparisons require a stable accuracy criterion.
For n equally likely stimulus-response alternatives, uncertainty H is log2(n) bits. The intercept a and slope b are estimated for a task, device, population, and speed-accuracy regime.
Where it earns its keep
Applications are strongest when the law changes a decision, measurement, model, or experiment rather than merely providing an analogy.
Estimate emergency choice load
ApplicationAlarm-response panels can reduce uncertainty through distinct signals, trained mappings, and prioritized actions.
Measure errors and response compatibility, not only option count.
Design controlled menu experiments
ApplicationThe law can predict a decision component when options are visible, known, and similarly accessible.
Real menu time also includes visual search, reading, pointing, and navigation depth.
Exploit probability and practice
ApplicationFrequent responses can become faster as users learn their distribution and mapping.
Changing layouts may destroy learned probability structure even when count stays fixed.
Where it stops working
The simple log2(n) form assumes equally likely alternatives with one response per stimulus. Unequal probabilities require entropy; sequential dependencies, ambiguous stimuli, incompatible mappings, and response repetition can change the relation.
Hick-Hyman is often misapplied to consumer menus. If a user scans text, recalls a goal, navigates categories, or points to a target, search models, memory, and Fitts's Law may explain more of the total time than choice uncertainty.
"Seven choices are always optimal"
Better: The law contains no universal ideal count."Hide options in more screens to make choice faster"
Better: Navigation and memory costs can exceed any reduction in local uncertainty."Count alone determines reaction time"
Better: Probability, mapping, practice, stimulus quality, and accuracy matter."The law measures preference"
Better: It models response selection time, not satisfaction or decision quality.Sources and further reading
Original publications and serious secondary scholarship are prioritized over summaries.
- Hick - On the Rate of Gain of InformationThe 1952 foundational choice reaction-time experiments.https://doi.org/10.1080/17470215208416600
- Hyman - Stimulus Information as a Determinant of Reaction TimeThe 1953 study extending the relation to stimulus probabilities and information.https://doi.org/10.1037/h0056940
- MIT OpenCourseWare - Human Factors Engineering, Hick-Hyman notesUniversity lecture treatment of information and response time.https://ocw.mit.edu/courses/16-400-human-factors-engineering-fall-2011/7ab16b422ca0ba8a79c1b71fd75c12d2_MIT16_400F11_lec21.pdf
- Wifall et al. - Stimulus and Response Uncertainty in Forced ChoiceModern experiment separating stimulus uncertainty from response uncertainty.https://pubmed.ncbi.nlm.nih.gov/26059726/