Reaction Time & Hick's Law Lab

Try It Yourself

Choices N (Hick's Law) 2

Click "Start Live Trial", wait for the orange dot, then click it as fast as you can.

Simulated Population

Trials per batch 300

Response noise σ (ms) 35

Lapse tail τ (ms) 60

Live Readouts

Mean RT

– ms

SD RT

– ms

Trials run

Hick prediction

– ms

How it works

Hick's Law (Hick 1952, Hyman 1953) says choice reaction time grows logarithmically with the number of equally-likely options N:

RT(N) = a + b · log2(N + 1)

Here a ≈ 180 ms is the irreducible sensorimotor floor (nerve conduction + muscle activation) and b ≈ 150 ms/bit is the information-processing rate — doubling the choices costs a fixed number of milliseconds, not a fixed fraction, because each extra option adds one more bit of information to resolve.

Any single human trial isn't exactly RT(N) — it's a random draw. The standard model for a reaction-time distribution is the ex-Gaussian: a Gaussian decision-time component convolved with an exponential "lapse/attention" tail:

RT_trial = Normal(μ, σ) + Exponential(rate = 1/τ)
E[RT_trial] = μ + τ,  Var[RT_trial] = σ² + τ²

The simulator sets μ = RT(N) from Hick's Law, then samples σ (decision-time jitter) and τ (occasional slow/lapsed trials) from the sliders to build a population of trials — each rendered as an instanced sphere racing down the lane and landing in its histogram bin. The right-skewed shape you see is not noise in the simulation; it's the real, well-documented shape of human RT data.

Start Live Trial — an honest single-trial test: a random 0.6–2.5 s delay, then the dot appears and your own click time is measured and marked on the histogram in white.
Choices N — raises the simulated mean via Hick's Law (N=1 is simple reaction time; N>1 is choice reaction time).
Run Batch — draws "Trials per batch" ex-Gaussian samples at once and animates them into the 3D histogram.

100–1200 ms histogram, N=2 choices

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