Drift-Diffusion Decision Model

Evidence Accumulation

Drift rate v 0.60

Boundary separation a 1.20

Noise σ 1.00

Starting bias z₀/a 0.00

Live Statistics

Finished

Accuracy (upper)

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Mean RT

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Predicted P(upper)

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Active racers

How it works

Each racer is an independent sample path of a 1-D drift-diffusion process — the classic model of two-alternative forced-choice decisions (Ratcliff, 1978). Evidence x(t) accumulates as a biased random walk:

dx = v·dt + σ·dW(t)
choice = "upper" if x(t) reaches +a
choice = "lower" if x(t) reaches -a
RT = t at the moment a boundary is reached

v is the drift rate (how strongly the evidence favors one option), a is the boundary separation (response caution — wider a means slower but more accurate decisions), σ is moment-to-moment noise, and z₀ is a starting-point bias toward one boundary before any evidence arrives.

The probability of hitting the upper boundary has a closed form (a "gambler's ruin" solution), used here as the live "Predicted P(upper)" readout so you can watch simulated accuracy converge to theory:

z = z0 + a,  U = 2a
P(upper) = (1 - e^(-2vz/σ²)) / (1 - e^(-2vU/σ²))   (v ≠ 0)
P(upper) = z / U                                    (v = 0)

Drift rate v — raise it and racers commit to the upper boundary faster and more reliably; near 0 it becomes a coin flip.
Boundary separation a — wider boundaries trade speed for accuracy (the classic speed-accuracy tradeoff).
Noise σ — more noise means more racers cross the "wrong" boundary even with a strong drift.
Starting bias z₀/a — a prior/expectation that pre-loads evidence toward one option before the trial starts.

Real-world relevance: this exact model fits human reaction-time distributions in perceptual and memory decisions across thousands of published experiments, and is the standard account of the speed-accuracy tradeoff in cognitive psychology and neuroscience.

Racing (undecided) Hit upper boundary Hit lower boundary

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