Simple vs Choice Reaction Time and Hick's Law

The first reaction time number I ever cared about was a simple one. Light turns green, I click, I get a number. Around 248 ms on a good day. Then I tried a test where the dot could show up in one of four spots and I had to hit the matching key, and my number fell off a cliff. Suddenly I was in the 400s. Same brain, same fingers, way slower. I thought something was wrong with me. Nothing was wrong with me. That gap has a name, and it’s been measured since the 1950s.

simple vs choice: what’s actually different

Simple reaction time is one stimulus, one response. Light flashes, you click. There’s no decision to make: you already know what you’re going to do, you’re just waiting for the go signal. That’s what you’re measuring on the main visual reaction test. Lab simple RT runs roughly 150-300 ms, and large online aggregates sit around a 273 ms median once you add display and input lag. That figure comes from Human Benchmark’s public statistics, a big pool of self-reported scores, not a controlled study.

Choice reaction time is different in one specific way: now there are multiple possible signals, each tied to a different response, and you have to pick. Red means left, blue means right. Or in my case, four positions, four keys. You can’t pre-load a single answer anymore because you don’t know which one you’ll need until the signal appears. That picking step is the cost. Choice RT typically lands somewhere in the 300-700 ms range, and you can feel it happen. There’s a tiny hitch where your brain goes “which one?” before your hand moves. If you want to feel the jump yourself, the choice reaction test is the cleanest way to see your simple and choice numbers side by side.

hick’s law, in plain terms

Here’s the part that surprised me most. The slowdown isn’t random, and it isn’t proportional to the number of options. It follows a clean logarithmic rule that W. E. Hick published in 1952:

RT = a + b × log₂(N)

N is the number of equally likely choices. The constant a (illustratively around 200 ms) covers everything that isn’t deciding: seeing the signal, sending the motor command, the muscle actually firing. The constant b (illustratively around 150 ms per bit) is the price of each unit of decision. I’m using these as round teaching numbers, not settled constants. The actual values vary a lot across studies and setups, as Proctor and Schneider’s 2018 review in QJEP lays out, though the underlying logarithmic relationship has held up across decades of testing.

The log₂(N) is the clever bit. log base 2 of N is, roughly, “how many yes/no questions do I need to find the answer.” Two options is one question, one bit. Four options is two questions. Eight is three. Your brain isn’t checking every option one by one; it’s narrowing down by halving, like a binary search.

a worked example: 2, 4, and 8 choices

Let me run the numbers with the illustrative a ≈ 200 ms and b ≈ 150 ms/bit from above. Your own constants will differ, but the shape of the curve is the point.

Choices (N)	log₂(N) (bits)	RT = 200 + 150 × bits
2	1	350 ms
4	2	500 ms
8	3	650 ms

Look at the right column. Going from 2 to 4 options adds 150 ms. Going from 4 to 8 also adds 150 ms. Doubling again, to 16, would add another 150. Every doubling costs the same flat amount, because each doubling adds exactly one bit, one more yes/no question. That’s the whole reason the curve flattens out. Going from 2 to 4 choices feels expensive. Going from 64 to 128 barely registers, because you’re only adding one more bit to an already-large pile.

This clicked for me as a gamer. The difference between a 1v1 and a 1v2 is brutal. The difference between an 8-man chaos fight and a 9-man one? You barely notice. Same math.

why this matters outside a test

If you design anything people interact with, Hick’s law is a design tool. Pile twelve options into a menu and every selection pays a log₂(12) ≈ 3.6-bit tax. Split them into two clean groups of fewer choices and you cut the per-decision cost. The flip side is real too: sometimes one big sorted list beats nested submenus, because hunting through layers stacks up multiple choice penalties instead of one. The right answer depends on whether people can predict where things live.

Driving is where this stops being abstract and gets scary. A lab choice reaction might be half a second. But real perception-reaction time in traffic is often cited around 1.5 seconds, because the road isn’t a clean 4-choice test: you have to notice the brake lights, figure out what’s happening, then decide and move. Every extra possible thing that could go wrong is another branch in your decision tree, and the log₂ tax compounds. Add a phone, and you’ve shoved a competing task in front of the whole chain. Your reaction stretches well past that 1.5 s, and at speed those extra meters are the difference between stopping and not. Thinking distance scales directly with how long that chain takes, and at highway speed those extra meters add up fast. You can get a feel for the gap between a clean lab response and a messy real-world one on the driving reaction time test.

what I’d actually take from this

Don’t compare your choice RT to your simple RT and feel slow. They’re measuring different things, and the difference is the decision step working as designed. If you want to lower your choice numbers, the trainable part is that decision chunk: warm up, get the response mappings deeply familiar so picking becomes near-automatic, and reduce how many live options your brain is juggling. The a term (eyes, nerves, muscle) barely budges. The b × log₂(N) term is where the practice lives.

Run a few rounds on the choice reaction test, then go back to the plain visual test and watch the gap. Once you see Hick’s law in your own numbers, it stops being a curve in a 1952 paper and starts being a thing you can feel every time your brain pauses to ask “which one.”

Sources

• Proctor & Schneider (2018), QJEP: review of Hick’s law
• Human Benchmark: Reaction Time statistics (self-reported online aggregate)

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