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Why a Fitts'-Law Number Survives Swapping Your Mouse and a Millisecond Doesn't

Aim-trainer scores are reported in bits per second rather than raw milliseconds because throughput stays stable across hardware while raw times don't. Here's the math behind that stability, and why the effective-width correction was deliberately left out.

By Eric, BlinkBench Founder · Last reviewed: July 2026

Swap a wired gaming mouse for a trackpad and your raw movement times change immediately. Your Fitts'-law throughput, measured in bits per second, barely moves. That gap between the two numbers is not a coincidence, and understanding it explains every design choice in the aim trainer's scoring system.

What Fitts' law actually says

Fitts' law describes a trade-off that anyone who has ever reached for a small button already knows intuitively: smaller targets and longer distances take more time to acquire. The formal statement is that movement time scales linearly with the log of the ratio of distance to target width. That log term is the index of difficulty, measured in bits, and it captures the information-theoretic demand of the task — how precisely you have to resolve your position to land inside the target.

The Shannon formulation used in this site's lib/fitts.js writes the index of difficulty as:

ID = log2(D / W + 1)

where D is the centre-to-centre distance and W is the target width. Adding 1 inside the log keeps the expression defined when D equals zero and matches the Shannon channel-capacity analogy more cleanly than the original Fitts formulation. Throughput is then the index of difficulty divided by actual movement time:

TP = ID / MT   (bits per second)

That division is the whole story. You are computing a rate — how many bits of positional information your motor system resolves per second — rather than a raw duration.

Why a rate survives a hardware swap

Consider what changes when you move from a high-precision optical mouse to a trackpad. The trackpad is slower for large movements and less precise for small ones. Both movement time and effective landing scatter increase. But they increase together, in a way that is broadly consistent with the linear model. The numerator (index of difficulty) stays fixed because you set it by choosing target size and distance. The denominator (movement time) rises, but it rises roughly in proportion to the task demand the hardware is now struggling with. The ratio stays in a recognisable range.

Soukoreff and MacKenzie's 2004 review of 27 years of Fitts' law research makes this concrete with numbers. Across studies that conformed to the standard — consistent task geometry, proper randomisation of conditions, no cherry-picked target sizes — mouse throughput landed in a band of roughly 3.7 to 4.9 bits per second regardless of the specific device tested. Raw movement times across the same literature ranged from around 200 ms to over 1,500 ms. A millisecond count tells you about one device in one condition. A throughput figure tells you something closer to a property of the operator.

Non-conforming studies, where task geometry was inconsistent or conditions were not properly counterbalanced, showed effective throughput ranging from 2.6 to 12.5 bits per second — a five-fold spread. The measurement did not change; the discipline of the experimental design did. This is why the aim trainer enforces a fixed geometry rather than letting you choose your own target size and distance. A self-selected easy layout would inflate throughput just as a non-conforming study does.

The effective-width correction and why it was declined

The ISO 9241-9 standard for pointing device evaluation recommends an additional step: replacing the nominal target width W with an effective width W_e derived from the actual spatial scatter of your clicks. The idea is that if you consistently land in a tight cluster well inside the target, your effective task difficulty was higher than the nominal geometry implied, and your throughput should be adjusted upward accordingly.

The correction is statistically sound in principle. In practice, it requires enough trials to estimate the standard deviation of landing positions reliably. Soukoreff and MacKenzie note that the effective-width method introduces its own error when sample sizes are small, and that error is not trivial. A twelve-move run — the length of a session in the aim trainer — produces a landing-scatter estimate with wide confidence intervals. Applying the correction to that estimate would add noise rather than remove it. The baseline error from using nominal width instead of effective width sits around 4% in well-designed studies. Introducing an unreliable scatter estimate on top of a twelve-move sample would likely exceed that error, not reduce it.

Declining the correction is therefore an act of restraint, not an oversight. The tool reports nominal-geometry throughput and says so plainly, rather than applying a formula that would look more rigorous while being less accurate at this sample size.

What your score actually reflects

A throughput figure from a single twelve-move session reflects your motor system, your input device, your display's refresh rate, and the specific geometry of the task — all at once, inseparably. It is not a pure measure of hand speed, and it is not a pure measure of hardware. It is a measure of the system as a whole, which is precisely what makes it stable across sessions on the same setup and meaningfully different across sessions on different hardware.

If you run the test on a gaming mouse and then on a trackpad, the throughput difference tells you something real about how much the device is costing you in this specific task. If you run it twice on the same mouse, the difference tells you something about variability in the system — fatigue, attention, warm-up. Neither reading is a verdict on your ability in isolation.

This is the same logic that makes reaction time worth measuring carefully rather than casually: the number is only as meaningful as the conditions are consistent. The aim trainer holds geometry, target count, and scoring formula fixed so that comparisons across sessions are at least internally valid, even if the absolute figure carries the fingerprint of your hardware.

Frequently asked questions

Why bits per second rather than targets per second?

Targets per second depends entirely on how large and how far apart the targets are, so it cannot be compared across different layouts. Bits per second normalises for task difficulty, which means a score from one geometry is at least in the same units as a score from another.

Does a higher throughput score mean I am a better aimer?

Not in isolation. It means the combination of your motor system and your current input device resolved positional information at that rate under those conditions. A faster mouse with lower pointer acceleration will typically produce higher throughput than a slow trackpad, regardless of the operator's skill.

Why twelve targets specifically?

Twelve trials is enough to produce a stable mean movement time while keeping the session short enough that fatigue does not become a confound. It is not enough to support the effective-width correction reliably, which is one reason that correction was not applied.

What is the Shannon formulation and why use it instead of the original?

Fitts' original formula uses log2(2D / W), which can produce negative difficulty values when the target is wider than twice the distance. The Shannon version, log2(D / W + 1), avoids that problem and maps more cleanly onto information-channel analogies. Soukoreff and MacKenzie recommend it as the standard formulation for this reason.

Can I compare my score to published research averages?

Broadly, yes. The 3.7–4.9 bits per second band from conforming mouse studies is a reasonable reference point. But published studies use controlled laboratory conditions, calibrated displays, and many more trials than twelve. Treat the comparison as an order-of-magnitude check rather than a precise benchmark.

Sources

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