The number of submovements determines total movement time

What it is

The variation in total time across different attempts at the same target-acquisition task doesn't mainly come from how fast the initial impulse ran — that phase's duration is fairly stable. What actually makes total time run long or short is how many rounds of "nudge a bit, check again" the correction phase needed to land. In other words, when one attempt is slower than another, the answer usually isn't in the opening burst — it's in those final few correction steps.

Why it happens

Each submovement has to independently run a full round of checking the current state, generating a new command, and executing that command, and this round has a relatively fixed minimum duration; total correction time is roughly that minimum multiplied by however many submovements actually occurred. The submovement count itself isn't a fixed value — it fluctuates with how far off the initial impulse's landing point was from the target on a given attempt, and how strictly "close enough" is judged. Sometimes the gap after the impulse is already small and one or two submovements finish it off; sometimes the impulse is off by a bit more, or the required precision is higher, and it takes several more steps. This fluctuation is naturally somewhat random, and it's the main reason the same person doing the same thing repeatedly doesn't take exactly the same amount of time every time.

Studying it

Researchers typically count the number of secondary velocity peaks in the correction phase from the velocity curve as an estimate of submovement count for that attempt, then correlate that count with total movement time: if more submovements do correspond to longer total time, and this relationship explains most of the variance in time differences, total time is mainly set by submovement count rather than by variation in initial-impulse speed. Another approach artificially manipulates factors known to affect submovement count (tightening the tolerance for a successful hit, for instance) and observes whether movement time increases accordingly.

Where it stops holding

This describes the main source of time variation between different attempts within the same class of task — it can't be generalized to mean total time depends only on submovement count and is unrelated to distance or target size. Distance and target size do shape submovement count, but through affecting how precisely the impulse phase lands; they're linked through submovement count as an intermediate step, not two independent, unrelated paths. Also, detecting submovements itself depends on being able to distinguish clear secondary peaks in the velocity curve, and measurement error introduces some noise into the count.

Applying it

• To shorten the average time a fine-precision operation takes, rather than trying to make the user's initial movement faster, look for ways to reduce the average number of submovements the operation needs — snapping, magnetic alignment, enlarging the effective target area — so the impulse phase more easily lands close to the target and fewer correction steps are needed.
• When comparing two interaction designs, comparing only average total time is easily skewed by a handful of slow attempts; it helps to also log the distribution of submovement counts. A design with a tighter distribution and fewer extreme multi-correction cases usually means a more stable, more predictable completion time.
• How to check: have the same users complete the same operation under two designs, extract the submovement-count distribution from the movement trajectories, and compute the average. If the new design shows a clearly lower average submovement count, expect total completion time to shorten accordingly, even if the initial-impulse phase's duration hasn't changed.

Related

• Same group: A8.08.1 The initial impulse phase covers most of the distance quickly · A8.08.2 The correction phase closes in on the target with small submovements · A8.08.4 Smaller targets require more submovements · A8.08.5 Undershoot and overshoot of the initial impulse carry different costs
• Nearby: A8.09 Speed-Accuracy Tradeoff · A8.07 Closed-Loop Control
• Search terms: submovement count · movement time variability · target acquisition time