Undershoot and overshoot of the initial impulse carry different costs

What it is

If the initial impulse doesn't land exactly on the target, there are only two ways it can miss: falling short of the target (undershoot) or passing beyond it (overshoot). These two kinds of deviation don't carry the same cost for the correction that follows: after an undershoot, the remaining submovements only need to keep nudging forward in the same direction — no direction change needed; after an overshoot, the submovements have to reverse direction first, pulling back — a direction switch has occurred. Being "off by a bit" in either case, an undershoot is cheaper to wrap up, and an overshoot is more troublesome.

Why it happens

A direction switch itself carries an extra cost, because a submovement's direction is also set in advance, based on the relationship between the current state and the target, before it's issued. Once it turns out the direction originally set was wrong — it should have gone backward instead of continuing forward — the whole "check state, generate new command" chain has to run again, and this time the new command's direction is exactly opposite to the previous step, which carries a higher chance of error and hesitation. Nudging further in the same direction extends an existing movement trend; reversing course negates a movement trend that just occurred, and the latter places greater demands on the motor control system. Precisely because the overshoot cleanup cost is higher, the motor system tends to set the force of the initial impulse with a slight conservative bias toward undershoot: better to fall a bit short than to risk flying past — and this bias is itself an adaptation to the fact that correction costs are asymmetric.

Studying it

A common way to verify this asymmetry tallies the direction of deviation of the initial impulse's landing point across a large number of repeated attempts: if undershoots occur systematically more often than overshoots, and this bias becomes more pronounced under conditions demanding higher speed, this supports the explanation that the motor system is actively favoring undershoot. Another approach separately measures the number of submovements or the time needed to complete the remaining correction after an undershoot versus after an overshoot; if the overshoot group clearly needs more corrections and takes longer, this directly confirms the asymmetric cleanup cost.

Where it stops holding

The strength of this conservative bias shifts with how much speed the task demands — the faster required, the larger the impulse's own output variability, and the more this bias matters; if a task doesn't demand much speed, the impulse can be fired more carefully and accurately, and undershoot and overshoot frequencies come closer together, with the bias not necessarily showing clearly. This fact also describes the asymmetric cleanup cost for deviations of the same size in different directions — it doesn't address how large the deviation itself is or how many steps are needed to fix it, which belongs to the relationship between submovement count and target width and isn't repeated here.

Applying it

• For scenarios where passing beyond the target carries an especially high cost (sliding past a boundary into a hazardous action zone, swiping across an option and immediately triggering a side effect), add a slight resistance or deceleration feel to the target so the impulse more readily stops short of it rather than sailing past — deliberately pushing the landing-point distribution toward undershoot, using the fact that undershoot is cheaper to clean up to reduce mis-hits.
• For ordinary fine-positioning tasks, if users are observed to commonly overshoot (a slider frequently sliding past and having to be pulled back), consider increasing damping or lowering the movement-to-displacement ratio near the target — directly suppressing overshoot through the physical feel of the control rather than relying on users to be more careful on their own.
• How to check: tally the proportion of undershoots versus overshoots for the target operation, along with the extra time each requires to clean up. If the average time after an overshoot is clearly longer, adding tail-end damping to suppress overshoot for that operation will yield a more noticeable overall time benefit than continuing to fine-tune the precision of the impulse phase itself.

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 · A8.08.3 The number of submovements determines total movement time · A8.08.4 Smaller targets require more submovements
• Nearby: A8.09 Speed-Accuracy Tradeoff · A10.06 Error-Proofing Design
• Search terms: undershoot bias · overshoot correction cost · asymmetric aiming error