Pointing is a channel with a measured capacity, and the capacity belongs to the task

Year 2 / Module 15 Interaction techniques and usability evaluation / Unit 1 / Pointing is a channel with a measured capacity, and the capacity belongs to the task

Pointing is a channel with a measured capacity, and the capacity belongs to the task

HCI2107 · Unit 1 of 10

Fitts's law earns its place in HCI as an engineering model rather than a law of the motor system: the index of difficulty predicts acquisition time well enough to rank devices and to read a layout before it is built, but the systematic deviations it fails to explain, the curvature at low difficulty, the disproportionate cost of narrow targets and the repair of nominal by effective width, mean that a throughput figure is a claim about a task configuration rather than a property of a device or a person.

Pointing is a channel with a measured capacity, and the capacity belongs to the task

This first of ten units opens a sequence on measuring interaction. Fitts's law is the most dependable quantitative model in interaction design. It also rests on a narrower footing than its vocabulary suggests. The law predicts movement time well enough to rank devices, and it prices a layout before anyone builds it. It does not measure the capacity of a nervous system. Its deviations point one way, at low difficulty and at narrow targets. A throughput figure is a claim about a task configuration, not a property of a device or of a person.

The law prices movement on an index that is itself a choice

Fitts (1954) set the paradigm. Participants tapped alternately between two targets of varying width and separation. Movement time rose linearly with an index of difficulty, which Fitts formed from the logarithm of twice the amplitude divided by the width. MacKenzie's (1992) reanalysis puts the mean index of performance at 10.10 bits per second, and records that the factor of two was an arbitrary adjustment, added to keep the index above zero.

Fitts and Peterson (1964) recovered the same linear relation for a single discrete response, which licenses applying the law to a click. Card, English and Burr (1978) compared a mouse, an isometric joystick, step keys and text keys on text selection. The mouse was fastest and carried the lowest error rate. The law accounted for the times of the mouse and the joystick.

MacKenzie (1989) showed the founding equation is not derived. Fitts built on Shannon's theorem, but the equation he adopted deviates slightly from the principle it invokes. An exact adaptation of Shannon's equation, the logarithm of amplitude over width plus one, fits the same data at least as well. The canonical index is therefore one defensible choice among several.

The index also assumes a symmetry. Doubling the distance adds one bit, and halving the width adds one bit (MacKenzie, 1992). The reviewed data show that the motor system does not always honour that trade.

The linear model fails at the edges, and no mechanism explains it

MacKenzie (1992) catalogues the failures. Plots of movement time against difficulty curve upward away from the regression line at low values of the index. In Fitts's own data the one-bit condition yields 5.56 bits per second, which is 3.4 standard deviations below the mean of 10.10. Narrow targets cost more than the model allows. Errors rise as the target narrows, and amplitude has no corresponding effect. The repair is the effective width. A designer computes it from the spread of endpoints, under the assumption that a target behaves like noise when about four per cent of hits miss it. The model is then fitted to where the hits landed, not to the drawn rectangle.

A one-dimensional model applied to rectangular targets such as words can give unrealistically low or even negative difficulty ratings, and a two-dimensional reading of width restores sensible predictions (MacKenzie and Buxton, 1992).

The law can be fitted while the mechanism stays contested. Meyer and colleagues (1988) proposed the most successful account: a movement has a primary submovement and an optional corrective one, both programmed to minimise average total time while keeping the hit rate high. Soukoreff and MacKenzie (2004) state that no satisfactory psychomotor theory explains the law.

Throughput is one contested ratio

The derived quantity in HCI is throughput: difficulty divided by movement time. ISO 9241-9, superseded by the 9241-400 series, fixed the measure, and Soukoreff and MacKenzie (2004) set out seven recommendations supporting it. They reviewed twenty-four published mouse models and nine studies that had used the standard. Five published mouse models from four research groups fall between 3.7 and 4.9 bits per second, a spread of 1.2, against almost ten across the earlier heterogeneous studies.

Zhai (2004) objects to the quantity itself. Difficulty divided by movement time is ill-defined, he argues. It changes with the set of difficulty values the experimenter chose. It cannot be generalised. It equals a constant only when the intercept is zero.

Contested question: is throughput a property of the device or of the task configuration?

The first position holds that throughput is a well-defined device measure. Soukoreff and MacKenzie (2004) supply the evidence, since independent mouse models converge within 1.2 bits per second once the protocol is fixed. They argue that Zhai's conclusion rests on substituting the fitted regression line for the observed times, which they call invalid. Card, English and Burr (1978) support that reading, since the mouse's slope sat near a value found across eye-hand tasks.

The second position holds that throughput belongs to the configuration. Zhai (2004) supplies the internal argument, that difficulty divided by time varies with the difficulty range. MacKenzie (1992) adds cross-study evidence. The surveyed studies' prediction equations vary enough to prevent de facto standard equations, and nine intercepts are negative, which implies a negative predicted time for an easy task. Chakraborty and Yadav (2022) add touchscreens, where no consensus exists on whether the law is valid at all.

This unit takes a third position: the two sides estimate different quantities. A ranking within one protocol can be stable while an absolute figure remains a statement about the configuration that produced it. What would settle the dispute is a study that manipulates the difficulty range and target geometry as factors. Such a study holds participants and device constant. It reports throughput beside slope, intercept and error character, and it shows whether a device ranking survives. Until one is published, report throughput with its configuration.

The evidence is not symmetric. Zhai (2004) argues from the mathematics of the fitted line, a theoretical objection rather than a new experiment, while Soukoreff and MacKenzie (2004) rest on a review of twenty-four mouse models and nine standardised studies. The strongest objection is that the unit's third position is untested, since no study here manipulates the difficulty range while holding device and participants fixed. A designer should treat a throughput figure as local to its configuration while the dispute is open.

Apparent violations change the task, not the person

Designers try, because screen space is finite. Balakrishnan (2004) surveys the virtual enhancements built for the purpose. He sorts them into those that shorten the distance to a target, those that enlarge it, and those that do both. They are promising for single isolated targets, but many do not scale to several targets in close proximity, because an enlargement that helps one target takes space from its neighbours. An apparent violation of the law is therefore more often a change in the effective width of a task than in the capacity of a person.

Leahy and Hix (1990) give the enlargement a measured instance on a touch screen. Participants touched below the target and towards the screen's sides, and the vertical error grew as the target moved down the screen. A 36 square millimetre target in the top-left sector was therefore expected to register 99 per cent of its touches.

Where the argument is heading

Berard (2024) tests an assumption the law inherits rather than states: the space in which the hand moves is the space in which the pointer appears. In congruent indirect touch the finger works on a desk while small pointers on a vertical display show its position, and six participants new to the technique performed target acquisition on eight separate days. Four were notably more efficient with indirect touch by the last session, an average improvement of fourteen per cent. Amini and colleagues (2025) reviewed 119 publications covering 122 studies that applied the law in three-dimensional extended reality. More than half cited it without examining throughput, movement time or error rate at all, and against ISO 9241-411 the applications vary enough to prevent comparison.

MacKenzie, Kauppinen and Silfverberg (2001) show that measures taken during a trial discriminate between devices where time, error rate and throughput do not. A throughput figure travels only as far as its configuration does, including the head pointer or switch a user with limited hand movement drives.

The sources this unit rests on

Amini, M., Stuerzlinger, W., Teather, R. J. and Batmaz, A. U. (2025). A Systematic Review of Fitts' law in 3D Extended Reality. Proceedings of the 2025 CHI Conference on Human Factors in Computing Systems. doi:10.1145/3706598.3713623 A systematic review of 119 publications covering 122 studies that used the law in three-dimensional extended reality found more than half cited it without examining throughput, movement time or error rate. Against ISO 9241-411 the studies vary enough to prevent comparison, which grounds the unit's configuration reading.
Balakrishnan, R. (2004). "Beating" Fitts' law: virtual enhancements for pointing facilitation. International Journal of Human-Computer Studies. doi:10.1016/j.ijhcs.2004.09.002 The survey covers techniques that shorten the distance to a target, enlarge it, or both, and reviews the competing motor control accounts of the law. It finds them promising for single isolated targets but reports that many do not scale to nearby targets.
Berard, F. (2024). Congruent Indirect Touch vs. mouse pointing performance. International Journal of Human-Computer Studies. doi:10.1016/j.ijhcs.2024.103261 The study separates motor space from display space, the finger on a desk while pointers on a vertical display show its position, and measured throughput against the mouse over eight sessions. Four of the six participants were more efficient with indirect touch in the last session, an average improvement of fourteen per cent.
Card, S. K., English, W. K. and Burr, B. J. (1978). Evaluation of mouse, rate-controlled isometric joystick, step keys, and text keys for text selection on a CRT. Ergonomics. doi:10.1080/00140137808931762 Four devices were compared on text selection and the mouse was fastest with the lowest error rate; mouse and joystick positioning times followed Fitts's law. It is the study that carried the law into interface design.
Chakraborty, P. and Yadav, S. (2022). Applicability of Fitts' law to interaction with touchscreen: review of experimental results. Theoretical Issues in Ergonomics Science. doi:10.1080/1463922x.2022.2114034 The review collects touchscreen studies reporting positive, null and negative results on whether the law applies. It reports that the work remains small after roughly forty years and that there is no consensus on validity for touch, so the law's parameters are context-bound rather than device-invariant.
Fitts, P. M. (1954). The information capacity of the human motor system in controlling the amplitude of movement. Journal of Experimental Psychology. doi:10.1037/h0055392 Participants tapped alternately between two targets of varying width and separation, and movement time increased linearly with an index of difficulty formed from the logarithm of twice the amplitude divided by the width. It is the founding model the unit interrogates.
Fitts, P. M. and Peterson, J. R. (1964). Information capacity of discrete motor responses. Journal of Experimental Psychology. doi:10.1037/h0045689 The authors carried the paradigm from reciprocal tapping to a single discrete response and recovered the same linear relation, which licenses applying the law to the single click an interface asks for.
MacKenzie, I. S. (1989). A note on the information-theoretic basis for Fitts' law. J. Motor Behav. 21, 323-330. doi:10.1080/00222895.1989.10735486 MacKenzie reanalysed Fitts's original data against Shannon's theorem and showed Fitts had chosen an equation deviating slightly from the principle it invokes, since an exact adaptation of Shannon's equation fits the data at least as well. The canonical index is a modelling choice, not a derived quantity.
MacKenzie, I. S. (1992). Fitts' law as a research and design tool in human-computer interaction. Human-Computer Interaction. doi:10.1207/s15327051hci0701_3 MacKenzie argues for the Shannon formulation and reanalyses six studies using the mouse, trackball, joystick, touchpad, helmet-mounted sight and eye tracker. He documents the curvature at low difficulty, the inconsistency of the studies' prediction equations, nine negative intercepts and the effective target width. It is both the case for the law as a design tool and the evidence that throughput is configuration-bound.
MacKenzie, I. S. and Buxton, W. (1992). Extending Fitts' law to two-dimensional tasks. Proceedings of the SIGCHI Conference on Human Factors in Computing Systems. doi:10.1145/142750.142794 The authors show that the one-dimensional model applied to rectangular targets such as words can yield unrealistically low or even negative difficulty ratings, and that the Shannon formulation keeps the index at or above zero.
MacKenzie, I. S., Kauppinen, T. and Silfverberg, M. (2001). Accuracy measures for evaluating computer pointing devices. Proceedings of the SIGCHI Conference on Human Factors in Computing Systems. doi:10.1145/365024.365028 The authors propose seven measures taken during a trial rather than once per trial, including target re-entry, task axis crossing and movement direction change, and validate them on four devices. The measures discriminated between devices where time, error rate and throughput showed no difference.
Leahy, M. and Hix, D. (1990). Effect of Touch Screen Target Location on User Accuracy. Proceedings of the Human Factors Society Annual Meeting. doi:10.1177/154193129003400429 A controlled experiment found participants touched below the target, with the vertical error growing down the screen, and towards the sides. Per-sector curves relate target size to expected accuracy.
Meyer, D. E., Abrams, R. A., Kornblum, S., Wright, C. E. and Smith, J. E. K. (1988). Optimality in human motor performance: ideal control of rapid aimed movements. Psychological Review. doi:10.1037/0033-295x.95.3.340 The authors propose a stochastic optimised-submovement model in which a movement is a primary submovement plus an optional correction, programmed to minimise average total time while keeping the hit rate high; two wrist-rotation experiments supported it. It is the mechanism that opens the box the law leaves closed.
Soukoreff, R. W. and MacKenzie, I. S. (2004). Towards a standard for pointing device evaluation, perspectives on 27 years of Fitts' law research in HCI. International Journal of Human-Computer Studies. doi:10.1016/j.ijhcs.2004.09.001 The authors make seven recommendations supporting the ISO 9241-9 standard and review twenty-four published mouse models and nine studies that used it, finding five models from four research groups within 1.2 bits per second of each other. They call Zhai's substitution of the fitted line for the observed times invalid, and they are one side of the contested question.
Zhai, S. (2004). Characterizing computer input with Fitts' law parameters: the information and non-information aspects of pointing. International Journal of Human-Computer Studies. doi:10.1016/j.ijhcs.2004.09.006 Zhai argues that difficulty divided by movement time is ill-defined, because it varies with the set of difficulty values the experimenter chose and cannot be generalised beyond the distances and sizes tested. He would report the slope and intercept instead, and he is the other side of the contested question.

Check your understanding & apply it · 4 questions, 1 essay

1A procurement team compares two published throughput values: a mouse measured under the ISO 9241-9 protocol, inside the 3.7 to 4.9 bits per second bracket that Soukoreff and MacKenzie (2004) review across five mouse models, and 10.10 bits per second from MacKenzie's (1992) reanalysis of Fitts's original tapping studies. It concludes that the second device is more than twice as fast as the first. Which diagnosis does the unit support?

2A researcher repeats one pointing experiment over two different difficulty ranges, holding the participants, the device and the protocol constant, and reports a throughput value for each range. What does the unit predict?

3A laboratory must publish one throughput number for a new stylus. Which report does the position this unit takes license?

4A reviewer reads that in Fitts's own data the one-bit condition yielded 5.56 bits per second against a mean of 10.10, and that errors rose as targets narrowed with no corresponding effect of amplitude. The reviewer calls both findings ordinary scatter around a sound fit. Which diagnosis does the unit support?

5Essay Choose a pointing task you can actually observe, such as a button on a phone toolbar, a row of browser tabs, or a control in a car display. State the movement and the target so that an index of difficulty could be computed, naming the amplitude, the width and the treatment of errors you would use. Then argue whether a throughput figure measured on that task would report the device, the person or the configuration. Use Fitts (1954) and Card, English and Burr (1978) for what the law was built to predict, MacKenzie (1992) and MacKenzie and Buxton (1992) for the deviations it leaves and the effective width that repairs them, Zhai (2004) and Soukoreff and MacKenzie (2004) for the two sides of the measurement dispute, and Balakrishnan (2004) for a technique that claims to beat the constraint. Close by naming the comparison that would settle whether your throughput figure transfers.

Begin by making the task computable, because the whole argument turns on it. Name the amplitude as the distance from the resting position of the pointing device or thumb to the centre of the target, and the width as the extent of the target along the axis of approach. Say how you would treat errors: if you use the nominal width you are assuming the four per cent error condition that MacKenzie (1992) shows is needed for the target to behave like noise, so a task with a different error rate should be reported with an effective width taken from the spread of the endpoints, and a target you would describe as a word or a tab should be handled with the two-dimensional reading of width that MacKenzie and Buxton (1992) propose, since a one-dimensional index for a rectangular target can come out unrealistically low or even negative. Say also that this is what the law was built to do: Fitts (1954) found movement time rising linearly with difficulty in reciprocal tapping, and Card, English and Burr (1978) showed that pointing with a mouse is accounted for by the same relation, close to the minimum achievable, which is why a device can be ranked before a single user is recruited. Now take a position on what your figure reports. If you hold the configuration fixed, report the throughput with it and compare two devices on the same task, you are making a relative claim, and the convergence of five published mouse models within 1.2 bits per second that Soukoreff and MacKenzie (2004) report is good evidence that such claims are reproducible. If you then carry the number to a different distance, a different target shape or a different device, you are making an absolute claim that Zhai (2004) argues the measure cannot support, because difficulty divided by movement time moves with the range of difficulty values you chose and equals a true constant only when the regression intercept is zero. The strongest way to write this up is to report the regression as well: slope, intercept, error character, and the difficulty range, which is exactly what Zhai asks for and what Soukoreff and MacKenzie's own recommendations support. Treat Balakrishnan's (2004) survey as the warning about a shortcut: a technique that shrinks distances or grows targets looks as though it beats the constraint, and it often does help for a single isolated target, but the gains largely reconstruct the configuration the law describes and many such techniques do not scale when targets sit close together. Close by naming the comparison that would settle the question for your chosen task: measure the same participants on the same device across at least two difficulty ranges or two target geometries, report throughput beside slope, intercept and error character for each, and show whether the ranking of two devices changes. If it does not change, your figure is portable within the class of configurations you tested; if it does, the figure was always a statement about the configuration.