Fitts' Law: Predictive Model of Motor Capability

1. Fitts’ law: a predictive model of motor capability(note: the word “motor” here refers to something that creates movement)

2. Motor capabilities in pointing tasks Why study pointing tasks? • Pointing devices (mice, touchpads and touchscreens, and styluses) are very common, and often are used for all input except text. These devices are almost always used for pointing tasks. • We can leverage known psychomotor theories

3. Exercise: reciprocal pointing task • (sketch the below circles on the blackboard) • We need a volunteer to attempt the reciprocal tapping task for each pair of circles • What happens to the time required to go back-and-forth in each case?

4. Paul Fitts’ 1954 experimentinvolving 1D pointing

5. Fitts law • At first, was used to model reciprocal tapping in 1D (Fitts 1954) • Subsequently used to model discrete pointing ("one shot") in 1D (Fitts and Peterson 1964) • Hundreds (thousands?) of studies have confirmed the law under different conditions • Remains one of the only robust mathematical models available to user interface designers and HCI researchers

6. Fitts’ Law: T = a + b log2(D/W + 1) • Rapid pointing motion toward a target (button, widget, etc.) • T: average movement time, in seconds (or milliseconds);also sometimes called MT ("movement time") • D: distance to the center of the target; also sometimes called A (movement amplitude) • W: width of the target; in 1D, W is measured along the axis of motion • The logarithm (in bits) is sometimes called the index of difficultly ID • a (in s) and b (in s/bit): constants that are measured experimentally,that depend on the nature of the pointing task (1D, 2D, mouse, stylus, hand, foot, etc.) • IP = 1/b (in bits/s): index of performance, or bandwidth Cursor(or finger, etc.) 1D pointing(infinitely tall target): Target W D

7. Fitts’ Law: T = a + b log2(D/W + 1) • If the target is a rectangle of height H0 and width W0, we can define W = min(H0,W0) in the Fitts equation. This is a good approximation. In reality, however, a 10×1 cm target will be easier to point at than a 2×1 cm target, no matter what direction of motion, even though this difference is not captured by our suggested approximation. • If the target is a square width edge length L, or a circle of diameter L, we can define W = L • Be careful: the values of a and b won’t be the same in 2D pointing as in 1D Cursor(or finger, etc.) 2D pointing: Target H0 W0 D

8. Fitts’ law (rapid pointing motion) A Cible Curseur W

9. Fitts’ law Cible 1 Cible 2 Same ID → Same difficulty

10. Fitts’ law Cible 1 Cible 2 Smaller ID → Easier

11. Fitts’ law Cible 1 Cible 2 Larger ID → More difficult

12. MT (seconds) * * * * * * * * * * * * * * * * * * b = slope IP = 1/b * * * * * * * * * * * * a ID (bits) log2(D/W + 1) ID = index of difficulty IP = 1/b = index of performance

13. More than 50 years of studies Reference: I. S. MacKenzie. Fitts’ Law as a research and design tool in human computer interaction. Human Computer Interaction,1992, Vol. 7, pp. 91-139

14. Notes • IP is a measure of speed of a limb or of a pointing device, independent of the targets • The mouse is almost optimal!IP(mouse) ≈ 10.4, IP(hand) ≈ 10.6(however, these values vary from one study to another) • Limbs that are extremal (i.e., those further from the center of the body) and smaller are fasterIP(eyes) > IP(fingers) > IP(arms) > IP(legs)

15. 3M ergonomic mouse • What is this device’s IP, compared to a normal mouse? • Answer: It will probably be lower, because instead of using the wrist, the elbow is used 3M ergonomic mousehttp://www.fentek-ind.com/images/l3m_mouse.jpg

16. “minicute” mouse

17. Fitts’ law models • Reciprocal movements ("round trip") and discrete movements ("one shot") in 1D and 2D and applies in the following situations: • Movements of the hands and feet • Movements in air, under water, under a microscope • Grabbing, pointing with a finger, throwing a dart • Mouse, track ball, joystick, touch pad / track pad, helmet with sight, eye tracker • Position control and rate control • Linear motions and rotational motions (e.g., turning a knob on a radio to adjust the volume) • Preschool children, mentally retarded individuals, people under the effect of drugs • Monkeys In each case, the values of a and b are different!

18. Math refresher • Do you know how to calculate log2(5),for example, on your calculator?This could be important on an exam. • To change base, use the identitylogBX = (logAX)/(logAB) = (ln X)/(ln B) • Example: Log2(5) = (ln 5)/(ln 2) = 2.321928…

19. Notes on Fitts’ law • Speed/accuracy tradeoff • Targets that are closer or bigger can be selected faster • Time is scale-invariant • It’s the D/W ratio that matters • We can use Fitts’ law to… • Predict movement time (if a and b are known) • Compare two devices (by comparing their IP values) • Guide us in design choices.Example: avoid having small targets!

20. Excessively small targets W = 3 pixels, D ≈ 500 pixelsso ID ≈ 7.4 bits But with W = 10, D = 500, ID = 5.7 bits Lesson: don’t impose a Wthat is too small!

21. Excessively small targets • User interface in a free Wacom application that shipped with their Cintiq Companion Hybrid tablet in 2014 • Each of these 3 targets is ≈1×1 mm ! • Designed for use with a fine-tipped stylus, but these targets are still excessively small!

22. Example in Microsoft Explorer • Targets to see/hide the contents of a folder • In Vista, the user must click on the triangle to see/hide a folder, whereas in XP the user could click anywhere on the filename. Does this change the ID of the targets? • Answer: according to the heuristic of W=min(W0,H0), no, but in reality it will make the targets a bit more difficult In MS Windows XP In MS Windows Vista

23. Try to minimize the number of clicksIn the below examples, shortcuts allow the user to backtrack several levels in a single click.

24. http://www.bennetyee.org/http_webster.cgi : each word is a clickable hyperlink, enabling single-click lookup!

25. Avoid having small targets • A few places that are very easy to acquire with a cursor are • The pixel already under the cursor(example: using a popup menu instead of a pulldown menu) • The 4 corners of the screen, and the 4 edges of the screen(examples: the application menu in Mac OS; the start menu in Microsoft Windows) • What is W in this case? • What happens if there is a margin of 1-2 pixels between the menu and the edge of the screen? (Like in MS Windows 95, if I recall correctly.) In Windows 7, clicking in the screen corner still opens the menu, even though there appears to be an empty space.

26. The NeXT scrollbar • Question: why are the arrow buttons right beside each other? • Answer: to reduce D • If D ≈ W, then ID ≈ 1 bit only

27. Dialog boxes in "xv" • A different way to reduce D (to zero!)

28. Click …

29. Click …

30. Click …

31. Click !

32. Split Menus (Sears and Shneiderman, 1992) http://psychology.wichita.edu/surl/usabilitynews/41/adapt_menus.htm

33. Alarm clock on Google Nexus 4 Why is the “Snooze” button so much bigger than the “Dismiss” button?

34. Calculator on the Samsung Galaxy Note II(5.5 inch screen) Option to reduce size of keyboard

35. Thanko Thumb Extender (from Japan)

36. Area cursors • The "hotspot" of a normal cursor is just 1 pixel • The hotspot of an "area cursor" is larger, which facilitates selection of small targets (Kabbash and Buxton 1995; Hoffmann 1995; Worden et al. 1997) • For an "area cursor",W = size of cursor + size of target hotspot hotspot Normal cursor Area cursor Small targets

37. Bubble Cursor (Grossman and Balakrishnan 2005)http://www.dgp.toronto.edu/~ravin/videos/chi2005_bubblecursor.mov • A dynamic "area cursor": the size of the hotspot changes dynamically to always contain just one target, the closest target, within the hotspot. Observe that each target corresponds to a cell of a Voronoi diagram, hence the input space is completely covered ("tiled") with targets. No space is wasted.

38. Miniature keyboards for 2-thumb typing:Where’s the best place for the spacebar ? http://www.yorku.ca/mack/gi2002.html

39. Using Fitts’ Law to model 2-thumb typing • Take into account size and spacing between buttons • Assume thumbs alternate in typing whenever possible (to maximize speed) • Given a corpus of text, compute frequencies of sequences of letters • Weigh the time to type in each sequence by its frequency • Arrive at (upper bound for) average typing speed • MacKenzie and Soukoreff’s (2002) estimate: 60.7 wpm (words per minute) ! • Assumes spacebar in centre. If spacebar is on left or right, estimate drops to 49.9, 56.5 wpm respectively.

40. Goal Crossing • Rapid motion toward, between, and past two goal points, without any constraint on where to stop. The goal is a constraint that is perpendicular to the axis of motion, whereas in normal 1D Fitts poiting, the constraint is along the same direction as the axis of motion. • Can be modeled with the same equation as Fitts’ law! (Accot and Zhai 1997) • In the equation to model this task, W is the width of the goal • Note: the values of a and b are not the same here as in normal pointing tasks Goal Cursor W D

41. To model the opening of a menu below, one approach that we mentioned earlier is to model it as a Fitts’ pointing task, but with W=∞ • However, another approach is to model the opening of such menus as a goal crossing task. In this case, what value should be given to W?

42. Video game with goal crossing tasks Fruit Ninja https://lh6.ggpht.com/YwB1PlUYiFAwtvjpy59JfsovJ8Lge_y7LNIRs_WW9orli5ynONYCylbvUFNFWNLSP4I=h900

43. CrossYhttp://www.cs.umd.edu/hcil/crossy/http://www.acm.org/uist/archive/videos/2004/p3-apitz.movCrossYhttp://www.cs.umd.edu/hcil/crossy/http://www.acm.org/uist/archive/videos/2004/p3-apitz.mov

44. Hick-Hyman Law (Hick 1952; Hyman 1953) • Reaction time = a + b log2(N+1), where • N is the number of choices • a, b are experimentally measured constants (different from the constants in Fitts’ law) • log2(N+1) is the number of bits expressed by the choice • Examples where the Hick-Hyman law applies: • User is surrounded by N light bulbs and N buttons; when a bulb lights up, the user must press the corresponding button as fast as possible • User wants to click on a menu item (with a known label) in a menu that the user has never seen before, where the items are in alphabetical order • Counter-example where the Hick-Hyman law does not apply: • If the items in the menu are in some random order, the time to find the correct item will be linear, not logarithmic

45. Question • What does Hick’s law predict? Is it better to have a 3-level hierarchical menu with 2×2×2 choices, or a single-level menu with 8 choices? • 2×2×2 menu: 3×( a + b log2(2+1) )= 3a + b log2(3×3×3)= 3a + b log2(27) • 8-item flat menu: a + b log2(8+1) = a + b log2(9) • So, Hick’s law predicts (and studies confirm) that shallow and broad menus are generally better (https://scholar.google.ca/scholar?q=landauer+nachbar+menu+trees+breadth+depth+width ) • What would happen if we instead modeled these two kinds of menus with Fitts’ law? Would we get the same prediction?

46. In many cases, it’s actually better to model the time for visual search, and the time for a pointing movement with Fitts’ law, rather than to use the Hick-Hyman law. In two of the below examples, we see why the total time turns out to be logarithmic and therefore well-modeled by Hick-Hyman, but using Hick-Hyman is not necessary to model this total time. * Matches prediction by Hick-Hyman law

47. Pop-up Linear Menu Pop-up Pie Menu Today Sunday Monday Tuesday Wednesday Thursday Friday Saturday Using these law’s to predict performance • Can we model the above menus with Fitts’ law, or Goal crossing, or Hick-Hyman law? What result would we get? Which model is most appropriate? Can we compare two menus if the a, b constants in their models are different and unknown? • Which menu should we expect to be faster on average? • pie menu (bigger targets & less distance)?

48. Linear menu of N items, modelled with Fitts’ law • Each item is H high; menu’s total height is NH • Average distance to travel is NH/2 • IDaverage = log2(NH/(2H)+1) = log2(N/2+1) = log2(N+2)-1 ≈ log2(N)-1 (a good approximation for large N) • (Math experts: if E() is expected value, I’m pretending that E(log(X)) = log(E(X)), which isn’t quite true) • Linear menu, modelled with Hick-Hyman • ID = log2(N+1) ≈ log2(N)(a good approximation for large N) • Notice that we get the same expression for ID by applying the Hick-Hyman model to a radial menu of N items

49. Radial menu of N items, modelled with Fitts’ law • Each pie slice covers an angle of 2π/N radians • Maybe we can model each pie slice with a circle of radius r that inscribes the pie slice, where the circle’s center is a distance R from the menu center. This circle will be treated like a Fitts’ target. We assume the user is aiming at these imaginary circles. • ID = log2(R/(2r) + 1) = log2(1/(2sin(π/N)) + 1)≈ log2(N/(2π)) (a good approximation for large N)= log2(N) - log2(2π) = log2(N) - 2.651 • Notice that ID doesn’t depend directly on R, nor on r! It only depends on the ratio of R/r, so we can imagine these circular targets at any distance from the center and get the same ID. • Notice the we get the same expression for ID by applying a goal crossing model to a radial menu

50. My personal intuition is that the linear menu is best modeled with Fitts, and the goal crossing model is the best way to model a radial menu. Unfortunately, these two models have different a, b values. Thus, we could look up those values from some recent studies, or we could use the Fitts models for both kinds of menus, in which case a and b are the same and we can directly compare the ID values. • Comparing the two Fitts models at N=8 : • log2(8+2)-1 = 2.322 bits • log2(1/(2sin(π/8)) + 1) = 1.206 bits • Studies have found radial menus to be faster than linear menushttps://scholar.google.ca/scholar?q=kurtenbach+buxton+marking+menus ; https://scholar.google.ca/scholar?q=callahan+hopkins+shneiderman+pie ;https://scholar.google.ca/scholar?q=hopkins+design+implementation+pie+menus ;