## Hick's Law and Fitts's Law

Analysis of timings on real-world interfaces sometimes yields suggestive curves. That is, suggestive to a statistician, who may be able to recognize a powerful qualitative principle in the numbers. One such regularity is Hick's Law,[26] which for our purposes we can paraphrase as: The time M(n) required to make a choice from a menu of n items rises with the log to the base two of n.

The key fact here is that the rise of M(n) is sublinear. Thus, the Rule of Large Menus: one large menu is more time-efficient than several small submenus supporting the same choices, even if we ignore the time overhead of moving among submenus.

A related result is Fitts's Law, which predicts that the time T(D,S) to move the mouse pointer to a region on a screen, when is initially D units away from the region border and the region is S units deep in the direction of motion, rises with the log to the base two of D/S.

Since you can't control D — the user will start his mouse movements from unpredictable locations — it follows that the way to reduce the D/S ratio that predicts select time in a point-and-click interface is to make the target larger. But not huge; the log to the base two in the formula means that, as with Hick's Law, the efficiency gains are sublinear and fall off as the ratio rises, and that gain has to be traded off against the value of other uses for the screen space.

Still, we get from this the Rule of Target Size: The size of a button should be proportional to its expected frequency of use.

Macintosh fans like to point out that Fitts's Law implies a very large advantage for Mac-style edge-of-screen menus with no borders, because they effectively extend the depth of the target area offscreen. This prediction is borne out by experiment. Under Unix. we can capture this benefit with a (borderless) taskbar adjacent to any screen edge, but the standard Unix toolkits don't give us a way to harness it within applications (because application windows have borders and anyway don't typically appear nestled up to a sctreen edge).[27]

We can get from this the Rule of the Infinite Edge: The easiest target rectangles on the screen are those adjacent to its edges.

Hick's Law and Fitts's Law come from a place even deeper than evolved human instinctual wiring. They're related to the Shannon-Hartley Theorem in information theory and would probably just hold as true for intelligent squids, robots, or anything else with an eye-brain-hand loop that has to check whether the mouse pointer has landed in the right spot by tracking progress against a visual boundary.

For more on the application of Fitts's Law, including some marvelously detailed case studies, see Bruce Tognazzini's February 1999 Ask Tog[28].

[26] For the precise mathematical statements of both Hick's Law and Fitts's Law, see the discussion in [Raskin].

[27] In fact Fitts's Law tells us that the most easily targeted areas would be the (unbordered) four corners of the screen, which have offscreen landing zones on two sides. No GUI toolkit in history has actually used this fact.