# Combining Fitts' law with Hick's law

I'm working through a textbook and got stumped on this particular question:

Use Hicks’ and Fitt’s Laws to derive an expression for the time for a user to select an item in a menu where b is the branching factor, the number of alternatives at each level, and n is the total number of options in the full menu. Assume the distance to move and target size are independent of b.

What does your expression predict would be the optimal choice for b in order to minimize the overall selection time?

If I define Fitts law as: `T = Im*log_2(2d/s)` where T is the time to acquire target of size s at distance d.

And Hicks as: `Td = Ic*log_2(n+1)` for n equally probable alternatives.

Would my answer simply be: `total time = b*(Ic*log_2(n+1)) + (Im*log_2(2d/s))`?

Or maybe: `total time = (Ic*log_2(n+1/b)) + (Im*log_2(2d/s))`?

The takeaway from Fitts' Law is that small objects are more difficult to click on the more you have to move your mouse. Since you cannot (usually) predict where a user's pointer/mouse is you have to assume a smaller target is more difficult to select.

More formally Fitts' Law, applied to HCI, shows that the time required for a person to move the pointer to a target area is based upon the distance to the target and the size of the target. The screen edge, as it turns out, is a large target because the cursor is stopped when it reaches it. Therefore one can place a small tool bar at the edge and have it seem larger. I think this is the way many people apply Fitts' Law.

It must be remembered that Fitt's studies were not based on Human Computer Interaction but production line tasks. Hence we must factor in the fact that we move a mouse - and not the cursor. The user may have to pick the mouse up and place it back down again.

Hick's Law refers to the decision making process. Too many unrelated, unorganized choices bad. Fewer, or better organized choices, good. Or, to put it more formally, the cognitive load is increased as choices increase. This increases the time necessary to make a decision and can lead the user to opt out of the process as the burden in making a choice is greater than the reward of completing the task.

I have never seen anyone in the UX community applying mathematical formulas for where to place a navigation bar. We will be at that point when we are in a VR world and designs take into consideration a far greater range of human motion.

Now to begin to answer your question. You're correct that you would have to add the two equations together. The time necessary to make a decision is separate from the time and effort necessary to bring your cursor to your target. Keep in mind that the location of the menu (screen edge or center of the screen) is important.

• Stuff like this is fascinatingly confusing. Is trying to apply Fitts to UI an academia or industry thing? I only see people using graphical size and distance. Is reach built-in? How mouses move in one direction exponentially easier and more accurately than in the other because of how our hands work? – moot Apr 19 '18 at 20:41
• Fitts' Law is interesting to know but I don't "use" it when sketching out a design. In fact I never think about it when working on a design. I would say it's important in the physical world - it also explains why it's harder to select a small item in the middle of the screen as opposed to the edge of the screen, – Mayo Apr 19 '18 at 20:55
• "The user may have to pick the mouse up and place it back down again." And it takes time to switch from keyboard to mouse and to re-orient, as reflected in Keystroke-Level Models. – Ken Mohnkern Apr 20 '18 at 13:59
• One common use of Fitts' Law is to include as much space in a click target as possible. For example, in a product grid, rather than just linking the product name to the details page, link the photo, the description, the whole bounding container. – Ken Mohnkern Apr 20 '18 at 14:01
• @KenMohnkern - absolutely. – Mayo Apr 20 '18 at 14:30