Great question and observation!

I'm not sure this is exactly what you're getting at, but it's related:

One of Ted Selker's students at MIT Media Lab came up with an idea of (normal linear) menus that "second guess" the user's favorite item, by measuring how much time they spend in each item, and guess their second favorite choice as the non-selected item they spent the most time pointing at.

I thought it was such an insidiously simple yet evil idea that I had to try implementing it with pie menus.

This video shows the Internet Explorer JavaScript ActiveX Behavior control running in Internet Explorer version 5. (Please excuse the ugly HTML and XML and XSLT!)

At 4:25 there's a demo of "Pie Menu Second Choice Guessing". The basic idea could be applied to any menus, but you're right that people tend to browse around menus by pointing at the items, and that definitely applies to pie menus.

But with linear menu, once you've browsed down to the bottom item, you've gone a long way in the same direction, so you're far away from the first item, and have to move back up to select it.

But with pie menus, you only go a little way in each direction, which cancels out and brings you back to where you started, and you stay near the center adjacent to all the items, so it's easy to change your mind and reselect any item without moving your mouse very far.

In other computer science words: Linear menus are O(n), while pie menus are O(1).

JavaScript Pie Menus:
Pie menus for JavaScript on Internet Explorer version 5, configured in XML, rendered with dynamic HTML, by Don Hopkins.

https://youtu.be/R5k4gJK-aWw?t=4m25s

>This was inspired by some research at MIT Media Labs. This is a demonstration of pie menus that try to guess what your second choice would be. So when I click up, it allows me to select my favorite color. Let me zoom in here. Well, I think it's blue... No, red! Ok. So it says: "I think your favorite color is red, but I guess your second favorite color is blue." And that's based on the fact that when I popped it up, even though I selected red, I spent the most time selecting blue. People tend to browse pie menus like this, looking at things, and when they find what they like, they click it, but then they'll pause to consider things. So I can click up the menu and go: Yellow? Oh, no. I'll just cancel it. And now it's guessing that my favorite color is yellow, even though I didn't select one. This is a simple elegant idea that I applied to pie menus, and it could be applied to a lot of other things, and used for e-commerce and art galleries or whatever.

If you're not living in 1999, you might prefer the jQuery pie menus that run in any browser. You could easily implement the "second choice" feature without modifying the code by using tracking callbacks, which are all documented here:

http://www.donhopkins.com/mediawiki/index.php/JQuery_Pie_Men...

And here's the source code:

https://github.com/SimHacker/jquery-pie

I don't know what other menu implementations give you callbacks for changing the selected item before you select one, as well as continuous pointer tracking (passing the current item, direction and distance), but pie menus definitely should.

Callbacks like that are very useful for researchers evaluating and comparing menu performance. And also for developers, who can provide nice application specific feedback in the menu or on the page.

Callbacks can use the distance as a parameter, for selecting between multiple items in the slice, or pulling out a continuous value like a "slider", changing the font size, selecting a hue and saturation with direction and distance (with an outer ring you can dip into to set the brightness), etc.

https://cdn-images-1.medium.com/max/600/0*ngAv4gwWUcFCfQeJ.g...

I hate jQuery as much as the next person, so I'm sorry I haven't implemented them in a trendier more modern framework yet, but I'm having a hard time deciding which one, and they all seem to either suck or not have a very big following. I'm open to suggestions!

It's even better for menus to display more information during browsing when you point at each item (including for disabled items, telling you WHY they're disabled and WHAT to do to enable them, instead of mysteriously ignoring you and not selecting), and hide (or shrink or make translucent) unselected items, so you don't have to put so much cluttered distracting information about every item on the screen at the same time.

These PyGTK SimCity pie menus show icons only (which correspond to the icons on the tool pallet), but show titles when you point at them, and a description of the menu when it pops up and nothing is selected, along the bottom of the menu.

SimCity Tools Static Pie Menu with “Build” Selected:

https://cdn-images-1.medium.com/max/600/0*-x3kctcC1nbZeT9H.p...

SimCity Build Static Pie Menu with “Park” Selected:

https://cdn-images-1.medium.com/max/600/0*I6jUSzJFSTeiJ_38.p...