The biggest advantage of radial or pie menus is their speed. To quote this article.
Radial Menus Are Fast
Radial menus are faster to access than list-based menus in every kind
of pointer-based UI, including cursor, stylus, and touch. One big part
of that is because every option is spaced at the same distance from
the pointer. That’s classic Fitts’ Law: the closer the target and the
bigger it is, the easier and faster it is to hit.
Even better: you get faster with radial menus over time, because they
take advantage of muscle memory in a way that list-based menus cannot.
Radial menus are essentially gesture-based: touch-swipe-release.
That’s why some call radial menus “marker menus”: it’s like making a
mark on the screen. Swiping to 2 o’clock has one meaning, and swiping
to 6 o’clock another. Like all physical actions—playing an instrument,
typing a keyboard, serving a tennis ball—gestures get embedded in
muscle memory, which is faster to access than visual memory. Tap-swipe
is faster than scanning for an item in a linear list, just like
touch-typing is faster than hunt-and-peck.
The same article references two rather old research papers which have this to say on the merits of radial selections
Research paper 1 : Do note this paper is no longer available on the net hence there is no way to validate if the reference is correct.To quote the article
The research on this has been in the can for nearly 25 years. A 1988
study did the comparison and found that for a specific test of
eight-item lists, users were faster with radial menus than linear
ones. And it turns out that speed only improves.
Research paper (2) - User Learning and Performance with Marking Menus : This is the article linked in the earlier extract and the summary is given below
The more you use radial menus, the faster you become. That was borne
out in a 1994 study by Bill Buxton and Gordon Kurtenbach, who tested
radial-menu speed with a stylus. Over time, they found that expert
users stopped looking at the menu at all. They no longer needed the
visual cues and went entirely “blind,” marking the screen with
gestures, or “marks,” instead of pecking at buttons:
Using a mark on average was 3.5 times faster than selection using the menu. … A user begins by using the menu, but, with practice,
graduates to making marks. Users reported that marking was relatively
error free and empirical data showed marking was substantially faster
than using the menu. … Marking menus, however, are not appropiate when
the list of items changes dynamically. In this situation, users can
still use the menus but will never graduate to using marks since menu
item locations change.
There have also been multiple usability tests conducted on the usability of radial menus as quoted in this article
Jack Callahan's study compares the seek time and error rates in pies
versus linear menus. There is a hypothesis known as Fitt's law, which
states that the "seek time" required to point the cursor at the target
depends on the target's area and distance. The wedge-shaped slices of
a pie menu are all large and close to the cursor, so Fitt's law
predicts good times for pie menus. In comparison, the rectangular
target areas of a traditional linear menu are small, and each is
placed at a different distance from the starting location.
Callahan's controlled experiment supports the result predicted by
Fitt's law. Three types of eight-item menu task groupings were used:
Pie tasks (North, NE, East, and so on), linear tasks (First, Second,
Third, and so on), and unclassified tasks (Center, Bold, Italic, and
so on). Subjects with little or no mouse experience were presented
menus in both linear and pie formats, and told to make a certain
selection from each. Those subjects uising pie menus were able to make
selection significantly faster and with fewer errors for all three
The fewer the items, the faster and more reliable pie menus are,
because of their bigger slices. But other factors contribute to their
efficiency. Pies with an even number of items are symmetric, so the
directional angles are convenient to remember and articulate. Certain
numbers of items work well with various metaphors, such as a clock, an
on/off switch, or a compass. Eight-item pies are optimal for many
tasks: They're symmetric, evenly divisible along vertical, horizontal,
and diagonal axes, and have distinct, well-known directions.
Gordon Kurtenbach carried out an experiment comparing pie menus with
different visual feedback styles, numbers of slices, and input
devices. One interesting result was that menus with an even number of
items were generally better than those with odd numbers. Also, menus
with eight items were especially fast and easy to learn, because of
their primary and secondary compass directions. Another result of
Kurtenbach's experiment was that, with regard to speed and accuracy,
pens were better than mice, and mice were better than trackballs.