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Trying to understand how ball bearings work

I understand the basic mechanics behind ball bearings and how they allow
rotation between two surfaces, one usually being fixed.  Here's the basic
mechanism I'm referring to:

http://en.wikipedia.org/wiki/File:BallBearing.gif

What has me puzzled is this - the inner surface (or "race") where the ball
bearings make contact usually has a smaller diameter and circumference with
respect to the outer surface.  So if the ball were moved against the inner
surface without any slippage, it would seem that for every rotation made by
the ball, a larger inner surface area would be covered, in degrees, than for
the outer surface.  The ball is turning just as fast on the inside as the
outside, so in order to cover the same number of degrees on the outer
surface area, it would seem some slippage would be inevitable in order to
cover the same number of degrees.

Another way to visualize the concept I'm envisioning would be to imagine
each circle as string, "cutting" them somewhere and then stretching them
out - the outer "ring" would be longer than the inner one, so if you were to
take a ball bearing and roll it along the length of each, there would
naturally be more total ball rotations along the longer string.  This has me
wondering whether there is an element of slippage that is unavoidable within
the ball bearing casing, albeit at a reduced rate compared to simpler
bearing mechanisms such as sleeves, for instance.

I'm not mechanically inclined, so I'd be very interested in hearing opinions
from people with more knowledge on the subject.

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