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Having the reflector pushed out farther from the point of rotation (the base of your neck) allows for farther travel within the same movement. As the dot travels more, it is recorded as moving across more pixels within the camera. More pixels being used to calculate your position translates to a higher degree of accuracy.

ok, sounds rational, thanks

http://www.naturalpoint.com/smartnav/st ... ories.html says "With built-in tracking surfaces on the brim and back, the SmartNav Hat improves the ease-of-use and accuracy of your SmartNav.". Why would using the SmartNAV hat improve accuracy?