A fast lens, such as Canon’s 85mm f1.2L II USM, can do wonders in terms of improving noise levels in indoor sports photos. When shooting wide open, at f/1.2, I can regularly use the shutter speed of about 1/800 sec and an ISO of 8000 in very dim light during basketball games or kendo events. For comparison, the same shutter speed at f/2.8 pushes the ISO to 16500 or even 25000. For a Canon EOS-1D X camera body, this increase in the ISO means a step from minimal noise levels to those that require dedicated post-processing.
The problem with the 85mm f1.2L II USM lens is that it focusses very slowly. Its optical elements are so massive that even thought the camera’s autofocus system sends correct commands, it takes considerable time for the motors to physically move the glass into position. The 70-200mm f/2.8L IS II USM lens, on the other hand, focusses lightning-fast, particularly if the subject is shot from farther away, at the focal length of 200 mm (compared to 85 mm.)
The advantage of shooting from far away using a longer focal length is that an equivalent motion of the subject causes smaller apparent displacement on the sensor of the camera (think about the classical example of an airplane appearing to move very slowly when viewed from far away, while a bicyclist at 1 m away shooting through your field of view in a fraction of a second.) Because the apparent displacement is small, the optics has to be only slightly adjusted to track the subject.
The bottom line is that a longer but slower (higher minimum f-number) lens will produce noisier images, but will yield a higher success rate in terms of the number of sharp images. Therefore, for a critical photo shoot, I would start with the 70-200mm f/2.8L IS II USM lens, and after making sure that I have captured a few sharp images, I would switch to the 85mm f1.2L II USM to potentially get one or two spectacular ones.