I heared the best way to shoot basket ball action at the critical movements you want to capture is 1/350 s
Ilkka shots his figure scaters that seem to move faster at 1/1250 to 1/1600s
My understanding is that every sport requires its own critical shutter speed with respect to the movement.
It also depends on final presentation medium and size, and how much blur the viewer will tolerate. Some photographers use slow speeds intentionally to create a sense of movement. I have never been any good in this technique.
When the skater spins really fast you can see a bit of blur even at 1/1600s. But I find 1/1250s to 1/1600s a good compromise for singles. For couples 1/500s tends to include some noticeable movement blur at times but may still be acceptable. I think 1/800s is a pretty good compromise for pairs and couples. I suppose if one were using 600mm to take a close-up of a throw, then very fast shutter speeds would be useful again.
The pair dance is not so great at f/1.4 or f/2.0 because only one of the faces is sharp and the other is not blurred enough to make is look intentional, so f/2.8 or f/4.0 are required which means higher ISO or flash if possible in the situation....
It’s more a question that the couple spin around each other and block each other from the camera’s view frequently, and to use wide apertures would be very demanding in terms of moving the focus point around. I felt for ice dance, 1/800s, f/2.8 and ISO 1600 worked well with group area AF on the subject facing the camera. I started with 1/1600s, f/4 and ISO 5000 at first. This was ok and allowed me to use less specific AF area mode (auto area) which makes it easier to shoot and concentrate more on composition and timing. But I prefer the results at f/2.8 1/800s and ISO 1600 as long as I was willing to move the group area around for more specific focus. Nicer image quality and background separation but still acceptable depth of field in most cases as long as some manual control on the focus area was exercised. With auto area AF, shooting at f/2.8 would at times result in focus on the back of the head (if the other skater whose face was towards the camera but further from the cameras), and I prefer f/4 when using that mode. Visually f/2.8 looks good to my eye in this situation but it requires more specific instructions on AF by the photographer. I have shot ice dancers even at f/2 in the past but think either 2.8 or 4 is easier to shoot and may be more equal to the two skaters.
At the world championships (in Helsinki) there were quite many long lenses at the far ends of the arena. I noticed that many shooters used a long lens to shoot the skater at the opposite end of the rink and they were using high fps. As the skaters got closer the cameras went quiet. I’m not sure but I suspect they chose to shoot that way because when the subjects are far away and a long lens is used, there is more time to shoot (when they are close the time window where they are the right size is often short), also subject isolation from background is more effective and finally the rapid fire sound from multiple cameras shooting long bursts would not be so loud to the skater. I personally like the perspective of the skater at physically close distance - it makes the subjects feel more 3D and closer in the images, and lower ISO can be used with shorter lenses.
Flash photography is forbidden at figure skating competitions for safety reasons (the skater could be momentarily blinded by the flash and this could result in injury).