Panning is a technique used to create the illusion of motion by making a subject appear stationary against a blurred background. It's a bit like shooting clay targets with a gun; the camera is moved in an arc with the subject, keeping it in the same spot in the viewfinder during an exposure which is long enough to blur the background as the object travels across it.

The key factors in determining the speed to set the shutter when panning are the speed of the object, and the distance it travels during the exposure relative to the field of view of the lens capturing it, and how far the camera is from it.

In a wide shot the movement of the subject relative to the overall field of view really isn't that much so there will not be much blur of the background as the camera tracks a moving subject. The same shot at the same shutter speed but with a telephoto that filled the frame more with the subject will blur more in the direction of travel because the camera will pan faster relative to the background to keep the subject in the same position in the viewfinder during the exposure.

It's a bit counter--intuitive perhaps, but it relates to the arc of motion the lens must track to cover the distance the object moves during the exposure. In a wide shot the distance the subject covers is only a small percentage of the total field-of-view (FOV) of the lens so as it is panned with the action it will describe a small arc. But with a close-up crop the distance the subject travels during the exposure may be as great or greater than the FOV requiring the lens to be moved in a wider arc to keep in the same place in the frame. For the same exposure time, the wider the arc the lens travels more the subject blurs.

Something else to consider when panning and trying to keep the subject sharp...

Because the moving action is typically on a linear plane but the camera is rotating around a fixed point (the neck of the photographer) the exposure of the subject and the background will have a rotary component which is proportional to the arc of the lens. The only exception would be a camera placed in the center of a rotating object like a playground merry-go-round shooting outward where the relationship of camera to subject is fixed and only the background moves in a circle relative to the camera.

Thus the distance from the subject is a factor in how sharp the subject will appear. Consider that a shot can be framed identically with different focal lengths. As the FL is increased the distance to the subject increases an the arc of travel during a panning exposure - time being equal - decreases. So to get the best blurred background with the least amount of rotary motion induced blur in the subject you want to shoot with a telephoto which puts you far away and keep the subject relatively large as a percentage of the FOV.

But more distance also means there will be a smaller arc, which means and less background blur than shooting closer with a shorter FL! The solution to this dilemma is: Shoot from as far away as possible to keep the subject sharpest with the slowest possible speed to blur the background, keeping the subject large relative to the FOV.

One of the more interesting panning shots I've ever seen was posted in a DPR forum last year. It was a photo of a taken from a moving train. Everything in the photo had a rotary blur except a man standing on the side of the track in the dead center of the frame. His body was only slightly blurred, and this face was as tack sharp as if taken at 1/1000 sec. How was that possible? The guy in the center had turned his head to watch the photographer taking the photo come and go at the exact same speed the train was moving and the photographer had panned the camera. Relative to the camera his face was stationary during the entire exposure. Because the photographer had placed him in the center of the viewfinder his body was near the axis of rotation and only slightly blurred and wider than normal.

Finally, focal plane shutters will induce distortion in panned shots.

Remember that the shutter curtains move vertically across the frame. That means the exposure begins and ends at slightly different times at the top and bottom of the frame. That will distort vertical lines or regular shapes moving sideways. For example, wheels of vehicles will appear oval instead of round, slanting forward in the direction of shutter curtain travel. It can be more exaggerated in panned shots where the subject is kept in the same place in the frame because the exposure times are longer.