Not only can they run !!!
They dodge, hide, back-track, flush up between your legs and play the wind. When they flush, they make one heck of a noise and as they fly away, they will kackle/crow at you. Love to hunt them, especially the "long-Spurs" ...
Try this shot. Pheasant flushes up a foot on front of you, against the wind. Then hangs there while you are leading with your first shot. Does a 180, catches the wind while you take your second and third shot. No time for a fourth shot. Bye, Bye !!! .....
Now, flushing up between your legs is a real treat. They explode straight up, out of the cover and by the time you regain your balance, it's too late. Bye, Bye !!...
Be Safe !!!!