Let's talk about shooting action sports under the lights as doing such is fraught with challenges. The big problem is of course the lights themselves. They are seldom bright enough, usually light the field unevenly, typically lack a full light spectrum and often have a nasty flicker that times horribly with the frame rate of your DSLR.
Unless you have the means to have ideal lighting installed, you need to deal with what you are given to work with. And for some reason unknown to me, most consider photography secondary to the sport being contested.
I usually want a shutter speed of 1/1250 or faster to stop field sports action with a 400mm lens. Even with Canon's widest aperture 400mm lens mounted, the conditions on this field required ISO 12800 for the shutter speed I desired. This resulting image is not an amazing capture, but impressive for the conditions it was captured in.