Photographing sports requires that a great majority of your shooting with have you focused on trying to fill the frame with your subject as much as possible. There are times when you will photograph subject wide and that is important but most of your time will be capturing subjects that won’t be as close to you and that you cannon direct in your favor. So having a good understanding of the sport you are covering, what your general proximity will be to the subject and then making an assessment of how capable that lens will be of achieving those things is most important. For field sports like football, the ideal is to have at least 300mm of focal length between your lens millimeter and also the crop ratio in your camera. Even more ideal for field sports is between 400mm and 500mm. This could be accomplished by purchasing a very expensive prime lens or it could be from putting a 75-300mm lens on a 1.5 crop sensor camera. Despite some of the potential limitations this will still get you in the range that you need to be able to capture the action at a distance close enough to make a usable frame with cropping if needed. If you are covering basketball or indoor gymnastics, then your range can be much more limited because those sports don’t require really long millimeter lenses for general coverage. For basketball I generally use lenses from the 24mm to 200mm range and occasionally a 300mm lens for action at the other side of the court. So the first consideration in purchasing a lens for sports should be if this lens and camera combination will allow me to get close enough (or far away enough) from the action with regularity, even if/when my mobility is limited.
While lens image quality can be somewhat subjective, there are some general quality observations that can be made about certain lenses and there is a universal sort of standard for judging them. Sharpness around the frame, color rendition, pleasing contrast etc. are all things that factor into how our final images will render when using certain lenses. Certain lenses will just be natural sharper, adjust better to challenging light conditions and render an overall more pleasing image in the same scenario with the same settings and camera body. The natural assumption is often that the more expensive glass is the more optimal glass but this is not always factual. There are a number of lenses that are able to hold their own in terms of image quality despite having a much lower price tag than the traditionally top of the line lenses in the company lineup. Doing your homework on certain lenses in terms of reading multiple reviews, asking other sports photographers about their experiences and (of course) testing them in the actual fields to compare is the best way to go.