Odds of Getting In
Let's start by examining a team physician's relationship with the team he or she supports. On the high school level, the sports doc is probably playing an advisory role, evaluating and treating players as needed while he or she maintains a private practice. In this case, you might be the coach's buddy, the guy who approached the athletic director first, or simply the guy who can respond to an injury emergency before anyone else. Your odds of getting this gig depend on your ability to learn about the system and find a way to make it work for you.
Now we move on to college sports programs, which are a lot more structured and often have more staff support positions. You might encounter some of the same "it's who you know" factors prevalent in high school sports, but now a budget variable rears its ugly head, too. At larger schools with bigger budgets, it's entirely possible the school has a staff sports physician who supports all the school's athletes. Smaller, less-affluent athletic programs might work with a specific on-call physician, similar to a high school sports program scenario. Again, you've got to get the lay of the land before you can determine your spot in the game.
Finally, it's time to talk about pro sports physicians, who quite literally operate in an alternate universe. Each team probably has its own version of the following scheme, er…business arrangement. Let's say a pro basketball team locks in a physicians' practice to be the team's only medical service provider. Sounds like a good deal for both parties, right? Well, also consider that the physicians' group usually has another contract that allows them to promote themselves as the official team physicians. Obviously, lots of money changes hands to make all this happen. If you're a lucky member of that physicians' group, you're golden. Otherwise, you need to scramble around for another pro team to hook up with.