3 answers
Robert’s Answer
Both comments above are spot on. You will be paid significantly less working in sports but the connections and experience you can gain are invaluable. You'll most likely work nights and weekends and have little free-time, but you get to work in an environment that you have a passion for.
A Bachelor's Degree in Sports Management, Communications or Marketing are the areas that you would want to look into.
Best of luck.
Sean’s Answer
The most difficult part is that there are 10 million other folks who are the same as you. They played sports growing up and want to make it a career. The sad reality for people to get involved in sports is the only entry level positions are either in season ticket sales (commission only) or as a Junior Scout (work for free).
Those that are exceptions to the rule are people who played professionally. Then maybe they can get a job as an analyst/etc.
The other way to get into sports is through a functional area like marketing/finance/technology/PR/etc. These positions exist and are available however, because everyone wants to work in sports they pay significantly less than positions at non-sports companies. The demand is so high for teams like the Yankees/Red Sox/etc. they don't need to pay market value for people.
Lindsay’s Answer
I technically worked in Sports Marketing, or as it is generally referred to here: the Outdoor Industry. The hardest part about this field is that it is generally extremely low paying and has a high turnover rate. I assume this is because you generally find "hubs" of these opportunities in areas that are known for outdoor recreation. This means that you will find an endless stream of people willing to work for you for very, very little and who are willing to work in abusive conditions. TL;DR version: everyone wants to get in, and employers know this.