Odds of Hanging On
Assuming no injuries or financial issues take you out of the game prematurely, you'll last half a dozen years to a couple decades.
Statistically, you're more likely to play only one season than you are to last twenty seasons. About one in five of the lucky rookies who actually steps foot on a Major League Baseball field will play only one season in the majors. Better recruitment processes, sports training, and medicine have given players another year or two. Only about one percent of players last the full twenty.
Now take that number, and compare it to how long most people work in their professions, and you can see why being a baseball player isn't the best long-term career choice. You won't leave baseball because you have a great new idea for a Silicon Valley startup. The majority of players leave because they have to, either forced out by injuries or lapsed contracts.
Surprisingly, there aren't a whole lot of alternative jobs out there for people who spent most of their twenties and thirties hitting balls and running around bases.