Odds of Getting In
Judging from the amount of students enrolled in film schools around the country, as well as the amount of independent films being entered into festivals every year, the number of people who try to break into directing is pretty high. And if you define "getting in" as simply making a movie, then the odds would be pretty good.
If you define "getting in" as making a living from Directing, or as making studio films, then that number shrinks drastically. The number of movies being made has fallen every year for the last decade. The shift to digital cameras and home computer-based editing software has also made it much easier to make your first film—meaning that the competition for the paying gigs is very high. The best advice is to get as good as you can possibly get and then network. Meet people. Make them like you.
Or, better yet, make them owe you something.