Odds of Getting In
Until a mad scientist finally invents that machine that prevents us from aging, we're all going to get old. This is good primarily because it means that eventually we'll all have the opportunity to use motorized scooters. It's also good you because it means we'll always need geriatricians. That, combined with the shortage of geriatricians in America, means your odds of getting into this field are pretty good (source).
It's estimated that between 2010 and 2030 one in five Americans will be over the age of sixty-five and need geriatric care. But as of 2013 there were only about 7,000 registered geriatricians in America (source). You don't need to be a rocket scientist to know that there are going to be a whole lot of old people, and very few doctors for 'em.
The downside is that it's a little difficult to break into…unless you consider medical school a cakewalk.