From what I have experienced and seen, the number of people that APPLY remains somewhat constant over short periods of time. It is dependant on PR, military popularity, etc. I am sure there is someone on here that has a better idea of what causes people to apply.
What I can tell you is that the number of people that are ACCEPTED or SLOTTED varies GREATLY. Especially in these times. For example, my NRD slotted 80 pilots in the BDCP program last FY. This FY, they have only slotted 2, and we are somewhat far in to the FY. They are on track to slot a total of 9 if they keep this pace up.
There are two words that you should know and understand like the back of your hand that describe your "chances" of getting slotted. TIMING & NUMBERS. Or synonymously Just as vette said, "the needs of the navy."
Stay after your dreams. I was shooting for a flight slot, but it just isn't happening right now (denied). The slots are too few. I plan on applying for a redesignation in a year or so, if that fails, I will try to redesignate at OCS, if that doesn't work, I will gladly serve the navy as a supply officer (what i am currently slotted for) for four years. After that, I will be 26 years old (still young enough to go to flight training), and will apply for a lateral transfer.
I am hoping that out of those 4 opportunities, timing and numbers will be on my side. If you have the same "keep trying" mentality, you will get what you want.
Many of these selected SNFO's and SNA's had to apply more than once (some more than twice) to get in. Don't let competition affect you at all. You are in charge of your life. Go for it, and MAKE IT HAPPEN.