Felt like delving into the numbers. Found a thread on Reddit. Contrast these two posts and you will find the truth, I think.
All of these numbers we're looking at are 2015 numbers. Just so people in the future aren't confused, because tomorrow we'll get the data tables for 2016 from the NRMP.
The two posts are saying the exact same thing, although looking at it in two different directions.
The first post:
There are 27K ACGME positions + 3K AOA positions = 30K positions total.
There are 18K AMGs + 5K DO's = 23K US Grads
Therefore, there are 7K extra spots, so plenty of room.
This math ignores the 1.5K Previous grads. But even if you still include them, plenty of room.
The second post:
There are 27K ACGME positions. They ignore the 3K AOA positions.
There are 18K AMG's + 3K DO's in the ACGME match. They ignore the 2K DO's that participate in the AOA match.
The two oversights above just about cancel out each other.
Therefore, in the ACGME match alone, there are 27K spots - 21K applicants = 6K spots left.
But, then there are 5K US IMG's and 7K FMG's. So if you want to give spots to all the US IMG's, then you can't let the FMG's have much of anything.
The scary number in the second post is that 2561 US grads get no spots. That number is the US seniors (1093) + DO's (610) + US prior grads (858) who don't match. This is misleading. All of these numbers are pre-SOAP. Of those 1000 US grads, about 600 get a spot in SOAP. The DO's often get an AOA spot that has remained unfilled. I don't know about the prior grads -- some may need a spot (i.e. only completed a PGY-1 and need further training), and some may just want a spot (already training in something, trying to get a spot in something else). In any case, many of these students get a spot, not measured in these match data.
To be fair, all of this is based upon PGY-1 slots available. Some of those PGY-1 slots are prelim only. To be completely kosher about it, we should subtract out the sum of Advanced and Reserved spots minus the number of prelim only spots, to get the number of "terminal residency" spots. In 2015, there were about 3K A + R spots combined, and about 4K IM prelim, GS prelim, and TY's combined. So, there really were about 26K "true" training spots available in the NRMP, and 29K in all matches combined.
This also ignores the SF match, although the number of spots there is very small and won't make much of a difference.