According to the Sundance Institute, the total number of U.S. feature films submitted to the festival was 1,920 for the 2010 festival, 1,905 for the 2009 festival, and 2,021 for 2008. Taking an average of these three years we arrive at 1,949.
At any one time, there are about 1,949 U.S. films waiting to be picked up for distribution. This assumes, that all applicants to Sundance have no distribution already in place.
To see how many of these films are distributed. Films with no theatrical distribution in place prior to financing (i.e., most of the films applying to Sundance) end up opening at 1,000 domestic theaters or less, if they open theatrically at all. Hence, a good a place to turn for some rate of success analysis is this pool of limited opening films (specialty films)
The definition a specialty film is any film that opened theatrically at 1,000 domestic venues or fewer, “domestic” meaning the U.S. and Canada.