On another note, I think I may have understated the number of teams that have the minimum number of players at a position. I just re-ran the query and came up with 1236 of them, 811 of which are 18-man teams. That is a lot of poorly constructed teams. Also surprisingly, 11 of the remaining 217 30-man teams (a little more than 5%) fall into this boat. These include 21-kicker guy and 17-defense guy.
Weird tidbit for this morning... I was just flagging all the "junk" entries in the database, and I thought I had some kind of glitch where I was double-counting the rows because I kept coming up with 2472. I couldn't figure out what the problem was, though. Then I remembered that I had added all the eliminated entries since the last time I ran this, and as it turns out, there were exactly 1236 junk entries that have already been eliminated. That is, there were 2472 junk entries to start the contest, and exactly half of them have been eliminated so far. Not very interesting, I suppose, but I just thought it was strange.