Chess uses the constant of 400 based on a suggestion by Elo that a difference of 200 between players should correspond with an expected score of 0.75 for the better player. 400 is a round number that achieves a value close to that (.76). Other than that preference it looks like that constant is rather arbitrary.

In American college basketball, there are 353 Division 1 Basketball teams that play approximately 30 games each year prior to postseason tournaments. Each team belongs to a conference which acts as a league where teams in a similar geographic area play against each other. There are 32 conferences in Division 1 basketball. So, yeah college basketball has a lot of teams because it isn't a traditional league, but a group of 32 "leagues" where the teams that all play against each other in the first half of the season and then play within their conference the second half of the season.