Another curious pattern is where the rightmost Rook starts on the e-file. There are 102 such positions, shown in the following table (the second column is the count of chess960 positions that share that pattern).
These patterns are special because castling O-O displaces the Rook from the central e-file to the off-center f-file, at the risk of undeveloping it. From the f-file, it might have to be moved back to its start square by Rf1-e1 (or Rf8-e8). When this happens, castling O-O actually loses a tempo. In cases where the Rook is already performing an important duty, the move O-O might even be too dangerous to consider.
This quirk doesn't happen with castling O-O-O. When the Rook starts on the d-file, as in the following patterns, the O-O-O move leaves the Rook in place, where it is often already active.
Considerations like these make the castling move so important to chess960. That's why I always consider the castling options when evaluating a new start position.