Comparing two ordered lists
What about a model stating that you have two vectors of size N (where N is the total number of players, maybe unknown to us) where each element belongs to a space of {B,S} sequences, maybe empty. If you then define a distance function between two arbitrary sequences (say, normalized Levenshtein distance for two non-empty ones and some fixed cost when one is missing), you can define cosine similarity between the vectors.

(Obviously, you just consider your sequence a compact representation of sparse vector in this case.)