I try to avoid possessives in formal writing, but in some cases the brevity is necessary. With a plural possessive construction such as
the players' gloves
is it ambiguous grammatically whether this refers to either (a) a single pair of gloves owned by all of the players, or (b) the individual pair of gloves owned by each player?
Hopefully the reader would understand the meaning to be the latter, but it always nags me that there could be a misunderstanding here.