Well, maybe not a single formula, but an approach you can take.
Set up a table with the list of teams in column A starting in A2.
Highlight A2:A20 and click <copy>, then move the cursor to B1 and use
Paste Special | Transpose to get the same list in the top row. This
table represents the fixtures, with teams from column A playing teams
in row 1. Usually HOME teams are in column A and AWAY teams in row 1,
but this may not apply if you are all playing at one venue.
Clearly, Team A cannot play itself, nor can Team B etc, so the leading
diagonal of this table is not used (marked with x below):
A B C D E F etc
A x
B x
C x
D x
E x
F x
etc
Then you can just fill in the blanks to represent games, ensuring that
no team plays more than 10 times - you can a COUNTIF formula in V2 to
count the number of matches on that row and for column B to get the
total matches for team A.
Hope this helps.
Pete