Brainteaser 1567: How many teams?

From The Sunday Times, 20th September 1992 [link]

The teams in our local football league each play each of the others once in a season, earning three points for a win and one point for a draw. After the last Saturday of the season (when all the teams had played one game that day) I worked out the league table (with the teams in alphabetical order). I then consistently replaced digits in the table by letters, using different letters for different digits.

Here is part of that table, showing some of the entries in three of the rows:

What is the number of teams in the league? And what is the number TEAMS?

This puzzle was selected for the book Brainteasers (2002, edited by Victor Bryant). The wording here is taken from the book and was only slightly changed from the original puzzle.