Duplicate Fields Problem in My Tables

I'm working on a DB for statistics for a small Hockey League. We've been
using Excel, but it's getting more and more unwieldy. I've read elsewhere in
this forum that Excel users usually have trouble switching to Access, and I'm
here to tell you it is true! Oh, well, here's what I have so far.

1. A Members table for storing names, addresses, etc.
2. A Roster table for members who are actively playing in the current
season, including team name, jersey number, etc.
3. A Stats table for saving the stats for each player for every game they
play, goals, assists, team, game, etc.

The problem is that all the data in the Roster table has to be duplicated in
the Stats table because Stats remembers everything uniquely and permanently,
while Roster changes from season to season. I understand that having
duplicate fields in different tables is poor design, and this approach has
certainly bogged down for me. I've searched the forum and googled this
issue, but I'm either asking the wrong question or not recognizing the answer
when I read it. Any help will be greatly appreciated. Thanks!