The TD only computes stats for players who are in your player database.
Because tournaments are saved in individual files, the TD has to know that "Jim" from tournament 1 is the same player as "Jim" from tournament 2. Name only doesn't work, because people tend to put different names, or different spellings, or nicknames sometimes and real names other times, or first names with initials, or first and last names, etc, etc, the list goes on. By putting player "Jim" in your database and then adding him to each tournament, internally the TD knows it is the same player. It can then generate statistics about this player over multiple tournaments.
So if you are passing tournaments around from one computer to another, you'll need to make sure your databases have the same players in them. If you are starting from scratch, the easiest thing to do is to backup your database on one computer and then restore it on the other.
This works fine at first, but eventually a tournament will be played on one computer and a new player added to the database. Then when you open that tournament on the other computer, the new player will not be in THAT computer's database. How do you synchronize them? Well, you don't just go to the Database tab and add a new player by the same name, because the TD will not recognize it as the "same" player. Instead, load the tournament and go to the Players tab. The new player will display in italics because he/she is not in the database. Just press the Add All to DB button and make sure the player(s) is/are selected, then press OK. Now you have the same player added on computer 1 in the database on computer 2.
