Good question. I calculate a 95% confidence interval for each player's win rate and rank players by their lower bound. Why? Say Player 1 has a record of 20-3, and Player 2 has a record of 1-0. I think it's only fair to rank Player 1 higher until Player 2 plays more games. The method mentioned above accomplishes exactly this. For more info read this.
Make sure you always log in with the same information. If you originally logged in with your Google account, your statistics will be linked to that account. If you log in the second time with a different social media account, the website will treat you as a new user.