In order to prevent this from happening, you can specify that statistics should only be displayed for players who have played more than a certain percentage of the total number of games that have been played in a season. Note that the "total number of games" is taken to mean the highest number of games played by any one team in the season (so if "Team A" has played 6 games, but "Team B" has played 8 games, the total number of games is taken to be 8).
To turn on this restriction, do the following:
1) Log in to the online control panel
2) Click Leagues
4) Click Fixtures
5) Click "Season Statistics"
6) In the box next to "Display percentage threshold", enter the percentage of games that a player must have played in before their stats will be displayed
7) At the bottom of the page, click "Save"
Now, only those players who have played more than that percentage of games will be displayed in the statistics list. For example, if the maximum number of games that any team in the league has played is 8, and you set the Display percentage threshold to 50%, only players who have played in 4 or more games will be displayed in the statistics lists.