Game stats can be entered by either an administrator or a coach (a coach can only enter stats for players who are on the team that he or she coaches). Additionally, stats can only be entered for games that have already passed.
If you don't want coaches to enter game scores, you can change the permissions of coaches by navigating in the Admin page to Setup->Organization->League(Admin tab) and select the tab named “Coach score/statistics entry”. Simply change the option allowing coaches to enter scores to yes/no.
Tags: admin, coach, game, permission, player, score, stat, statistic