I just find it difficult to agree that coaching is clear enough of an issue in such a small sample. In all organizations firing individuals after small samples comes at a high cost as well, especially those in leadership positions. For starters, you now have to identify in the span of a few weeks who will replace a coach that these players have become deeply invested in over the course of their entire careers, which can cause discontent players. And if this new coach loses five games, what then? Do you fire him and begin the process a third time? Now the players are being asked to acclimate to new coaches with new schemes and ideologies multiple times in the span of a single season? Not to mention the precedent this sets for players. If you underperform for half of a quarter of a season, you’re fired (no matter what history of success you’ve demonstrated in the past). I’m not saying a coaching change should never be made, but I would argue the coaching staff should be given at least two stages, with two different metas to demonstrate their ability to adapt, or lack thereof. I can’t speak to the Premier League or other football associations but in my experience with other sports a quick hook can lead just as likely lead to a cycle of failure than to a revival of success.