The players are carrying out the manager's systems and strategy. Of course they have their own input and abilities, good days, bad days, and they get dropped all the time. There is also a possibility that the manager and players, or more likely a couple of key players, are at loggerheads or just don't get on and are thus not giving their all, sort of "work to rule", ie go through the motions, get paid, go home etc. A chairman will take into account all of the above and conclude that the manager has to go. There are many examples of teams being turned around even in half a season by the introduction of a new manager that the players respect, understand and will put themselves out for. The premiership clubs in trouble at the moment will be hoping that the new manager if then get one will stave off relagation.