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The Dutchman, along with the West Ham’s Slaven Bilic, is the bookies’ favourite to be the first Premier League manager to be axed this season.
Everton have made a poor start to the season and are currently in the bottom three, having collected just four points from their first five top-flight games, and lost their opening Europa League group match 3-0 to Atalanta last week.
But Barton, a lifelong Toffees fan, doesn’t believe that will lead to a knee-jerk reaction from the club’s chiefs.