Burnley had four Premier League seasons in these nine: 2009/10, 2014/15, 2016/17 and 2017/18. The other five were spent outside the Premier League. Take City out and their fate doesn’t change once: relegated in 2009/10 and 2014/15 either way, safe in 2016/17 and 2017/18 either way.
Against City they took six points in eight league games: one win, three draws, four defeats. All six come off. In 2009/10, back in the top flight after 33 years, they drew 3–3 at City and were beaten 6–1 at home. The point goes, 30 becomes 29, and Burnley are 17th of 19, five short of safety. The later seasons are City’s place and no more: 15th on 40 in 2016/17, then 6th on 53 in 2017/18, Burnley’s best rebuilt finish.