Take Manchester City out of 2009/10 to 2017/18 and Arsenal finish in the top four in eight of the nine seasons. For real it was seven. The one that changes is 2016/17: fifth for real, outside the top four for the first time in 20 years; third without City, straight into the Champions League group stage.
Three more seasons move more quietly. In 2010/11, 2012/13 and 2013/14 Arsenal finished fourth, and fourth meant the Champions League play-off round. Without City they are third, third and second, and go straight into the group stage. In 2010/11 that holds even though the rebuild takes four points off them: the 3–0 win at City in October, when Boyata was sent off after five minutes, and the 0–0 at home in January.
Over the nine seasons Arsenal took 19 points off City in 18 league games: four wins, seven draws, seven defeats. All 19 come off. In 2011/12 it cancels the free place, the one every club below City gets: Arteta’s 87th-minute winner against City in April goes, and Arsenal stay third, now two points behind Spurs instead of one ahead.
Their rebuilt finishes run from second, three seasons running, to fifth in 2017/18, Wenger’s last season.
2013/14
Leaders in December, second in May
On 14 December Arsenal went to City top of the table, six points clear of them, and lost 6–3. Nobody led the league for longer that season. They finished fourth.
Without City, the 6–3 takes nothing away. The 1–1 at the Emirates on 29 March takes one point. 79 becomes 78, and fourth becomes second. Chelsea go from three points ahead of Arsenal to two behind, and Liverpool, champions without City, finish three clear. Second means no play-off in August.
2016/17
Third, with City worth one point
Arsenal took one league point off City in 2016/17. They lost 2–1 at City on 18 December and drew 2–2 at home on 2 April. The better afternoon came at Wembley in April, where Alexis Sánchez scored in the 101st minute of the FA Cup semi-final against City.
Take that league point off and Arsenal have 74. With City’s place gone, that is third, two points clear of Liverpool, who finished a point above them for real. The free place, and one more.
Sánchez played all 38 league games and was their top scorer, with 24. Danny Welbeck played 16. For real their league season ended in fifth and the Europa League, and on 27 May they beat Chelsea 2–1 in the FA Cup final, Arsenal’s 13th FA Cup and Wenger’s seventh. Without City, the league half of that season ends in the Champions League group stage.