There is almost no formula that can be explained with certainty why Arsenal failed to win the Premier League even though they dominated the previous three seasons at the start of the league. Next season will be much more difficult if they only rely on strength like last season because Liverpool and Man City have made changes by bringing in a number of players to complete positions that are considered quite weak.
Arsenal management needs to make efforts to make Arsenal's chances of winning the Premier League come true and maybe the most crucial thing is bringing in an attacking line so that next season they have a differentiating figure. If Arsenal does not take this opportunity then I doubt that next season they will be able to compete with several other strong teams.
I think I really agree with this your stance of "no formula that can be explained why Arsenal failed to win the league last season" yeah just like you said again that next season will be difficult. It will certainly be difficult because Manchester City will be back in form, Liverpool will still want to maintain their position and Chelsea is also looking like a team that will be better than last season. Call me crazy but for me, Arsenal missed their opportunity last season of becoming champions and I don't think I see that opportunity coming their way this season.
For the fact that Arsenal couldn't win the Premier League after becoming runners-up for three consecutive seasons when they even had the privilege of winning 2 out of the 3 seasons but lost it out twice to Manchester City, i wouldn't talk about last season because they were no where close to Liverpool, next season will be so tough for Arsenal because they won't even see that second position again, Liverpool, Manchester City and Chelsea will be very much at alert because with the way they all ended last season, it will be so competitive for all of them next season and Arsenal do not have the kind of force that these three teams have.