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Trophies will always be the legitimacy to measure a team success, Arsenal have played well in the last three seasons, there is no denying that. But to say they are playing great, I agree with you, Arsenal should be able to win trophies. Actually, if you look at Arsenal performance this season, their statistics have actually decreased slightly, only they still managed to finish in the runnerup position in the standings.
Maybe after going through many challenges and being experienced enough in the competition for trophies, Arsenal could get lucky next season. Otherwise, Arteta should be fired if Arsenal fails again, he has spent a lot of budget to build an ideal squad. Viktor Gyokeres is speculated to join Arsenal, I think that would be a very good recruitment, because it can increase their chances of winning a trophy next season.
Titles are a measure of a team's success, of course. Arsenal need the title to show that they are better than before, but the Premier League is always difficult for anyone. Only Manchester City have managed to maintain their best performance for four seasons in a row and win the title, everyone else is only a runner-up and Liverpool are the chain-breakers. Arsenal will not win the title as long as Liverpool and Manchester City are playing well, so Arsenal will only be a contender for a Champions League spot.
I am not sure when Arsenal can win the Premier League title. Arteta is trying to do it as soon as possible, but Arsenal's performance is not as consistent as expected. Next season is a different stage, it means Arsenal must be ready with everything to meet the demands of the fans. Arteta can be fired if he always fails, even if he can make Arsenal play in the Champions League.