令人心服 meaning in English

carry conviction

I complained the simple interpretation on identity , but i do not know how to offer a credible answer
我抱怨了那种简单的身份解读，却不知道如何提供那些足以令人心服的新解读。
Benitez could point to the champions league title at least whilst others could indicate that finishing up to 37 points behind the league champions or playing out “ friendlies ” that are supposed to be league games hardly indicates convincing success
贝尼特斯也许至少可以拿欧冠当借口，但同时别人也可以指出他们最后与冠军的37分的差距和在联赛中的比赛打得和友谊赛一样，就上面这些，把这个赛季说成出一个成功赛季是很难令人心服的