Innovative how?
They've done a lot on the commercial side of things and whilst much was made of the whole moneyball thing, aside from that period of Edwards, Klopp and co killing it, I can't say I've been super impressed by them.
Red Sox hadn't won the world series in over 80 plus years. Under FSG, they broke the curse, and have won it three times (?) since then. My understanding is that they have done an excellent job of transforming the area around Fenway Park.
Same with us. We have won the league once, challenged for the league multiple times under Klopp, and once under Rodgers also. If it was somewhat of a level playing field, we would have won the league multiple times under them.
While not exactly Bill James and Billy Beane Oakland A moneyball, they have promoted a careful analytics based scouting system which has worked at both Red Sox and us. People take DOF for granted but it was not the norm in England ten years ago. We had several journalist and fans (maybe including me, I have to search my posting history) poke fun at our "transfer committee". But they stuck with it. Definitely, Klopp was the catalyst but I don't think the truth is as simple as they lucked into Klopp. They were responsible for assembling the entire transfer committee. They setup the environment for someone like Klopp to come in and take it to a whole new level.
I also like them for not going for a new stadium and increasing the capacity gradually. On the commercial side, we look a completely different animal now.
Bottomline is that, yes, they have stumbled a bit. They have also been lucky. There maybe a ceiling on what their type of ownership can deliver at the highest level particularly in a not so level playing field. But at the same time, you don't break the duck with two franchises which have a history of underachievement for multiple decades by just luck.
Their flaws have been discussed in detail in multiple threads all through the forum. I wont present them here. For all of their flaws, Klopp has signed contract extensions multiple times to work under them. You are not naive enough to believe that it is just due to Kop chanting his name. Klopp must appreciate something about them to work with them.