Below is a summary of the full article. Click here for the full version or go back to LFC Live.net

Liverpool's second-ever Premier League title represents many things, and it's certainly a confirmation of this: When we talk about managers, we still don't really know what we're talking about.

Toward a cohesive theory of managers

Despite what managers tell us, we don't listen.

Their expected goal differential was the second-best in the league after Bayern Munich.

Liverpool hired Klopp and eventually won every trophy possible over the next half-decade.

But as Graham puts it in his book, "How to Win the Premier League": "There is some evidence that on the pitch, controlling for the players at his disposal, a good manager can add a few points per season." This is the same amount of value that a single good player provides, and that's how the market treats them, too: the best managers and best players get paid similar salaries.

A recent study from this year's Sloan Sports Analytics Conference, written by George Ferridge, attempted to control for player talent and the randomness of goal-scoring in order to isolate managerial impact.

So, even if we accept that managers really don't matter as much as conventional coverage suggests, Klopp really does seem like one of the managers who would fall into Trappatoni's 10% improvement zone or Graham's "couple points" club.

So, why, in the first season without Klopp, did Liverpool immediately get better?

How Liverpool and Arne Slot won the Premier League

Although he was born in the Netherlands, Robert Eenhoorn played for the New York Yankees for a couple years, bounced over to the then-California Angels, and then worked in baseball for another 10 years or so.

"There was never any doubt there."

All of Slot's success at Feyenoord ultimately led him to Liverpool, where he's now won 100% of the Premier League titles he's contested.

In his first season in charge of Liverpool, Dutch manager Arne Slot led them to winning the Premier League. AP Photo/Jon Super

The trickiest part about talking about managers is that no one can really know what kind of effect they have.

Virgil van Dijk and Mohamed Salah played almost every minute of every game, while a further eight featured at least 70% of the time in the league: Ryan Gravenberch, Alexis Mac Allister, Ibrahima Konaté, Alexander-Arnold, Robertson, Luis Díaz, and Alisson Becker.

The season prior, only five Liverpool players broke the 70% mark -- and that's without Liverpool facing the competitive demands of the Champions League, like they did this year.

They won 82 points in 38 games last season, and while it only took them 34 to get there this year, teams can fluctuate by about eight points in either direction from season to season for no reason other than random chance.

But in a way, Liverpool themselves have already answered the question of how much managers actually matter.