It probably matters alot what the pay is for the 7 years, not for the 11, I assume it is not just the same every year or the Royals would have massively overpaid.
They were going to have him for 4 more seasons as below market and then 3 years after he would have been a FA (he has 2 years service). Even if you assume the 3 bought out FA years are at $30M/year (maybe by then that would be low) the 7 years has to be somewhere around $120M . This seems like a very possible overpay by the Royals, of course depending on what the annual amounts are.
The other way to look at it I guess is that the Royals have a hard time getting players to stay after their 6 years are up, so this is a way to fix that.
Huge amount of money to risk on a guy who has had 2 pretty good seasons, but not crazy good. He has an .800 OPS, which is good, but not insane.