Savin Hillbilly said:
1. How would they have performed under those guys?
2. How do you know?
I think that was the idea behind Bobby Valentine.
Well Higgins reluctantly played a few African Americans in his second (post Williams and Jensen) stint as manager. There is reason to doubt that he would have positively motivated Smith, Scott and Foy (and yes, I know how hard Williams was on the Boomer). Herman was among those who told Earl Wilson to "forget about" the discrimination incident in Florida in 1966, which treatment led to Wilson being traded (whereafter he promptly won 22 for the Tigers in 1967). But that was another time.
When Johnny Pesky told Dick Stuart to shorten up his swings in order to get more hits, Stuart effectively told him to go to hell and that he hit homers for a living. All in all the pre-1967 teams were notoriously unruly. You can look it up. Williams was stern, to put it mildly, which is why Yaz got Yawkey to fire him in 1969.
Here are a few for instances, given that the three managed some of the same players that Williams did.
The two most important players on the '67 team were Yaz and Londborg. There is little doubt that Williams, shall we say, prompted Yaz to play at a higher level by taking away the title of captain (which some pundits believe pissed him off, caused him to get in shape and relieved him - CALLING DR. FREUD) and generally pushing him.
There is no doubt that Williams read Lonborg the riot act and got him to throw inside, which may have contributed to his 22 - 9 record.
Not a peep was heard out of Sal Conigliaro, as later occurred and so distracted the team. I am convinced he was intimidated by Williams.
In the must win next to last of the game of the season, the moment Jose Santiago faltered in the first inning, Williams got up two relievers, which Santiago clearly noticed. He immediately stepped it up a couple of notches and pitched a fine game.
Maybe it was just dumb luck, but he always seemed to know when to put Jerry Adair in the lineup.
Willliams won, essentially, wherever he managed. The three others neve managed anywhere else. Higgins killed a guy while DUI'ing and went to jail. Pesky became a mascot.
So, I dare to apply some common sense to reach my conclusions. BTW, I do not contend that Williams single handidly managed the Red Sox to an additional 20 wins or something like that. However, he was essential to the team getting into a brutal pennant race and prevailing.