Jim Bouton said that they always gave the manager too much credit when a team won, and too much blame when they lost. I have to agree.
On the other hand, I remember one manager who made a huge difference for a Washington team. From 1961 - 1968, mostly under Gil Hodges, the expansion Washington Senators went 521-768, 4 times losing over a hundred games. Their best season ever was a 7th place finish (ten team league) in 1967. In 1968 they finished 10th, dead last, with a 65-96 record. Then they hired Ted Williams to manage the team in 1969.
They contended for the title for a good portion of the season, and even after Baltimore pulled away, they continued to fight for 2nd place with the Tigers and Red Sox right up until the very end. They finished in 4th place with an 87-75 record, just a game behind the Sox and 3 behind the Tigers. Best season they ever had.
Let's face it, the O's had 3 Hall of Famers in the lineup, 3/4 of their infield + Paul Blair won Gold Gloves, and they had the best pitching staff on the planet. They ended up winning 109 games. Tough to beat.
But the Senators had a few players at their core - Frank Howard, Ken McMullen, Mike Epstein, Ed Brinkman - each of whom had the best offensive year they ever had, or ever WOULD have that year under Teddy Ballgame. Brinkman, a lifetime .224 hitter batted .266 that year, a number he'd never reach again. Epstein hit .278, 30, 85; 3 numbers he'd never reach again. McMullen hit .273, 19, 87; although he hit 20 homers a couple of times, he'd never equal the BA or RBI total again.
And then there's Frank Howard. Already a feared power hitter in his prime BEFORE Ted got there, he hit .296, his best ever - 48 homers, his best ever, and 111 RBI's, a number he'd eclipse a couple of times under Ted in the future. Here's the biggest thing TW did for Frank Howard (and most of his hitters): before TW, Howard struck out a total of 1,027 times while walking 401 times. After TW, Howard struck out 496 times and walked 496 times. Ted Williams taught all of his hitters how to be patient at the plate, and how to hit to their strengths rather than battle their weaknesses.
The team faded after that as they never had any pitching, and the front office continually traded away talent for nothing, and Ted's weaknesses became exposed - he wasn't especially good with pitchers or the media, and he wasn't very diplomatic (he had no patience for idiots) but their record under him was still better than under anybody else, and the work he did with those hitters has to be among the best I've ever heard of.