But when it came time for New York to play the Cleveland Indians in the World Series, Amalfitano, who was not on the postseason roster, had the best seat in the house.
Amalfitano was the bullpen catcher, in a bullpen that was in fair territory in right-center field, and from there, he was able to fully appreciate the way Willie Mays ranged into deep center field at the Polo Grounds and made what was arguably the most famous catch in baseball history.
That catch happened 62 years ago Thursday, and Amalfitano, who still works for the Giants, remembers it as if it were yesterday.
"Vic Wertz hit it," Amalfitano said on Thursday evening. "Don Liddle threw it. Willie caught it."
It wasn't, Amalfitano admitted with a laugh, quite that easy.
"As he turned to go back on this ball -- and he had to go a long ways -- by his body, you could tell he tracked it because he slowed down a bit," said Amalfitano, who at 82 still works for the Giants in player development. "He had it and caught the ball over his shoulder. The amazing thing to me is he has the presence of mind to throw the ball into the infield to second base. He kept the double play in order.
"The picture shows him almost doing pushups after he throws it. He has his back to the infield when he makes the catch. He takes a step with his right foot after he catches it and wheels and throws this thing all the way into the infield. … He did a lot of things other people couldn't do."
That catch kept the score at 2-2 in the eighth inning, setting the stage for Dusty Rhodes' pinch-hit three-run home run in the 10th inning of Game 1. That was the first step in the Giants' sweep of an Indians team that went 111-43 in the regular season, losing four in a row only once before they played the Giants.
The Series was on national television, which was rare in those days, allowing the baseball world to not only see the game, but to hear the description of NBC announcer Jack Brickhouse.
"There's a long drive way back in center field," said Brickhouse. "Way back, back! It is ... oh, what a catch by Mays! The runner on second, [Larry] Doby, is able to go to third. Willie Mays ... just brought this crowd to its feet ... with a catch ... which must have been an optical illusion to a lot of people. Boy!"
It was no illusion, though. It was for real, as Wertz can attest.
"I don't think I ever hit a ball better or harder than that one," said Wertz, who died in 1983. "Yes, I know I've put balls on the roof at Briggs Stadium [later renamed Tiger Stadium] at Detroit and hit some other real smashes, but this drive, which just ended up as a big out, was tagged as well or better than any of them. I never thought Mays had a chance to get the ball, but he did."
But then Wertz and the rest of the baseball world didn't really know Mays back then. It was only his second full big league season. Mays had won the NL Rookie of the Year Award in 1951, but he played in only 34 games in '52 and missed the entire '53 season after being drafted into the Army.
Mays returned in 1954 and began to make himself known. The Hall of Fame center fielder made that jaw-dropping catch on Wertz's line drive after a regular season in which Mays earned the first of his 24 selections to the NL All-Star team and the first of two NL MVP Awards. He also won the NL batting title that year.
Mays did not win his first Gold Glove until three years later, but it was the first of 12 in a row.
"When Mays was in center field, it was like five outfielders were out there," said Amalfitano. "He was the center fielder, left-center fielder and right-center fielder, especially in the Polo Grounds. There was a lot of territory there, and he covered it like a blanket."
But was that play in Game 1 of an eventual World Series sweep Mays' greatest catch? Well, Mays isn't telling.
"One of my assignments in the spring [with the Giants] is to introduce our Hall of Famers to the Minor League kids," Amalfitano said. "I asked Willie that question, 'Was that your greatest catch?' He said, 'Why do you ask me that question, Joe? I never rated any of them.' He just loved to play the game. I told him, 'You loved to play the game because the game was easy for you.'"
Even Mays would agree with that.