Perhaps you remember a post I did at the end of last year where I picked the best player in baseball at each position for 2008 (check that link if you need some of my methods explained). It was so much fun that I decided to compile the data for other years. Thanks to Baseball-Reference and its innings played data going back to 1956, I thought I'd publish my findings for the oldest season on file.
The 1956 season was a much different era for baseball. There were no Playoffs, there were only 16 teams, and the two leagues didn't make trades with each other. New York still had three teams, including both pennant-winners. A lot of players from that era are currently in the Hall of Fame, and it's fun to see how they stack up against each other.
There's no Dewan plus/minus data for those years, but thanks to Sean Smith's Total Zone data, I was able to factor in fielding in my admittedly amateurish way.
I made some changes to my criteria since the 2008 post. For one thing, the schedule was only 154 games rather than today's 162, so I made each infielder's minimum innings played requirement 800. Qualifying catchers and outfielders had a minimum of 700 innings played. In my first post I required catchers to play the same number of innings as the infielders, but I noticed that they tended to get rested more, likely due to the demands of the position. Does this mean some platoon players will sneak onto these tables? Probably, but if you're the best in the league at your position you're probably not going to get platooned.
So here are the results. Once again I'll name the best player at each position for each league, as well as the best in the Majors.
Catcher

It's neck and neck between Ed Bailey and Yogi Berra. Stan Lopata of the Phillies had a pretty good season too, but Bailey's offensive and defensive numbers were better, making him the NL's best backstop. Sherm Lollar's defensive numbers were slightly better than Berra's, but Yogi's bat was more than enough to make him the AL pick. As for the MLB pick, it's pretty close. Bailey had a slight edge with the bat and Berra had a slight edge with the glove. Since Berra caught more games, I'll take him.
AL: Yogi Berra
NL: Ed Bailey
MLB: Yogi Berra
First Base

Chicago wasn't a good place to live in 1956 if you were a fan of first basemen. Dee Fondy and Walt Dropo brought up the rear for first-baggers with significant playing time. The best of this bunch was Joe Adcock. Adcock had a reputation as a weak fielder, but Total Zone says he was about average. Stan Musial had a better career and was a better fielder, but I don't think it was enough to give him the edge for this season. Bill Skowron was the same defensively as Adcock, but his bat was the AL's best. Skowron is one of the more overlooked players from those Yankee teams, but he can claim "best in the league at his position" status for 1956, at least.
AL: Bill Skowron
NL: Joe Adcock
MLB: Joe Adcock
Second Base

Speaking of overlooked players from great teams, Jim Gilliam was clearly the best second baseman of 1956 both offensively and defensively. Gilliam's usually not one of the first names that comes to mind from those Dodger teams of the '50s and '60s, but he was a strong contributor during that period of glory. The AL's second basemen were generally a weak-fielding bunch, with weak-hitting Bobby Avila the best glove man of the qualifiers. Frank Bolling was the best offensively and only slightly below average defensively (-2 in TZ), which makes him my pick for the AL.
AL: Frank Bolling
NL: Jim Gilliam
MLB: Jim Gilliam
Third Base

Here's where the balance between fielding and hitting gets tricky. Eddie Mathews was clearly the NL's best offensive third baseman, but Ken Boyer was clearly its best fielder (15 TZ). Mathews was a better fielder than most of the NL's third basemen, but he was still a -2 in TZ. Hmmm. This is tough. I'll give Mathews the edge for his six stolen bases where he was never caught, since Boyer's ratio of steals to times caught hurt the team. Ray Boone was a weak fielder, but his offense was so far ahead of the rest of the AL's third basemen that he gets his league slot.
AL: Ray Boone
NL: Eddie Mathews
MLB: Eddie Mathews
Shortstop

Ah, shortstop. The most important defensive position on the field. Ernie Banks clearly won the offensive title, but he was only about average defensively. Roy McMillan's 19 TZ was the NL's best, but his 89 OPS+ was way behind Banks'. How about a guy who'd give you a balance of both? Johnny Logan's 112 OPS+ fell almost directly between Banks' and McMillan's, and his 10 TZ was directly between Banks' 1 and McMillan's 19. I'd love to give this one to Mr. Cub, but I think I have to give it to the guy in Milwaukee. Over in the AL, Harvey Kuenn's defensive numbers were average, but no other shortstop's defense was impressive enough to overshadow Kuenn's offensive numbers.
AL: Harvey Kuenn
NL: Johnny Logan
MLB: Johnny Logan
Left Field

Wow. There are two clear tiers here. The top half is the elite group and the bottom half is the mediocre group. There's a clear league split too. Four of the top five were in the AL, with Frank Robinson the only man from the NL in that select company. Ted Williams may have turned 38 that year, but he was still one of the most dangerous hitters in baseball, with an eye-popping 172 OPS+.
AL: Ted Williams
NL: Frank Robinson
MLB: Ted Williams
Center Field

Those three names at the top look familiar, don't they? Willie, Mickey and The Duke. New York baseball fans always had a good debate when the subject of the best center fielder in town came up. The man right behind them, Larry Doby, is a Hall of Famer too, as is Richie Ashburn in the middle, but neither one belongs in the argument for 1956. Mickey Mantle's defense that year was a -1 in TZ, but his Triple Crown-winning numbers were too good to overlook. He has to be the AL and MLB pick. Who was the NL's best? Willie or The Duke? In addition to a better OPS+, Snider slightly beat Mays in TZ, 12 to 11. Mays' 40 steals against only 10 times caught give him a good argument though. Hmmmm. This is close, but I'm going to give the edge to the Say Hey Kid.
AL: Mickey Mantle
NL: Willie Mays
MLB: Mickey Mantle
Right Field

This one's pretty clear-cut. Hank Aaron blew away the competition. Even his defense was pretty good. Al Kaline's offensive and defensive production were clearly AL-best, but they couldn't match Aaron's.
AL: Al Kaline
NL: Hank Aaron
MLB: Hank Aaron
To recap:
AL Team:
C: Yogi Berra
1B: Bill Skowron
2B: Frank Bolling
3B: Ray Boone
SS: Harvey Kuenn
LF: Ted Williams
CF: Mickey Mantle
RF: Al Kaline
NL Team:
C: Ed Bailey
1B: Joe Adcock
2B: Jim Gilliam
3B: Eddie Mathews
SS: Johnny Logan
LF: Frank Robinson
CF: Willie Mays
RF: Hank Aaron
MLB Team:
C: Yogi Berra
1B: Joe Adcock
2B: Jim Gilliam
3B: Eddie Mathews
SS: Johnny Logan
LF: Ted Williams
CF: Mickey Mantle
RF: Hank Aaron
These results are interesting.
The Braves had four players who I named as the best in the Majors at their respective positions, including three infield spots. Perhaps that has something to do with why they finished only one game out of first that year, then won pennants the next two years? Just a guess.
The Tigers had four players on the AL team, including three infield spots, but none on the MLB team. I guess their fifth-place finish that year can be attributed to their mediocre pitching staff. The Yankees had three spots on the AL team and two on the MLB team. In fact, Ted Williams is the only player on the AL team who didn't play for Detroit or New York.
Eddie Mathews is the only infielder on either team currently in the Hall of Fame, which suggests that several of these guys had short peaks.
Even though this season took place long before I was born, I still get a joy from learning about the heroes of yesteryear. It was a different time, and some of the stats I cite here didn't exist yet, but the game itself was just as beautiful. Maybe in 53 years another guy like me will be discovering just how good today's players were.