Here is a list for the next few seasons of which players qualify for our military exemption (can be kept as uncarded players without counting against roster limits):
The players listed are shown with their real-life teams, not Pre-Smiley teams.
1954:
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NYA: Billy Martin
CHA: Sammy Esposito
BOA: Faye Throneberry, Dick Brodowski
DEA: Bill Black
BAA: Jay Porter, Frank Saucier
PHA: Bill Harrington
NYN: Daryl Spencer
SLN: Vinegar Bend Mizell
CHN: Harry Chiti
PIN: Tony Bartirome, Dick Groat, Pete Naton, Eddie O'Brien, Johnny O'Brien, Ron Kline, Bill Bell, Bill Koski
1953:
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NYA: Jerry Coleman, Bobby Brown, Tom Morgan
CLA: Hal Naragon
CHA: Sammy Esposito, Joe Kirrene
BOA: Faye Throneberry, Norm Zauchin, Dick Brodowski, Leo Kiely
WAA: Dan Porter, Bob Ross
DEA: Frank House, Bill Black
PHA: Bill Harrington
SLA: Jay Porter, Frank Saucier
BRN: Don Newcombe
MLN: Chet Nichols, Phil Paine
SLN: Tom Poholsky
NYN: Willie Mays, Alex Konikowski
CIN: Lloyd Merriman
CHN: Harry Chiti
PIN: Pete Naton, Tony Bartirome, Dick Groat, Jim Mangan, Bill Bell, Ron Kline, Bill Koski, Vern Law, Ron Necciai
1952:
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NYA: Whitey Ford, Bob Wiesler
CLA: Hal Naragon, Al Aber, Dick Weik
CHA: Sammy Esposito, Herb Adams, Joe Kirrene, Bill Wilson
WAA: Don Porter, Bob Ross
BOA: Ted Williams, Karl Olson, Norm Zauchin, Leo Kiely
SLA: Owen Friend, Dick Kokos, Frank Saucier, Bob Turley
DEA: Frank House, Ray Herbert
BRN: Don Newcombe, Erv Palica
NYN: Sammy Calderone, Alex Konikowski
SLN: Tom Poholsky
CHN: Carl Sawatski, Preston Ward
CIN: Lloyd Merriman
BON: Del Crandall, Johnny Antonelli, Chet Nichols, PhilPaine
PIN: Danny O'Connell, Bill Koski, Vern Law, Bill MacDonald
1951:
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NYA: Whitey Ford
CLA: Al Aber, Dick Weik
CHA: Herb Adams, Bill Wilson
DEA: Art Houtteman, Ray Herbert
SLA: Owen Friend, Dick Kokos, Dave Madison
NYN: Sammy Calderone
BRN: Billy Loes
BON: Del Crandall, Johnny Antonelli
PHN: Curt Simmons
PIN: Danny O'Connell, Bill MacDonald
CHN: Carl Sawatski, Preston Ward
1947-1950:
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none
1946:
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DEA: Rip Radcliff
SLN: Danny Litwhiler, Creepy Crespi, Howie Krist
BRN: Tommy Brown, Bobby Bragan, Lou Rocheli, Cal McLish
BON: Max Macon, Ray Martin
PHN: Charlie Letchas, Bill Burich, Ray Hamrick, Moon Mullen, George Eyrich, Rogers McKee
CIN: Lonnie Goldman, Mike Modak, Kent Peterson
PIN: Roy Jarvis, Billy Sullivan
NYN: Vic Bradford, Whitey Lockman, Andy Hansen
From 1943-1945 (and insome cases 1942) the majority of players on each team probably qualify.
Alan