I've taken the top 128 teams by Pythagorean Record in the history of both leagues (not really, I'm only using current organizations; so if you're defunct, I didn't look at you; and I'm using the league you're currently in - so an Astros team from the 80s is still in AL team, as the Astros are in the AL now. Also - I pared the list of 19th century teams a bit. No one below a .600 Pythag is in the field.)
I'm using all 3 WAR systems (B-Ref, Davenport, Fangraphs) going position by position, then considering overall WAR for both batting and pitching - then, if needed, total WAR as a tiebreaker.
It's just more fun to do it position by position. Most innings at that position - you're the guy in the race. When I was a kid I'd do this with baseball cards, lay out all 18 guys, battle position by position, I'm trading the methodological flaw (yes, I understand) for the fun. Fun! (seriously, I have two jobs, all I do is work, 7 days a week, it never stops, just let me have this one)
American League
Round One Group One
1. 1939 NY Yankees (WS Winners)
v.
128. 1918 Boston Red Sox (WS Winners)
24 year old Joe DiMaggio leads the Yanks against 23 year old Babe Ruth and the Red Sox
C NYY - Dickey (that means Dickey has more WAR that season than the Red Sox catcher)
1B Bos - McInnis
2B NYY-Gordon
SS NYY-Crosetti
3B NYY-Rolfe
LF NYY-Selkirk
CF NYY-DiMaggio
RF Bos-Hooper
SP1 Bos-Mays (top 3 pitchers in IP for both teams chosen in order)
SP2 Bos-Bush
SP3 Bos-Ruth
Cl Push
Double: Bat WAR NYY (total offensive WAR, counts double)
Double: Pit WAR NYY (total pitching WAR, counts double)
NYY 10 Bos 5 - Winner 1939 Yankees; even with Boston's starting pitching advantage, NYY was still stronger on both sides of the field.
64. 1932 Philadelphia A's (2nd place in AL)
v.
65. 1915 Detroit Tigers (2nd place in AL)
24 year old Jimmie Foxx, 20 year old Mickey Cochrane, 32 year old Lefty Grove lead the A's against 28 year old Ty Cobb and the Tigers
C A's - Cochrane
1B A's - Foxx
2B A's-Bishop
SS Det - Bush
3B Det-Vitt
LF Det-Veach
CF Det-Cobb
RF Det-Crawford
SP1 A's-Grove
SP2 Tigers-Dauss
SP3 Tigers-Dubuc
Cl Push
Double: Bat WAR A's
Double: Pit WAR Tigers
Detroit 9 Philadelphia 6 - Winner 1915 Tigers-they swept the OF and had better arms.
32. 1906 Cleveland Indians (Naps) (finished third in AL)
v.
97. 1969 Minnesota Twins (lost ALCS)
31 year old Nap Lajoie, 25 year old Terry Turner lead the future Indians, 33 year old Harmon Killebrew and 23 year old Rod Carew pace the Twins.
C Cleve-Bemis
1B Min-Killebrew
2B Cleve-Lajoie
SS Cle-Turner
3B Min-Killebrew
LF Push
CF Cle-Flick
RF Min-Oliva
SP1 Min-Perry
SP2 Min-Boswell
SP3 Cle-Joss
Cl Min-Perranoski
Double: Bat WAR Indians
Double: Pit WAR Twins
Minnesota 8 Cleveland 7 - Winner 1969 Twins - an upset for the modern team by the slimmest of margins; superior Twins pitching moves them forward.
33. 2001 Oakland A's (lost ALDS)
v.
96. 1977 New York Yankees (Won WS)
Moneyball vs. Billy Ball; 30 year old Jason Giambi and the Hudson/Mulder/Zito pitching staff leads the A's against the Bronx Zoo - 31 year old Reggie Jackson, 30 year old Thurman Munson, 26 year old Ron Guidry.
C NYY-Munson
1B Oak-Giambi
2B NYY-Randolph
SS Oak-Tejada
3B Oak-Chavez
LF NYY-White
CF NYY-Rivers
RF NYY-Jackson
SP1 Oak-Hudson
SP2 Oak-Mulder
SP3 NYY-Guidry
Cl NYY-Lyle
DH Oak-Saenz
Double: Bat WAR NYY
Double: Pit WAR Oak
NYY 9 Oak 8 - Winner 1977 Yankees - super competitive, but this Oakland team gets their heartbroken again by the Yankees, the A's can't quite overcome the offensive edge from the Bombers.
16. 1936 New York Yankees (Won WS)
v.
113. 1977 Kansas City Royals (Lost ALCS)
33 year old Lou Gehrig, 29 year old Bill Dickey - a 21 year old Joe DiMaggio lead the World Champion Yankees; they take on a 24 year old George Brett and the Kansas City Royals
C NYY-Dickey
1B NYY-Gehrig
2B NYY-Lazzeri
SS NYY-Crosetti
3B KC-Brett
LF KC-Paquette
CF NYY-DiMaggio
RF KC-Cowens
SP1 KC-Leonard
SP2 NYY-Pearson
SP3 NYY-Splittorff
Cl NYY-Malone
DH KC-McRae (top hitting Yankee who didn't start acts as their DH)
Double: Bat WAR NYY
Double: Pit WAR KC
NYY 10 KCR 7 - a pitching advantage by the Royals made this one closer than you'd expect, but the Yankees prevailed.
49. 1949 Boston Red Sox (2nd in AL)
v.
80. 2011 New York Yankees (Lost ALDS)
30 year old Ted Williams against 28 year old Robinson Cano/35 year old Alex Rodriguez/41 year old Mariano Rivera. What's an all time tournament bracket without Yankees vs. Red Sox?
C NYY-Martin
1B NYY-Teixeira
2B NYY-Cano
SS Bos-Stephens
3B NYY-Rodriguez
LF Bos-Williams
CF NYY-Granderson
RF NYY-Swisher
SP1 Bos-Parnell
SP2 Bos-Kinder
SP3 NYY-Nova
Cl NYY-Rivera
DH Bos-Batts
Double: Bat WAR Bos
Double: Pit WAR NYY
NYY 10 Bos 7 - Ted Williams postseason struggles continue; the number of good Yankee position players+pitching depth carries the day.
17. 2017 Indians (lost in ALDS)
v.
112. 1978 Yankees (WS Winners)
It's 23 year old Francisco Lindor - 24 year old Jose Ramirez and 31 year old Corey Kluber trying to avenge their ALDS loss to the Yankees by taking out the World Champs from four decades prior - Reggie's 32, Willie Randolph is 24 - Ron Guidry is 27 years old. The '77 team already advanced in the bracket, can the back-to-back World Champions complete the sweep?
C NYY-Munson
1B Cle-Santana
2B NYY-Randolph
SS Cle-Lindor
3B Cle-Ramirez
LF NYY-Piniella
CF NYY-Rivers
RF NYY-Jackson
SP1 NYY-Guidry
SP2 Cle-Carrasco
SP3 Cle-Bauer
Cl NYY-Gossage
DH Cle-Encarnacion
Double: Bat WAR NYY
Double: Pit WAR Cle
NYY 9 Cle 8 - The Yankees swept the OF and had a slight batting advantage that allowed them to narrowly overcome the significant pitching gap. The Yankee organization continues to steamroll the bracket.
48. 1973 Baltimore Orioles (lost ALCS)
v.
81. 1930 Washington Senators (finished 2nd in AL)
Massively underappreciated 24 year old Bobby Grich and 27 year old Jim Palmer lead Earl Weaver's Orioles against 23 year old Joe Cronin and the Senators. The first round of bracket 1 comes to a close with this battle of local rivals.
C Balt-Williams
1B Wash-Judge
2B Balt-Grich
SS Wash-Cronin
3B Balt-Robinson
LF Balt-Baylor
CF Balt-Blair
RF Wash-Rice
SP1 Balt-Palmer
SP2 Wash-Crowder
SP3 Balt-McNally
Cl Balt-Reynolds
DH Wash-Harris
Double: Bat WAR Balt
Double: Pit WAR Wash
Balt 10 Wash 7 - the Orioles top line pitching was able to overcome the Senators depth, add that to the strength of their bats at the O's advance.
That wraps up this first bracket. Here's what we'll see when we return to this group in the Round of 64:
1939 Yankees
v.
1915 Tigers
1969 Tigers
v.
1977 Yankees
1936 Yankees
v.
2011 Yankees
1978 Yankees
v.
1973 Orioles
When I return - it will be with the first National League bracket - led by the top NL seed, the 1906 Cubs.