Prompted by a discussion @JMcGuireMLB started about low-WAR MVP winners and high-WAR MVP non-winners, I jumped down a DEEP rabbit hole and this thread will serve as a place to share some of my findings...
Three pitchers had multiple seasons of 10+ WAR without winning an MVP in either of those seasons:

Roger Clemens -- 1990, 1997 (10.4, 12.1)
Wilbur Wood -- 1971, 1972 (11.0, 10.3)
Steve Carlton -- 1972, 1980 (12.5, 10.1)
Dwight Gooden had the highest-ever WAR for a player who didn't win the MVP award that season.

He had a 12.2 WAR in 1985. That's the highest pitching single-season WAR since 1912.
The only AL player who had a top-10 all-time WAR in a non-winning MVP season who isn't in/won't be in the Hall of Fame:

Rico Petrocelli, who posted a 10.0 WAR in 1969, hitting .297 with 40 HR, 97 RBI for the Red Sox.
Only two AL position players have multiple 10+ WAR seasons in which they didn't win the MVP:

Ted Williams -- 1941, 1942 (10.4, 10.4)
Mike Trout -- 2013, 2018 (10.5, 10.2)
The highest AL MVP losing WAR ever is 10.5

Babe Ruth -- 1931
Carl Yastrzemski -- 1968
Mike Trout -- 2013
Willie Mays posted the top 3 non-MVP WAR seasons in NL history (position player) and four of the top 10...all in a seven-year span:

1958 -- 10.2
1962 -- 10.5
1963 -- 10.6
1964 -- 11.0
Sammy Sosa is the only NL position player not named Willie Mays who has a 10+ WAR season in which he didn't win MVP.

In 2001, Sosa finished second to Barry Bonds, who posted an 11.9 WAR.
Lowest WAR of MVP winners in each league:

National League: Frankie Frisch/Andre Dawson -- 4.0 (1931, 1987)
American League: Dennis Eckersley -- 2.9 (1992)
Three of the NL's 10 lowest WAR seasons for an MVP played for the #Cubs the season they won:

Gabby Harnett -- 4.9 -- 1935
Hank Sauer -- 5.6 -- 1952
Andre Dawson -- 4.0 -- 1987
Six of the 10 lowest WAR seasons in NL MVP history came in the 1940s and 1950s.

Yet, in AL MVP history, just two of the lowest 10 WAR seasons came in those decades.
All four sub-4.0 WAR season MVP winners in history came from the AL:

1. Dennis Eckersley — 2.9 — 1992
2. Jeff Burroughs — 3.6 — 1974
3. Don Baylor — 3.7 — 1979
4. Juan Gonzalez — 3.8 — 1996
Two near disasters in MVP voting:

1995 -- Dante Bichette finished a close second behind Barry Larkin with a 1.2 WAR (Larkin -- 5.9)

2008 -- Ryan Howard finished a close second behind Albert Pujols with a 1.8 WAR (Pujols -- 9.2)
Would love to see @theaceofspaeder weigh in on this thread. I'm sure he's dug into similar things before and can provide even more insight than I can from my hours-long deep dive.
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