WAR is a counting stat that is very good at accounting for player value. It's not perfect but it is better than traditional box scores.
In a given year, the player with the highest WAR value won't always win the MVP. You could understand a gap of a few points. Maybe consider narrative as part of the voting process.
But there are some years where the difference between the top WAR player and the actual MVP are bordering on egregious, if not outright robbery.
1984 stands out as probably the worst of all time. That season, the AL MVP was Detroit Tigers reliever Willie Hernandez. Hernandez posted a 9-3 record with a 1.92 ERA and 32 saves, striking out 112 in 140.1 innings. A fantastic season for a reliever. But his actual WAR value was just 4.8. Certainly All-Star level. But typically a far cry from MVP caliber.
What makes it worse is that the 2nd place AL MVP wasn't particularly deserving of the award either. Kent Hrbek slashed .311/.383/.522 with 27 HR and 107 RBI. Again, quite good. He posted a WAR of 5.6 -- more deserving of the award than Hernandez. But that's still not the worst part of this.
All the way down at the bottom of the AL MVP voting...literally the bottom vote-getter, is Cal Ripken Jr. In 1984 Ripken slashed .304/.374/.510 with 27 HR and 86 RBI. But Ripken as a SS was so good defensively that his WAR value was 10.0.
Ten point zero. More than double Hernandez. And it is somewhat odd that voters did not recognize Ripken's greatness as an overall better player since they voted him as the AL MVP in 1983.
I haven't looked at every MLB season but I cannot imagine there has ever been an instance where someone was literally HALF as deserving of an MVP award as another player and yet still actually won it.
Other gaps in the 1980s include:
1985 -- Don Mattingly took the AL MVP with 6.5 WAR even though Rickey Henderson (his teammate) posted 9.9/
1985 -- Willie McGee took the NL MVP with 8.2 WAR (usually hard to argue against that epic season) but Dwight Gooden posted a fukking insane 13.3 WAR.
1987 -- George Bell took the AL MVP with 5.0 WAR. Roger Clemens posted 9.4.
1987 -- Andre Dawson won the NL MVP with 4.0 WAR. Tony Gwynn posted 8.6.
1989 -- Robin Yount won the AL MVP with 5.8 WAR. Bret Saberhagen posted 9.7.
**I can understand not choosing Clemens in 1987 and Saberhagen in 1989 if you believe that pitchers should not be eligible for MVP. Even with that argument, neither Bell in 1987 or Yount in 1989 led in WAR among position players. Those leaders would have been Wade Boggs and Rickey Henderson, respectively.