The high-level formula is this:
WAR = (Batting Runs + Base Running Runs +Fielding Runs + Positional Adjustment + League Adjustment +Replacement Runs) / (Runs Per Win)
This statistic is very favorable to players like Mike Trout. Now Trout is an excellent player - let there be no doubt about that. He's one of the best hitters in the league, is an excellent fielder, and a strong baserunner who can steal bases. I just wonder if everything is calibrated properly.
Here's a snapshot from ESPN.com, showing the top 10 hitters in the American League, sorted by batting average. (Aside: batting average has largely been replaced by on-base percentage in the thinking of modern sabremetricians, but it still is used as a default stat for sorting.)
What interests me here is the disparity in WAR between Trout, Betts, and Altuve versus other hitters who seem to also be having good seasons, like Pedroia and Ortiz. I should make it clear that the WAR listed above is the total over hitting, baserunning, and fielding. But curiously, very little of Trout's WAR is from fielding. His OWAR ius 9.36, compared to Betts' 5.96 and Ortiz's 4.89. Betts gets a lot of WAR from his fielding - 3.1-3.2, depending on what the round-off error is. Trout has .6-.5, while Ortiz might get as little as .06 defensive WAR - an unsurprising fact since he only plays defense on the rare occasion that the Red Sox are playing on the road in a National League park (and even then he takes some games off.)
I simply don't believe that, as an offensive player, Mike Trout is worth twice as much in terms of WAR as David Ortiz. Trout has a slightly higher OBP, but a lower slugging percentage. He has 39 more runs scored, but 27 fewer RBIs, and is much lower in most power categories - fewer doubles and home runs. Many more walks, but also many more strikeouts. Trout has the advantage with stolen bases, but still, that's only 26 SBs - one per roughly every six games. I view stolen bases as analogous to walks - just extra bases to be added to the total base sum.
So - where does the huge number come from? I don't know. There are many explantions like the one above that indicate what WAR is supposed to mean, but I cannot find a closed formula for it that letss me plug in numbers. I have found a "Simple WAR calculator" at wahoosonfirst.com, but it doesn't produce the numbers I see above.