WAR may be even more confusing than you think.

1966 National League Pitching Leaders

Wins Above Replacement--all
1.	Koufax (LAD)	9.8
2.	Marichal (SFG)	9.8
3.	Mays (SFG)	9.0
4.	Santo (CHC)	8.9
5.	Bunning (PHI)	8.9
6.	Clemente (PIT)	8.2
7.	Aaron (ATL)	7.8
8.	Allen (PHI)	7.5
9.	Maloney (CIN)	7.4
10.	Hart (SFG)	6.6

WAR for Pitchers 1. Koufax (LAD) 10.3 2. Marichal (SFG) 9.1 3. Bunning (PHI) 8.9 4. Maloney (CIN) 7.1 5. Gibson (STL) 6.1 6. Cuellar (HOU) 5.6 7. Perry (SFG) 5.2 8. Regan (LAD) 5.0 9. Veale (PIT) 4.7 10. Bolin (SFG) 4.2

Even for pitchers there's a list which contains players and pitchers.  Then there's a list just for pitchers.  Let's look at the WAR (Wins Above Replacement) for pitchers on both lists.

pitcher, WAR, pWAR
Koufax 9.8, 10.3
Marichal 9.8, 9.1
Bunning 8.9, 8.9
Maloney 7.4, 7.1

Bob Gibson has pWAR 6.1 but is not on the list that includes players, so his total WAR must be less than that of Jim Ray Hart: 6.6.  How do we find it?

It does not appear to be on Gibson's main page, which defaults to his pitching stats:

http://www.baseball-reference.com/players/g/gibsobo01.shtml

Under "Player Value" there's one WAR column with 6.1.  What if I click on "More Stats"?

http://www.baseball-reference.com/players/g/gibsobo01-pitch.shtml

Nothing more on WAR that I can see.  Let's click on "Batting".

http://www.baseball-reference.com/players/g/gibsobo01-bat.shtml

There's WAR of 0.4; also oWAR and dWAR: 0.3 and 0.1, although I don't think you're supposed to add them up.

Maybe we're supposed to add the 0.4 to Gibson's pWAR of 6.1.  That would give us 6.5, which is still below Hart's 6.6 and would explain why Gibson is not listed in the top ten of the list of both players and pitchers.

Let's try Sandy Koufax since he's the prime example of a pitcher on both lists.

http://www.baseball-reference.com/players/k/koufasa01.shtml

Sure enough, Koufax has that single WAR column with his 1966 10.3 pWAR.  Let's look at Sandy's Batting page.

http://www.baseball-reference.com/players/k/koufasa01-bat.shtml

Sandy's batting WAR is -0.6; oWAR is -0.6 and dWAR is 0.0 but we're not supposed to add them.

10.3 - 0.6 = 9.7

That's pretty close to the total player WAR for Koufax of 9.8.  Maybe there's a rounding difference.

One problem here is I do not know where to find the total WAR for all pitchers for this season of 1966.

Let's take quick look at the AL for 1966 for something even more odd.

1966 American League Pitching Leaders

Wins Above Replacement--all 1. Wilson (2TM) 7.9 2. Robinson (BAL) 7.7 3. Agee (CHW) 6.4 4. Oliva (MIN) 6.4 5. Peters (CHW) 6.1 6. McAuliffe (DET) 6.0 7. Killebrew (MIN) 5.9 8. Kaline (DET) 5.6 9. Fregosi (CAL) 5.5 10. Yastrzemski (BOS) 5.5

WAR for Pitchers 1. Wilson (2TM) 6.1 2. Peters (CHW) 5.2 3. Hargan (CLE) 4.9 4. McDowell (CLE) 4.9 5. Siebert (CLE) 4.7 6. Aker (KCA) 4.6 7. Kaat (MIN) 4.5 8. Nash (KCA) 4.3 9. Bell (CLE) 4.2 10. Tiant (CLE)

Now remember, Baltimore outfielder Frank Robinson achieved the hitting triple crown and led the AL in BA, HR, RBI.  Yet pitcher Earl Wilson, who was traded from Boston to Detroit for outfielder Don Demeter during the 1966 season, is listed with a higher overall WAR than Robinson: 7.9 to 7.7.  This is even more bizarre given that Wilson's pWAR is only 6.1.  That means that Wilson picked up an additional 1.8 WAR from his hitting and fielding.  What a guy.

Wilson

In 1966 Wilson had an OPS+ batting of 120, which I think is enhanced because his batting stats are compared to other pitchers, not to baseball players.  Wilson did hit seven home runs that season, including a pinch hit three run homer.

And this mess doesn't even get into my not trusting the fielding data.