Its not like you can just add up WAR for the players in and out, you need to look at what you gain/lose at each position. Using steamers projections
C - +Martin - Navarro (+3.1 WAR) (and we haven't added anything for whoever he trades Navarro for)
1B- +Smoak - Lind (-0.4 WAR)
2B- hard to say
SS- no change
3B- +Donaldson - Lawrie (+1.8 WAR) (if Lawrie stays healthy)
LF- +Saundeers - Melky (0 WAR)
CF- +Pompey - Rasmus (-1.2 WAR). Pillar is projected at 1.2 WAR as well, but not sure how much he will play (hopefully not much in CF)
RF- no change
On the pitching side its harder to compare because we lost so many RP's and we don't know who will be replacing them, but none of Janssen, Graveman, or Nolin projected for much value and RP's are uber volatile anyway unless they are elite (none of those guys). Estrada in, but also little projection.
We lose JP Happ (1.2 WAR) but plunk in Norris or Sanchez. We also haven't factored in pitch framing wins that will show up in the pitchers WAR.
In adding wins, AA has also cleared payroll space which I truly hope he is in a position to spend.