Well, part of A-Rod's low WAR is the time he missed, coupled with the fact that he did struggle coming back from the injury. However (and I know you can't eliminate any time), he was a very different player after Girardi sat him for those first two games in Florida. If you go back to the second game of the Atlanta series, he finally appeared to be fully healthy, and he was really great from that point forward.
And that brings me back to my initial point. I'm not talking about exactly what the numbers say, but when A-Rod is producing, the Yankees are almost always winning. It's not something that can necessarily be quantified, but it's a trend I've noticed. Last year is a perfect example.
A-Rod missed the first 28 games, and the Yankees started out 13-15. When he came back, he wasn't hitting for a great average, but he hit his share of home runs, and the Yankees went on a nice little run. However, around the beginning of inter-league play, A-Rod was really scuffling, eventually leading to those two days off in Florida.
In my opinion, not only can you pinpoint the turnaround of the Yankees season to one game, you can pinpoint it to one moment, or one hit to be more exact. Second game of the Atlanta series, sixth inning, score tied 1-1, bases loaded for an ice cold A-Rod. A-Rod singles in two runs, the Yankees win the game, and then A-Rod suddenly starts really hitting. Furthermore, right when A-Rod turned his season around, the Yankees went on an absolute tear for the entire rest of the season (amazingly, almost having zero blips on the radar, besides the sweep out in Anaheim right before the ASB). A-Rod had his common cold patches during the rest of the year, but, for the most part, he was his old self and the Yankees were winning.
Then, for the first time since he's been a Yankee, A-Rod hits for the entire postseason, and the Yankees win the World Series.
Obviously there are times when the Yankees have won, and A-Rod hasn't been playing well, and vice-versa, but this has been a pretty solid trend, especially over the past couple years. Is A-Rod to the Yankees tantamount to LeBron James to the Cavs? Absolutely not. However, for whatever reason, the Yankees seem to play well when A-Rod is playing well, and that's why I think A-Rod coming back last season was a bigger lift to the club than people realize (especially when just looking at his pure numbers).