A-Rod will turn 37 years old in July. There haven't been many great seasons from old third basemen over the years. In fact, only two have ever turned in a 6+ WAR season, Mike Schmidt in 1986 and Chipper Jones in 2008. It doesn't look encouraging for Alex, who continued his decline in 2011 (his bWAR has dropped each of the last four years). Below are the top 20 seasons for third basemen aged 36 or older -
There are some good names on the list in addition to Schmidt and Jones: Robinson, Boggs, Rose and Nettles to name a few. But overall it's discouraging. What's considered an elite season? Maybe 7+ WAR. That means only one Yankee even came close last season (CC Sabathia at 6.9) and no 36+ third baseman's ever had an elite season.
One could make an argument that A-Rod will be an exception, considering he started his career at the more athletic position of shortstop and will go down as one of baseball's best players. The (former) athleticism should help as he approaches 40 and because of the money he's owed, he'll be guaranteed as much playing time as he can stand.
In terms of production, though, I'm not holding my breath. I think we'll be lucky to see Alex top 4 WAR in a season again. And even if he is producing, can he stay healthy for 140 games?