The Manager of the Year award is a curious one, which is why SB Nation isn't giving out this award. Basically, it's given to a manager whose team does really well, especially when it's unexpected.
Could the A.L. award this year have gone to the White Sox' Robin Ventura? Maybe, but they didn't win their division, even though by all accounts he did a great job (with no experience). Mike Matheny did the same thing with the Cardinals, but apparently since the Nationals won more games than the Cardinals did, Davey Johnson was the league's best manager. The Reds won just one fewer game than the Nats did, but I guess that's not enough.
Two teams in the American League were surprise playoff participants -- the Orioles and Athletics. Which manager did a better job getting his team into the postseason? Who knows, but the writers think Bob Melvin did a better job in Oakland. It could have gone either way -- I originally wrote this with "Buck Showalter" and "Baltimore" at the beginning of this sentence. The Yankees won more games than both of those teams, but they were supposed to, so Joe Girardi doesn't get it.
This award isn't really quantifiable nor are there really qualitative reasons that can be given for it. So maybe it's a popularity contest. In any case, congratulations to the winners. And if you want to find out who voted for whom, click here for the AL ballots and here for the NL ballots.