The team in May had no juice, also the reason why folks go to games in April - July is because partly because of the stadium and the fact that this stadium doesn't have the same amenities that many modern stadiums have.
You a Yankee fan, you know that most folks at games aren't really in their seats, they're too busy getting Garlic Fries or getting their son a $300 Jeter jersey. In this day in age, the games are secondary to the stadium. Obviously you can't have a baller stadium and a wack team and draw 30,000+ regularly, but a quality stadium and one in a great location is very important to a team's ability to draw.
If you don't believe me, peep the Nets when they were in Jersey(sans the last two years in downtown Newark), they were in a terrible location couldn't draw too well.