Do understand right that the Yankeee/TB game is the only one played on March 31 and therefore your whole team consists of Yankees or Devil Rays?
To elaborate on strategy for the newbies in the game....
Your whole team should consist of only players who are playing that day -- in this case, Yankees or Devil Rays.
While your first inclination may be to pick an "All-Star" team (to the extent that it's possible while staying within the salary cap), the main thing to remember is that
THIS IS A DAILY GAME
You get to change your roster and pitching staff (which is what you should build your team around every day, since the scoring system results in about 40% of your points on a typical day coming from pitching) every day, so if you pick players who are not playing on a particular day, you get no points from them.
On good day, you can figure on about 30-35 offensive points, and 20-25 pitching points, so having an offensive position un-filled could cost you 4 or 5 points or so, and having no pitching staff could cost 20-25, or more. Do that enough times during the season, and it adds up when everyone else is picking a full team every day.
However , bear in mind that each week the salary cap values of the good players usually increase. So, for example, if you have A. Rod, let's say, at a value of 5.0, as long as you keep him on your team he only counts for 5.0 against the cap. But let's say his value increases to 6.0, and the Yankees have an off day. If you replace him with another third baseman, when and if you want to use A. Rod again, you have to add him back at his new value. So you may want to sacrifice the potential points you can get from a replacement third baseman for one day in order to keep A. Rod at the lower price.
Another thing, RE: DB's comment about possibly not picking a pitching staff for the Yanks-Tampa:
The way the scoring system goes, if your pitcher gets bombed, it's possible to wind up with negative points for the day, so it's conceivable that if you have two really bad pitchers going in a small ballpark like they have in Japan, and the final score winds up 9-8 or something with lots of hits and walks, both pitchers could wind up with a negative total, in which case you would have been better off with no pitcher, and a zero score.
:p 
