I guess it's hard for me to grasp because the real-world equivalent is readily available. There is very little chance I'll ever go through basic training and participate in NATO wargames, but I grew up in Florida where Spring Training was all over the place and messing around with pencil and paper and dice doesn't make sense to me when I could so easily go sit in the stands.
On the other hand, I was addicted to Football Manager for awhile when I certainly could never have gone to see a League game, so I guess it's equivalent with your situation...
But Matt? Playing paper baseball when you can go to see an MLB or AAA game so easily? Weird-o!