This was my first introduction into baseball simulation:
Sher-Co Baseball
After that I went on to Strat-o-matic and Pursue the Pennant.
On the computer I played Micro-League and Earl Weaver on the Amiga, but computer games were more a diversion and the board games were the bread and butter until I got married and started a family and found less time for the accounting required by board games.
The first computer game I really got serious about was Tony LaRussa and its companion game Old Time Baseball.