Most of those games involved generic players who occasionally had different abilities but the games were basically simple.
There were two baseball games that actually used real players that I played as a kid. One was called All Star baseball. Every all star player was represented by a disc which fit into a spinner. One player from each position was selected, a lineup was made, and every at bat was a spin. Numbers ranged from 1-14 and the space for each number represented how often each possibility could occur.
The numbers were:
* 1 Home Run
* 2 Ground out, double play with runner on first base
* 3 Runner reaches base on error
* 4 Fly out, all runners advance
* 5 Triple
* 6 Ground out, all runners advance
* 7 Single, runners advance one base
* 8 Fly out, runner on third base scores, others hold
* 9 Walk (Base on balls)
* 10 Strikeout
* 11 Double
* 12 Ground out, runners advance if forced
* 13 Single, runners advance two bases
* 14 Fly out, runners hold their bases
Since my daughter's softball season ended last Monday, I decided to create a disc to represent her season: (Note: Not all possibilities are on the disc since those situations did not occur in her 22 plate appearances)

I added number 15 to represent hit by pitch.