I think this could be fun: include a player rating that reduces or increases the likelihood of them doing something ranging from moderately dumb to blooper-reel stupid during a game.   Dignified term: baseball IQ.  Much more fun term: idiot factor.

1. getting picked off base
2. miscommunicating with another fielder and letting a ball drop
3. throwing to the wrong bag or forgetting to look first at the runner on 3rd to freeze them
4. poor situational hitting decisions
5. losing fly ball in the sun
6. sliding headfirst (dumb dumb dumb)

The 'idiot factor' is also a category that one would reasonably expect to improve over a player's career, disproportionately penalizing younger players.  

Implementation could be complicated because it would be unfair to retroactively apply damaging or beneficial idiot factors to existing players.  That could be sidestepped by assigning all existing players a neutral rating of 50, and only future players would have variability in this category.  

1. getting picked off base- it's called baserunning rating
2. miscommunicating with another fielder and letting a ball drop - it's called range and glove
3. throwing to the wrong bag or forgetting to look first at the runner on 3rd to freeze them - it's called throwing accuracy
4. poor situational hitting decisions - it's called managerial settings
5. losing fly ball in the sun - it's called glove
6. sliding headfirst (dumb dumb dumb) - it's called baserunning

ie. it's already there.

Eh, not really, deathinahole:

1. getting picked off base- it's called baserunning rating
Agreed on this one

2. miscommunicating with another fielder and letting a ball drop - it's called range and glove
Even a good fielder could perceivably get into position and then, because the C is also in the area or something, let the ball drop due to poor communication.  This might effectively be in the game in the form of errors, but the play by could spell it out

3. throwing to the wrong bag or forgetting to look first at the runner on 3rd to freeze them - it's called throwing accuracy
I don't think guys throw entirely to the wrong bag all that often (other than, say, OF missing the cutoff man or something), but that's not exactly throwing ACCURACY as it is awareness.

4. poor situational hitting decisions - it's called managerial settings
I mostly agree, but this rating would influence it on a player by player basis.

5. losing fly ball in the sun - it's called glove
Again, this isn't so much "glove" (maybe "sunglasses"?), but is probably "in" the game...they could just add another colorful description of this on some occasions.

6. sliding headfirst (dumb dumb dumb) - it's called baserunning
It's not really baserunning at all.  Sliding head first, beyond being a dumb baseball play a lot of the time, could lead to injuries.  I don't think there's anything in the code wherein player with poor baserunning ratings get injured more often.