Another competitive game we play is one I call 'Bash and Dash'
Set up: Coach is throwing BP style from behind an L-screen. I put a temporary base at about 80-85 feet and then let the 2nd teamers hit with the 8 starters on the field. The starters are still throwing to the regular base but any time the hitter reaches the temporary base before the ball is caught he is safe (this is to equalize the speed of the jv guys being slower running to 1st.. puts pressure on the defense to get the ball to first simulating a fast runner)
If the ball is a hit into the outfield we have the DASH part of the game. The hitter keeps right on running up the right field line to a cone that is about 160-170 feet from home plate. The outfield is simulating a man going to home and the throw must arrive at home before the hitter (who is dashing) passes the cone.
The defense gets 2 points for every out. The offense gets 1 point for a single and 3 if they reach the cone ahead of the throw.
You can also have the OF throw the ball to 3rd and use the same deal where they have to beat the hitter to the cone.
The hitters get to swing and get some good running in. The defense has pressure on them on every ball... they even learn they must take care of the ball on a routine single and get it somewhere or it can cost them points.
if you try it you'll probably find a way to tweak it a little to suit your needs best. MY jv guys love this game and starters do NOT like losing to the 2nd team so it can get pretty competitive.