Folks who know tons about lithium polymer and other types of batteries are radio controlled model airplane enthusiasts! Some of them are extremely technical in knowledge. You can find them hanging out in this forum:
A very friendly group and willing to answer questions.
From what I know, lithium batteries are very sensitive to discharge levels so you have to stop using them after they drop below a certain voltage per cell. You can't necessarily run them until the ball machine drops below a certain performance level. Model airplane enthusiasts often monitor battery voltage with on-board electronics, or they use a timer.