Yeah, I have about 3-400. But I doubt that affects it much.
Eligible should mean all the games you have made badges for, right? So it's quite proportional to your level.
Eligible is all the games you have received all the card drops for. Doing a quick check of your Steam profile, you have 100 eligible games, give or take. Every tenth Steam level, your overall drop rate chance increases by 20%.
You can have 100 eligible games without crafting any badge, as long as you have played your games enough to receive all the card drops (about half of the required cards to craft the lvl 1 badge).