WhisperzQ: What I was proposing is already an exponential system since the amount varies according to your level. Actually increasing the slope over time I hadn't planned for and I'm not convinced it would work, But there's an alternative: have a fixed drop per month. That means that the percentage increases over time. Perhaps 2 BKR per day?

It would start only when you have a rating, i.e. have completed at least one game in game type. You could also bottom it out at 1300 and not subtract points below that since that is the hidden starting BKR.