I can still make 100000 lottery predictions, and get a good score. I look for a system which you cannot trick in that way. Ok, for each prediction, you can subtract the average score from your score. That should work. Assuming that all other predictions are rational, too, you get an expectation of 0 difference in the lottery predictions.

I've only been making the forecast well-specified

I think "impact here (10% confidence), no impact at that place (90% confidence)" is quite specific. It is a binary event.