This is where skill gets earned rather than claimed. A call isn't scored on whether it hit — it's scored on how well the stated confidence matched reality.
Because the penalty is squared, being 90% sure and wrong (0.81) costs almost 3× being 55% sure and wrong (0.30). Overconfidence is punished quadratically harder than honest uncertainty — the curve is the whole argument.
It's a proper scoring rule — the mathematically optimal strategy is to state your honest belief, no more and no less. That property only holds because confidence does exactly one job here: it is scored, and it is never used to compute a payout.