The prize is not in a special category. It is part of your earned income for the year, which is reduced by above the line deductions. So someone with a wife a two kids isn't have a very high effective rate even with the winnings.
I'm still really not sure what your point is. Those "for AGI" deductions are set flat rates. They aren't going to reduce the prize winnings at all which will go straight to your highest marginal rate, if not higher than your highest marginal rate. It's got nothing to do with your effective rate.
I'm no accountant though (but I did stay in a holiday inn express last night
), how about anyone else?