Part of the problem (I think) is that ticket_sales is doing something strange:
It records the amount_paid by participant_id for ticket_id between draw_id-1 and draw_id - i.e. the draw cycle is acting as your time-scale, rather than using a real date.

Nothing is indicating if a ticket participated in a draw. Rather than storing this as an associative entity, you are having to calculate/infer it. If you had this entity: sum(amount_paid)-count(ticket_draw_participations)*price gives your answer.