Two things move the number, and they work in different directions to what most people assume. Sailing late in the season, February and March, costs less than the Christmas and January peak. And booking early now beats booking late, because the market has shifted to early bird pricing and the deep last minute discounts have largely dried up.
The last minute strategy is the one that catches people out. It used to work. Operators would dump unsold cabins close to departure and patient travellers picked them up cheaply. That behaviour has mostly gone, and holding out for it now usually means paying more, or finding the departure you wanted has sold.
November and early December sit between the two extremes on price and are worth a look if peak season is out of budget but you want chicks or good snow.
Discount patterns and release schedules move around by operator and by season, so ask us what's open rather than working from a general rule.