https://www.ncl.com/latitudes-rewards-program#tier_benefits
Silver/Gold and Platinum get 10% off shore excursions
Sapphire and Diamond get 15% off
Ambassador get 20% off
this discount is applied after the free at sea 50 dollar credit. math looks like this:
retail price - $50 dollar free at sea credit - % latitude discount
for a sapphire latitude member with the free at sea shore excursion credit and the 15% discount, a $79 dollar excursion is only $24.65