Data suggests that there is no correlation between production budget and a film's chance of winning an Oscar. In fact, several winning best pictures between 1991 and 2015 had product budgets well below 20 million dollars while only a handful of nominated films had budgets that exceeded 100 million dollars.
One Best Picture nominee, "Beasts of the Southern Wild," cost only slightly more than 1 million dollars to make. Statistically, blockbusters do not fare well during awards seasons. The list of critically acclaimed blockbusters in the latter half of the 20th century and beginning of the 21st century is somewhat limited. It includes "Titanic," "Braveheart," "Gladiator," "Forrest Gump," the "Lord of the Rings" trilogy and "Avatar." Only five of those nominees actually went on to win the Oscar award for Best Picture.