Some kind of controversy always seems to surround the Oscars. If it isn’t outrage beforehand over who was snubbed, it is derision afterward about the embarrassing speeches or the taste-challenged outfits that were paraded down the red carpet.

Yet the “Oscar effect” on nominated movies can be transformative. In 2004, a low-key film about a female boxer had earned just $8.5 million. But after being nominated for best picture, “Million Dollar Baby” enjoyed a spectacular resurgence and raked in additional $56.4 million, according...