Dont want to match on stop words

Got an index with about a thousand movies names. If I search for a movie
that doesn't yet exist in the index, say "The Avengers: Age of Ultron", it
will come back with matches for things like "Sponge Bob: The Movie",
presumably because it matches on the word "the" even though its is
completely irrelevant in this case and I do NOT want to show these as
results, looks dumb!. I don't want to to completely eliminate stop words
either since a movie name like "Her" should still be valid and find a
match. I tried using cutoff_frequency = 0.001 but doesn't make any
difference here.
My query is like:
"query": {
"filtered": {
"query": {
"match": {
"movie_name": {
"query": "believe",
"cutoff_frequency": 0.01
}
}
}
}
}
An ideas on the best strategy here? is there way to specify that a minimum
percentage of words must match?

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