Which of the following phrases is correct? Could you explain why?
The more often you do this, the better the results.
The more often you do this, the better the results are.
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They're both fine in my opinion - you can think of the better the results are as the more general form:
The verb is especially important when you need to be specific about tense, but it's common to omit it - but it's still implied, the sentence doesn't make grammatical sense without a verb. Try it with a less familiar phrasing:
You want it to say the more the rain falls, or the more it rains, right? But when it's the copula (the be verb used as thing is something) it's often dropped, because people understand it's implied.