How to reduce student plagiarism?
It might be helpful if you can tell us what field you are in, or more specifically what kinds of class you are teaching. What is the subject, and is it a big lecture class or a small section, etc? Catching 50 plagiarists makes me think you are teaching big lecture sections. 

Here are two things I do: First, I have a very harsh plagiarism policy. I automatically fail anybody I catch plagiarizing. This raises the stakes.

Second, I consciously try to design assignments that are hard to plagiarize. There are a variety of ways to do this. For instance, you can give fairly specific assignments. Don't say: "Write a paper about Shakespeare" but instead "Write me a paper on the role of ghosts in King Lear and MacBeth." This doesn't make cheating impossible, but it makes it harder to google and get a prefabbed paper.