I think one of the biggest problems too is that when people cross train they approach things wrong. They notice that Judo guys are good at throwing, which is true. They also notice that BJJ guys are good on the ground, which is also true. Then they deduce that a Judo throwing strategy plus a BJJ ground strategy will be unstoppable in either sport. That is totally wrong.
If you take Judo techniques and strategies straight out of competition, most of them will fail miserably in BJJ competition. Likewise, if you take BJJ techniques and strategies straight out of competition, they will fail miserably in Judo. The benefit of cross training is learning the underlying concepts and then applying them in a relevant way to the particular situation you are in.
You need to learn the techniques of Judo when you train Judo (otherwise how else will you improve?) But learning the techniques is not the underlying goal. You really want to ultimately learn the concepts of Judo. You want to learn how to unbalance an opponent, how to time your entry correctly to take advantage of that moment, and how to throw your opponent in the most efficient way possible. Once you learn those, you can build a base of techniques for BJJ that differ from Judo competition techniques but still use good fundamentals. It works the same way in reverse when you try to apply BJJ to Judo competition groundwork.
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