The Half-Box is one of the first tricks jugglers learn
that includes a horizontal pass (the ball that goes directly between hands).
The pattern is almost universally known by its siteswap, and thus is usually
just called the 441. There have been attempts at giving it a name (some have
tried to call it Parallel Schizophrenic), but none of them have stuck. I
think the name Half-Box matches the trick quite nicely, as it is similar to
the normal Box, except slower and easier. This is not unlike the Half-Shower
and regular Shower patterns.
Regardless of the name, learning the Half-Box is fairly simple. Breaking the pattern down, we can see that there are three main components: a Two-in-One in the left hand, then a pass, then a Two-in-One in the right hand. Thus, you should already be proficient at the Two-in-One in both hands, and also be able to do a solid Cascade before attempting this trick.
To begin practicing, you are going to start with two balls—one in your left and one in your right. Then, you are going to make one throw straight up (as if doing a Two-in-One) from your dominant hand, and then right after that you are going to make a horizontal pass from your non-dominant hand to your now empty dominant hand. Then, you are going to make a second Two-in-One throw with that ball you just passed, and then catch the first ball. And finally, you are going to pass that first ball to your non-dominant and catch the second ball. The balls should end up in a different hand than when they started:
You are going to want to practice this in each hand, as it is the foundation of the Half-Box. Once you can reliably perform these throws in both directions, you are ready to link them together:
Now its just a matter of adding the third ball. Start with two balls in your dominant hand, one ball in the other. Throw one ball from your dominant hand, then throw the ball in your non-dominant hand. Right after you throw that second ball, do a horizontal pass from your dominant hand to your non-dominant hand, and then stop. You have just done one run of the Half-Box:
All that's left is just to remove the pause and keep the pattern going. This can be done by throwing another Two-in-One throw at the end of the flash, and just repeating the cycle again:
And there you have it. Just keep adding in more and more cycles and eventually you will be able to the Half-Box indefinitely. As the name suggests, this trick is perfect for practicing the Box (though I personally learned the Box first)but it can also be good training for the Shower pattern.