Percentage of border polygons within larger polygon

[QMT]

I have a bunch of large, roughly rectangular, contiguous polygons (X, Y, Z, etc) filled with hundreds of very irregular-shaped polygons (watersheds). I would like to be able to create a scenario where the edges of X polygon are determined by how much of each intersected watershed is within X polygon, say, >50% for instance. Such that if 50% or more of the watershed were in X, then X gets that watershed; if <50% then the watershed belongs to the neighboring Y polygon. Is there a tool that can do this? Or even a series of steps?

I have used clip to show which watersheds intersect the border of X. I don't know how to determine the percentage of each watershed that extends beyond that border, so that I can keep it or include it in another large polygon. Any suggestions? Thanks.

[JohannesLindner]

The answer to this question seems like it should work for you, too.

[QMT · Accepted solution]

No, Johannes, that is not what I'm looking for. I guess I wasn't clear. I am not wanting to find the sum of all the watersheds in the large polygon which overlap. I need to find the percentage of each individual one to determine whether it stays or goes, in terms of the border. I don't know whether this attachment will make it more clear.

I figured it out myself yesterday using "calculate geometry" on the inside border portions (purple in today's example) of the large polygon, then determined the percentages by comparing them to each whole watershed (the rest of which is in green) in the attribute table. In the image, you can see the blue section to the right where I have removed those watersheds which were <50% within the larger polygon of that example. It worked perfectly yesterday. 

Today I am getting an error message when I try to use "calculate geometry": 

The calculated value is invalid for the row with ObjectID =1. Examples for this error are: The calculated value is be (sic) too large for the field, or you are trying to add a string to a number field, or the string is not properly quoted (Use double quotes). This row will not be updated.

Do you want to process the rest of the rows? [Yes/No] - and then when I choose Yes:

All calculated values were invalid and none of the rows have been updated.

 Any idea what could be happening? I shut everything down and restarted, it didn't help. I don't know what else to do. Thanks for your help.

[QMT]

Allllllrighty then...! I figured this one out also. I simply had not chosen the correct field type when I created the new field. Yikes. Thanks guys.