I have a set of ~100 polygons in ArcMap 10.2.2 that were generated using the minimum bounding geometry tool. 

I have a second set of ~800 polygons generated the same way. What I need to know is for each individual polygon in set 1, how many polygons from set 2 does it overlap with.

I know I can use a tool like 'intersect' but this will produce a list of all unique combinations of overlapping polygons which would be a hugely cumbersome output for a 100 by 800 data set. 

Is there a way to get ArcGIS to simply return the number of polygons that each polygon overlaps with rather than a huge list of all unique intersections?