> 1) The number of docs in a subset containing a particular term

  -> `doc_count` in a bucket

> 2) The numbers of docs in a subset

 -> `doc_count` for the containing agg

> 3) The number of docs in the superset containing a particular term
> 4) The numbers of docs in the superset

I'd say that, more interesting than these numbers, is the expected count, or background count.  (4) above will be the same for every bucket. And the absolute number of superset docs containing that term is less interesting than the number of docs you would expect based on background frequencies.

How about:

         "aggregations" : {
             "significantCrimeTypes" : {
                 "doc_count": 47347,        # 1
                 "buckets" : [
                     {
                         "key": "Bicycle theft",
                         "doc_count": 3640,       # 2
                         "score": 7.7, # 3
                         "bg_count": 473  # 4
                     }

Where:

* 1 = the number of docs in the subset
* 2 = the number of docs in the subset containing the term
* 3 = `actual / expected`
* 4 = the expected count based on background frequencies