Some people measure a FCR in a different way. Instead of First Call Resolution, which is normally a percentage between 0 and 100%, they measure the repeat contact rate.
The repeat contact rate is the average number of calls per problem. At it's crudest level it is
Repeat contact rate = Total number of calls / Total number or problems raised
This gives a number greater than 1, e.g. 1.9 calls per problem.
Dividing the other way would give the First Call resolution rate
FCR = Total number or problems / Total number of calls
So 1.9 calls per problem = 53% FCR
At it's simplest level you can get "Total number of calls" from the ACD stats and "Total number or problems" from your help desk system. The problem being that it is possible to maniputate the "Total number or problems", for example giving
I agree with John that using Speech Analytics would probably give you a more realistic answer.