If you are using a 11.x version of BIG-IP, then you should be able to find a lot of information about connections through the specific profiles that are applied to the virtual server.
Let us say you have the tcp-wan-optimized profile for your clientside tcp profile.
If you go to the statistics for the virtual server and have that profile selected under Profiles > Select Profile then you can see a lot of useful information including things like:
Open
Accepted
Not Accepted
Established
Failed
Expired
Abandoned
If you have a HTTP profile attached to the virtual server, then you can select that and see statistics like:
Requests
GET
POST
Version 0.9
Version 1.0
Version 1.1
Max Requests Per Connection
Total
Responses
Successful
Redirection
Client Errors
Server Errors
Version 0.9
Version 1.0
Version 1.1
Other profile types will display additional information as well.