Is there a way to determine how many unauthenticated connections are currently clogging up my ssh queue?

Some tool being used by our developers is causing numerous unauthenticated ssh connections (still trying to track this down). I have set LoginGraceTime to 30 in sshd_config, but for whatever reason, some of these unauthenticated connections are not terminating. Thus, eventually the MaxStartups value is being reached and ssh connections are no longer possible.

Doing a ps and grep'ing for sshd shows me all the ssh connections, but I'm having trouble differentiating between real connections and the lingering unauthenticated connections. Searching for "authentication failure" in the logs gives me a rough count, but I am hoping for a command which will give me the exact count.

Thank you for any help you can provide.

you can see active remote logins with /usr/bin/w (it reads /var/run/utmp actually)