> ls -l /bin/ping
-rws--x--x 1 root root 32820 Jul 19 2012 /bin/ping*
To my limited understanding, more senior members may suggest better explanation. 'ping' needs to open raw sockets and 'root' can only do that so with SUID set to root when you run 'ping' it's as if 'root' is running it (but just as long as ping is running).
> ls -l /usr/bin/write
-rwxr-sr-x 1 root tty 10156 Aug 15 2012 /usr/bin/write*
In case of 'write' a user needs to write to another user's console, which is not normally allowed but a separate group (tty) is created and given access to write to TTYs. 'tty' group obviously was not given full 'root' access, so limiting the power as a security measure.
Now, I'm not sure why not create a separate group 'xgroup' and give it access to open/close sockets for 'ping' command.