And a simple ‘ping’ doesn’t indicate how much lag there is between when you fire and when shots appear in the game environment.
When a host fires, his bullets are immediate injected into the game environment and immediately take effect whereas when a client fires his game has to process the bullets and send the network data to windows which shapes it into networking data that can be transmitted which is then shaped it into a packet which is then shaped into a frame which then has to wait for its turn on the local medium (switch, router, etc) which then has to send the frame through 15-25 hops, with each hop analyzing the frame, verifying the CRC, looking up the next hop in a database, and then transmitting it. When it finally reaches your local network (switch, router, etc) it has to wait for the local medium to be free (on university networking with many ppl this can be a problem). When the frame is received it has to have its CRC verified and the packet extracted, the packet has to have its CRC verified and the network data extracted, windows has to pass the data to the game which then has to process it as game data from another user and then your bullets get injected into the game world.
As you can see, there’s ALOT going on and despite how fast it actually happens (newer cisco routers can process 2 million packets/sec) the sheer number of steps does add up. There’s also a million other things that could be done to your game data during transit, such as queuing, labeling, and traffic policing, but that’s getting a little technical for general discussion.
Dedicated servers don’t solve any of that, they simply put everyone on an equal playing field. That’s as fair as a match can get.