[Sophira]

There's a huge difference between the latency you get from connecting to each other via the Internet, and the latency you get going via a local network, even if that network is a wireless one.

There's an even bigger difference between that, and going online via the Internet back in the days when LAN parties were really popular, because the most common method of connecting to the internet was via modem.

[Cpoll]

IME WiFi always adds ~20ms, which might be more than a server in your city (though realistically 50ms is a good number and 100ms is acceptable).

But I expect this number gets worse in a LAN party due to contention.