Doesn't matter how big your pipe is, what matters is how long it takes to send something from one end to the other. Physical distance matters, but usually the problem is how many hops (routers, etc) you have to make before hitting the remote server.

A lot of games give a "ping" stat as a very rough measurement of your lag. You can try measuring this outside of the game, but unless you know how to specifically target the game server, you won't be able to get a very accurate measurement.

Are you on wireless? You may see some improvement on a wired connection.