I'm no expert by a long shot, so take what I post here with that in mind. From what I've read, studied, etc; connection speed isn't much of a problem. What is a problem is jitter and bufferbloat; for any shooter gaming, with bufferbloat most of the problem.
Jitter will cause jerky forward and backward movements, but not warping and such. Bufferbloat problems will be more prevalent for upstream packets. To make it simple; since I'm a simple person!
The game sends packets to your router which in turn gathers them in the buffer until it's told told send them. The more sitting in the buffer the longer the game server waits for the data. If full and not sent fast enough packets get dropped. Example: It may wait for 2 or more packets before sending; then send. Milliseconds have passed which turn into larger numbers as the packet goes from your computer to the trunk line routers to the game server. Meantime the game server is pushing packets to you at steady state.
Ever notice a player who just as you pull the trigger they warp out of your gunsite? How about the bullet sponge (your shooting at where they were on your frontend), but in game they aren't there? How about the plane you PK that blows up behind you after you pull up from your pass or after you quit squeezing the trigger you get a PK? These are all symptoms of bufferbloat from what I understand. Basically the plane isn't where the game thinks it is. Hence ack shoots at thin air as the milliseconds in delay of packet input makes it so. Add in movement such as rolling and other movements and voila.
Downstream packet bufferbloat is practically no problem for gaming. There are some things you can do to help with bufferbloat, but most consumer grade routers don't have the software to effect results from what I gather. I use a business connection with "supposedly" higher end hardware.
Take this info for what it's worth. Maybe a pile of cowpie or not.
Test your connection using this:
http://www.dslreports.com/speedtestTesting:
Log view of results:
http://www.dslreports.com/speedtest/4290743My laptop through wifi: