Does having your knife out make you move faster? If not, what does?

Solution 1:

Sprint Jumping is the fastest method of getting from A to B, with the caveats that you become more visible and less capable of quickly killing a target thanks to the time it takes for your aim (the random spread, not your physical view) to settle down.

The part of the animation when you land from a sprinting jump moves your avatar faster forwards than the regular sprint speed, so continuously jumping while sprinting causes this part of the animation to repeat and over time this adds up to a significant bon

For proof: see this video where two people run side by side, one sprinting, the other sprint jumping. Also just spend a couple of minutes with a friend to test will show you that sprint jumping and the sprint perk are the only way to increase sprint speed, no matter the weapon held or loadout equipped.

The sprint perk raises your speed by 10%, as seen in the game data files themselves.

Solution 2:

I have no official word from DICE on this one, but running with a knife does not make you run faster (even if it seems like it does). Also, Squad perks spread evenly to the squad, so if the leader has 30% increased speed, so do the squadmates. On a further note, perks do not stack so the only way for you to get to the flag first is to take the most direct route and cut corners ever so perfectly.

Or, alternativley take one of those humvees at the spawn (I think they're on Metro) and drive right in there like a boss. (Joking)

Solution 3:

No.

However, you do move slightly faster when aiming with certain guns.

E.g. moving while aiming with a pistol is faster than moving while aiming with a heavy assault rifle, or LMG.

It's a fairly mild effect.