Paradigm of depth
Write poems with thumb sticks
Pens are for schmucks
Ahem. ‘Depth’ is when some mechanism that the player interacts with grows larger. Like, if you make it possible to see which classes the enemy team members are using, you now have access to an extra layer of tactical information that you can interact with. Now, not only are you faced with a group of enemies, but you can adapt your priorities to take account of threat, objective classes, medics that could revive the objective classes, etc. Your objective play just got more deep, because there’s more in there.
If you replace one mechanism like “Aim and click to simulate aiming and trigger pulling with a 1:1 interface”, with another like “Move thumbstick to control the derivative of the motion of the aiming and trigger pulling with a deadzone and curved non 1:1 response” , it doesn’t add depth. It’s a replacement.
If analog sticks had some extra interface, like a third dimension that let you focus shots in 3d embedded in a 4d space or something, sure, depth. If it offered any additional aspect that mouse control doesn’t offer, yep, depth.
It doesn’t. It’s just the replacement of a control system with an inferior control system.
Also: Using bad controls to make a game artificially harder was already old 25 years ago.
On topic stuff: I’d be interested in knowing who did the testing for Brink.

, but no Brink doesn’t support 3D Vision… no idea about Battlefield. 3D would work on your 120hz TV, but nvidias nvision glasses need direct sight to the infra-red receiver that you place on top of the TV/monitor, so if you’re too far away it may possibly cut out and lose the signal.