is there a command in battlefield 3 to change the mouse sensitivity with a numerical value in the console?
You can edit your config file for a more precise sensitivity adjustment.
Configs are located in:
My Documents/Battlefield 3/PROF_SAVE_profile
Back this file up before making any changes.
Open in Notepad and edit these values. I haven't tweaked these in the config since beta when there was a bug with the sensitivity slider, so I couldn't tell you what the scheme0/1/2 values affect.
GstInput.MouseSensitivity GstInput.Scheme0Sensitivity GstInput.Scheme1Sensitivity GstInput.Scheme2Sensitivity
Edit: Try this in the console
Edit the value to your preference.