This comes from https://wiki.archlinux.org/index.php/Logitech_Marble_Mouse
Append the following to /usr/share/X11/xorg.conf.d/10-evdev.conf (and then restart X)
# - - - Logitech Marble Mouse Settings - - -
#
# The Logitech Marble Mouse buttons are mapped [A-D] from left to right:
# A (large); B (small) | C (small); D (large).
#
# Preferred options for right-handed usage:
# A = normal click [1]
# B = middle-click [2]
# C = middle-click [2]
# D = right-click [3]
# Hold button B while rolling trackball to emulate wheel-scrolling.
#
# Preferred options for left-handed usage:
# A = right-click [3]
# B = middle-click [2]
# C = middle-click [2]
# D = normal click [1]
# Hold button C while rolling trackball to emulate wheel-scrolling.
# Pressing both large buttons simultaneously (b) produces a "back" action.
Section "InputClass"
Identifier "Marble Mouse"
MatchProduct "Logitech USB Trackball"
MatchIsPointer "on"
MatchDevicePath "/dev/input/event*"
Driver "evdev"
# Physical button #s: A b D - - - - B C
# Option "ButtonMapping" "1 8 3 4 5 6 7 2 2" right-hand placement
# Option "ButtonMapping" "3 8 1 4 5 6 7 2 2" left-hand placement
# b = A & D
Option "ButtonMapping" "3 8 1 4 5 6 7 2 2"
# EmulateWheel: Use Marble Mouse trackball as mouse wheel
# Factory Default: 8; Use 9 for right side small button
Option "EmulateWheel" "true"
Option "EmulateWheelButton" "9"
# EmulateWheelInertia: How far (in pixels) the pointer must move to
# generate button press/release events in wheel emulation mode.
# Factory Default: 50
Option "EmulateWheelInertia" "10"
# Axis Mapping: Enable vertical [ZAxis] and horizontal [XAxis] scrolling
Option "ZAxisMapping" "4 5"
Option "XAxisMapping" "6 7"
# Emulate3Buttons: Required to interpret simultaneous press of two large
# buttons, A & D, as a seperate command, b.
# Factory Default: true
Option "Emulate3Buttons" "true"
EndSection
