On your computer,
use program Putty and SSH to your PI’s ip address.
login: pi
Password: raspberry (unless updated by you)

Add:
usbhid.mousepoll=0
to cmdline.txt

sudo nano /boot/cmdline.txt
on the same line separated from other stuff by spaces
This parameter enforces a mouse polling rate of ? 62.5Hz ? and reduces any quick movement lag.
0 or 1 - 1000Hz, 2 - 500Hz, 4 - 250Hz, 8 - 125Hz, 16 - 62.5Hz
(Micro-controller is updating mouse as fast as main loop() and any axes interrupt(s) being serviced. avg 40 - 100 µS)

   (using lsusb command {after installing} lists - ID ####:#### or Vender and Product-ID
   for your custom Trackball controller; using grep as root to find Iv1=polling interval, to be
         1ms or 1000Hz
   grep -B3 -A15 ####.*#### /sys/kernel/debug/usb/devices
   device info starts with T: line, and ends with E: line
   find I: line with driver=usbhid or hid)

sudo reboot

Under Arcade or MAME select your favourite trackball game.
TAB to bring up the Game Menu
Select Analog Controls
Adjust the X Sensitivity & Y Sensitivity values