
I believe that the "A-D converters" found on a joystick port are really
timers that tick off how long it takes an R-C circuit (the R being your
paddle) to charge up to something like 1/2 Vcc.  For games this works
pretty well, but you certainly wouldn't want to try to take lab
measurements off something as non-linear as that.

Hmm... I suppose you could linearize it in software, but the real problem
is that the precision of your measurement is no longer constant (higher
voltages would be more precise).

On the other hand, I could be wrong and perhaps the game card designers
splurged for the extra $.50 to make a cheap constant current source out of
an op amp.  But I wouldn't expect that...