IMO, it is neither the computer's fault, nor does the battery affects average.
My guess is; when you changed car's battery, the car's ECU did not get reqd. power for some time and it got reset. Then when you connected the battery terminals and it got power, it did a sort of "Idle Re-learn Procedure" and adjusted some parameters by its own, resulting in good fuel efficiency.
If there is no malfunction, and your car is not misbehaving, then you should be happy and keep driving your car. 