Reduction of Noise is just as effective (on average) as reducing bias when it comes to correcting system error.
For a single measurement:
For the Mean Squared Error (MSE) of multiple measurements:
MSE = Bias^2 + Noise
Reduction is either bias or noise will reduce overall error.
This means, when optimizing for greater accuracy, you can focus on the noise in the results even before you know how they are biased.