Generally speaking, a decent ADC is as accurate as its voltage reference.
The properties of an ADC itself are defined in terms of monotonicity (each output value corresponds to an input voltage higher than the previous one), linearity (if output C corresponds to a voltage V1, output NxC should correspond to voltage NxV1), and uniformity (the difference in input voltage between output C and output C+1 should be about the same for all C).
Assuming all those are suitably well behaved, the output values are defined as fractions of the ADC's reference voltage. If the reference is accurate and stable, the output values should be correspondingly accurate and stable.
Creating a really good voltage reference is a specialized job though. Most voltage regulators are only accurate to between 1% and 5% of their nominal value, and their job is to keep their output within a reasonable distance of the nominal voltage across a wide range of operating currents. Translating a 1% error to a 13-bit ADC means you can expect error of +/-82 LSB in any reading.
Our LM4040 voltage references are designed for 0.1% accuracy, or +/-8 LSB on a 13-bit ADC:https://www.adafruit.com/products/2200