Perception of a stimulus variable (e.g., the angular orientation of a line segment) can be typically characterized by two fundamental psychophysical measures: perceptual bias and discrimination threshold. It has been long believed that these two measures are independent. However, we argue that this is not the case and that they are tightly coupled instead. We propose a new perceptual law that defines the relationship between perceptual bias and discrimination threshold. The law is derived from a recently proposed theory of perception that assumes that the representation of sensory information (encoding) as well as its interpretation (decoding) are optimally adapted to the statistics of the sensory input (Wei and Stocker, Nature Neuroscience, 2015). The theory predicts that both, perceptual bias and discrimination threshold, are directly constrained by the input statistics and thus are linked. We have now formalized this link, which results in a surprisingly simple mathematical relationship between perceptual bias and discrimination threshold. The relationship allows us to predict one measure from the other (up to a scaling factor and an offset), and vice versa. We tested the proposed relationship against a wide range of published data-sets for many different sensory variables (such as for e.g., local orientation, spatial frequency, motion direction, pursuit direction, heading direction, biological motion), and found that it is well supported. Importantly, we also find the relationship to hold for measured changes in discrimination threshold and perceptual bias under varying temporal and spatial context (e.g. adaptation, perceptual learning, or surround effects such as the tilt-illusion). Based on the wide empirical support, we argue that we have derived and identified a new perceptual law, which is testament to a more holistic understanding of perception.