The brain exhibits organized fluctuations of neural activity, even in the absence of tasks or sensory input. A prominent type of such spontaneous activity is the alpha rhythm, which influences perception and interacts with other ongoing neural activity. It is currently hypothesized that states of decreased prestimulus α oscillations indicate enhanced neural excitability, resulting in improved perceptual acuity. Nevertheless, it remains debated how changes in excitability manifest at the behavioral level in perceptual tasks. We addressed this issue by comparing two alternative models describing the effect of spontaneous α power on signal detection. The first model assumes that decreased α power increases baseline excitability, amplifying the response to both signal and noise, predicting a liberal detection criterion with no effect on sensitivity. The second model predicts that decreased α power increases the trial-by-trial precision of the sensory response, resulting in improved sensitivity. We tested these models in two EEG experiments in humans where we analyzed the effects of prestimulus α power on visual detection and discrimination using a signal detection framework. Both experiments provide strong evidence that decreased α power reflects a more liberal detection criterion, rather than improved sensitivity, consistent with the baseline model. In other words, when the task requires detecting stimulus presence versus absence, reduced α oscillations make observers more likely to report the stimulus regardless of actual stimulus presence. Contrary to previous interpretations, these results suggest that states of decreased α oscillations increase the global baseline excitability of sensory systems without affecting perceptual acuity. SIGNIFICANCE STATEMENT Spontaneous fluctuations of brain activity explain why a faint sensory stimulus is sometimes perceived and sometimes not. The prevailing view is that heightened neural excitability, indexed by decreased α oscillations, promotes better perceptual performance. Here, we provide evidence that heightened neural excitability instead reflects a state of biased perception, during which a person is more likely to see a stimulus, whether or not it is actually present. Therefore, we propose that changes in neural excitability leave the precision of sensory processing unaffected. These results establish the link between spontaneous brain activity and the variability in human perception.