Pump-probe-based photoacoustic imaging is an innovative technique for high-specificity molecular imaging in deep tissues. Compared with conventional photoacoustic imaging, this method effectively eliminates the interference from blood signal and other background signal, enabling the detection of subtle target molecules. Additionally, the manipulating of the time delay between the pump laser and probe laser can facilitate non-invasive mapping of oxygen partial pressure distribution within tissues. To quantify the photoacoustic pump-probe imaging, we use methylene blue as the molecular probe to monitor changes in oxygen partial pressure within a hemoglobin solution. Utilizing a Gaussian noise model, we investigate the relationship between the stability of the triplet-state difference signal and the average number, and also evaluate the error associated with measuring oxygen partial pressure. The results demonstrate that the detection accuracy of the system is better than 33 mmHg (1 mmHg = 133 Pa) in the oxygen partial pressure range of about 300 to 550 mmHg after 200 times of averaging. This research will play a significant role in guiding the further advancement and application of pump-probe-based photoacoustic imaging technology.