The successful integration of computer vision, robotic actuation, and photoacoustic imaging to find and follow targets of interest during surgical and interventional procedures requires accurate photoacoustic target detectability. This detectability has traditionally been assessed with image quality metrics, such as contrast, contrast-to-noise ratio, and signal-to-noise ratio (SNR). However, predicting target tracking performance expectations when using these traditional metrics is difficult due to unbounded values and sensitivity to image manipulation techniques like thresholding. The generalized contrast-to-noise ratio (gCNR) is a recently introduced alternative target detectability metric, with previous work dedicated to empirical demonstrations of applicability to photoacoustic images. In this article, we present theoretical approaches to model and predict the gCNR of photoacoustic images with an associated theoretical framework to analyze relationships between imaging system parameters and computer vision task performance. Our theoretical gCNR predictions are validated with histogram-based gCNR measurements from simulated, experimental phantom, ex vivo, and in vivo datasets. The mean absolute errors between predicted and measured gCNR values ranged from 3.2 × 10-3 to 2.3 × 10-2 for each dataset, with channel SNRs ranging -40 to 40 dB and laser energies ranging 0.07 μJ to 68 mJ. Relationships among gCNR, laser energy, target and background image parameters, target segmentation, and threshold levels were also investigated. Results provide a promising foundation to enable predictions of photoacoustic gCNR and visual servoing segmentation accuracy. The efficiency of precursory surgical and interventional tasks (e.g., energy selection for photoacoustic-guided surgeries) may also be improved with the proposed framework.