Recently, near infrared (NIR) organic photodetectors (OPDs) have been extensively studied. Bulk heterojunction NIR OPDs composed of a high-bandgap polymer donor (PD) and a low-bandgap non-fullerene acceptor (NFA) showed the best performance, whereas the low-bandgap PD-based OPDs were relatively unsuccessful due to the high level of dark current density (Jd) under a negative bias. In this study, we synthesized three low-bandgap PDs based on a thieno[3,4-b]pyrazine (TP) moiety and developed red-NIR OPDs by blending them with a low-bandgap NFA. We found that the PD having a shallow HOMO energy level generated the largest ground-state electron transfer at negative bias, which overestimated the responsivity (R) and detectivity (D*) in OPDs. Notably, under weak light irradiation of 0.1 mW/cm2 at -2V, the contribution of Jd on Jph reached 99.6%. Thus, we modified the existing R and D* equations to better understand photodetecting properties at low light intensity, and these modified equations gave more realistic R and D* values in OPDs. On the other hand, a low-bandgap PD showing low Jd in OPDs was highly beneficial to detect a low light signal because the Jd negligibly contributed to Jph in OPDs. The low Jd values of OPDs at negative bias resulted in a high on/off signal ratio and constant R and D* values at different light intensities.