In Eccentrically Braced Frames (EBFs), the link beam acts as the primary seismic fuse, accommodating large inelastic rotations and providing the main source of energy dissipation. Capacity design requires surrounding members to remain essentially elastic when the link reaches its ultimate expected shear strength of 1.5Vp according to AISC 341-22. However, strain hardening in short shear links can result in excessive overstrength, potentially affecting the intended yield hierarchy. This study investigates the cyclic performance, ultimate shear strength, and overstrength behavior of short ASTM A36 shear links with circular web openings using a probabilistic finite element framework. Uncertainties in material properties and geometric parameters were modeled as independent random variables using Monte Carlo simulation. Three configurations were examined: a conventional solid-web link, a link with one circular web opening, and a link with two circular web openings within the stiffener spacing. A total of 900 explicit nonlinear finite element analyses were performed in ABAQUS. The cyclic response, including hysteretic behavior, backbone response, energy dissipation, stiffness degradation, and damage initiation characteristics, was evaluated, while probability density functions (PDFs) and cumulative distribution functions (CDFs) were used to quantify variations in ultimate shear strength and overstrength. The results showed that circular web openings reduced the mean ultimate shear strength and significantly decreased the probability of exceeding the AISC 341-22 overstrength limit. For the investigated configurations, one circular opening reduced the exceedance probability from 90% for the conventional link to 12%, while two circular openings resulted in nearly all realizations remaining at or below the code-prescribed value. These findings indicate that controlled circular web openings can reduce excessive overstrength while maintaining stable cyclic performance within the investigated range.