Single photon avalanche diodes (SPADs) are key enabling technologies for a wide range of applications in the near-infrared wavelength range. Recently, AlAs <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0.56</sub> Sb <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0.44</sub> (hereafter AlAsSb) lattice-matched to InP has been demonstrated for extremely low excess noise avalanche photodiodes (APDs) due to its large disparity between electron and hole ionization coefficients ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\beta $ </tex-math></inline-formula> respectively). The <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha /\beta $ </tex-math></inline-formula> ratio also plays a role in Geiger mode operation as it affects the avalanche breakdown probability and hence detection efficiency. In this work, we theoretically investigate the performance of AlAsSb based SPADs. The probability of breakdown for electron-initiated Geiger mode operation increases more sharply with multiplication region width due to progressively more dissimilar ionization coefficients. In comparison with other common avalanche materials, such as InAlAs, InP and Si, our result also suggests that SPADs based on AlAsSb have a sharper breakdown probability than the other three materials under similar low overbias ratio. The calculated breakdown probability of 0.81 in AlAsSb is 0.18 and 0.28 higher than that of InAlAs/Si and InP respectively at 5% overbias ratio and with avalanche region width of 1500 nm.