The maximum earthquake magnitude recorded for subduction zone plate boundaries varies considerably on Earth, with some subduction zone segments producing giant subduction zone thrust earthquakes (e.g. Chile, Alaska, Sumatra–Andaman, Japan) and others producing relatively small earthquakes (e.g. Mariana, Scotia). Here we show how such variability might depend on various subduction zone parameters. We present 24 physical parameters that characterize these subduction zones in terms of their geometry, kinematics, geology and dynamics. We have investigated correlations between these parameters and the maximum recorded moment magnitude (MW) for subduction zone segments in the period 1900–June 2012. The investigations were done for one dataset using a geological subduction zone segmentation (44 segments) and for two datasets (rupture zone dataset and epicenter dataset) using a 200km segmentation (241 segments). All linear correlations for the rupture zone dataset and the epicenter dataset (|R|=0.00–0.30) and for the geological dataset (|R|=0.02–0.51) are negligible-low, indicating that even for the highest correlation the best-fit regression line can only explain 26% of the variance. A comparative investigation of the observed ranges of the physical parameters for subduction segments with MW>8.5 and the observed ranges for all subduction segments gives more useful insight into the spatial distribution of giant subduction thrust earthquakes. For segments with MW>8.5 distinct (narrow) ranges are observed for several parameters, most notably the trench-normal overriding plate deformation rate (vOPD⊥, i.e. the relative velocity between forearc and stable far-field backarc), trench-normal absolute trench rollback velocity (vT⊥), subduction partitioning ratio (vSP⊥/vS⊥, the fraction of the subduction velocity that is accommodated by subducting plate motion), subduction thrust dip angle (δST), subduction thrust curvature (CST), and trench curvature angle (αT). The results indicate that MW>8.5 subduction earthquakes occur for rapidly shortening to slowly extending overriding plates (−3.0⩽vOPD⊥⩽2.3cm/yr), slow trench velocities (−2.9⩽vT⊥⩽2.8cm/yr), moderate to high subduction partitioning ratios (vSP⊥/vS⊥⩽0.3–1.4), low subduction thrust dip angles (δST⩽30°), low subduction thrust curvature (CST⩽2.0×10−13m−2) and low trench curvature angles (−6.3°⩽αT⩽9.8°). Epicenters of giant earthquakes with MW>8.5 only occur at trench segments bordering overriding plates that experience shortening or are neutral (vOPD⊥⩽0), suggesting that such earthquakes initiate at mechanically highly coupled segments of the subduction zone interface that have a relatively high normal stress (deviatoric compression) on the interface (i.e. a normal stress asperity). Notably, for the three largest recorded earthquakes (Chile 1960, Alaska 1964, Sumatra–Andaman 2004) the earthquake rupture propagated from a zone of compressive deviatoric normal stress on the subduction zone interface to a region of lower normal stress (neutral or deviatoric tension). Stress asperities should be seen separately from frictional asperities that result from a variation in friction coefficient along the subduction zone interface. We have developed a global map in which individual subduction zone segments have been ranked in terms of their predicted capability of generating a giant subduction zone earthquake (MW>8.5) using the six most indicative subduction zone parameters (vOPD⊥, vT⊥, vSP⊥/vS⊥, δST, CST and αT). We identify a number of subduction zones and segments that rank highly, which implies a capability to generate MW>8.5 earthquakes. These include Sunda, North Sulawesi, Hikurangi, Nankai-northern Ryukyu, Kamchatka-Kuril-Japan, Aleutians-Alaska, Cascadia, Mexico-Central America, South America, Lesser Antilles, western Hellenic and Makran. Several subduction segments have a low score, most notably Scotia, New Hebrides and Mariana.