Submillimeter dust polarization measurements of a sample of 50 star-forming regions, observed with the Submillimeter Array (SMA) and the Caltech Submillimeter Observatory (CSO) covering parsec-scale clouds to milliparsec-scale cores, are analyzed in order to quantify the magnetic field importance. The magnetic field misalignment δ—the local angle between magnetic field and dust emission gradient—is found to be a prime observable, revealing distinct distributions for sources where the magnetic field is preferentially aligned with or perpendicular to the source minor axis. Source-averaged misalignment angles lang|δ|rang fall into systematically different ranges, reflecting the different source-magnetic field configurations. Possible bimodal lang|δ|rang distributions are found for the separate SMA and CSO samples. Combining both samples broadens the distribution with a wide maximum peak at small lang|δ|rang values. Assuming the 50 sources to be representative, the prevailing source-magnetic field configuration is one that statistically prefers small magnetic field misalignments |δ|. When interpreting |δ| together with a magnetohydrodynamics force equation, as developed in the framework of the polarization-intensity gradient method, a sample-based log-linear scaling fits the magnetic field tension-to-gravity force ratio langΣ B rang versus lang|δ|rang with langΣ B rang = 0.116 • exp (0.047 • lang|δ|rang) ± 0.20 (mean error), providing a way to estimate the relative importance of the magnetic field, only based on measurable field misalignments |δ|. The force ratio Σ B discriminates systems that are collapsible on average (langΣ B rang rang B rang > 1). The sample-wide trend shows a transition around lang|δ|rang ≈ 45°. Defining an effective gravitational force ~1 – langΣ B rang, the average magnetic-field-reduced star formation efficiency is at least a factor of two smaller than the free-fall efficiency. For about one fourth of the sources the average efficiency drops to zero. The force ratio Σ B can further be linked to the normalized mass-to-flux ratio, yielding an estimate for the latter one without the need of field strength measurements. Across the sample, a transition from magnetically supercritical to subcritcal is observed with growing misalignment lang|δ|rang.
