Both of these values are attempts to quantify the probability that a source detection arises not from a real point source but from a chance fluctuation of background. It would be nice to be able to say absolutely whether a given detection arose from source or background, instead of having to rely on fuzzy estimates of probability. But without knowing the origin of every x-ray photon, either within this simulation or in the real world, it is not possible to know whether even the brightest and seemingly most significant bunch of events on a CCD is really due to a bright source at that location or just due to a chance grouping in space and time of photons in the far PSF wings of distant, perhaps faint sources. All that one can do is to calculate a probability for it, based on the average level of background and the number of events comprising the detection. This number is DETEC_PNULL.
Within the context of the simulation we are a bit better off, since we have a priori knowledge of both the positions of the sources in any instance and the probability density of their distribution in general. This extra information enables us to make a more accurate estimate of the null probability, which is MATCH_PNULL. By comparing DETEC_PNULL (which is calculated by the detection script, thus via a method not under the direct control of eimsim) with MATCH_PNULL we can assess how effectively the detection task is calculating this probability.
XMM-Newton SOC -- 2021-11-30