A difficult case is when a possible criticism is made relatively immune to investigation. This immunity may take the forms of:
unexplained claims of exemption from principles commonly thought relevant to the subject matter
Example: I'm not relying on faith in small probabilities here. These are slot machines, not roulette wheels. They are different.
claims to data that are inherently unverifiable, perhaps because too remote or impossible to define clearly
Example: Cocaine use should be legal. Like all drugs, it does have some adverse health effects, but cocaine is different from other drugs. Many have benefited from the effects of cocaine.
In the classic distinction among informal (material), psychological, and formal (logical) fallacies, special pleading most likely falls within the category of psychological fallacy, as it would seem to relate to "lip service", rationalization and diversion (abandonment of discussion). Special pleading also often resembles the "appeal to" logical fallacies.
In medieval philosophy, it was not assumed that wherever a distinction is claimed, a relevant basis for the distinction should exist and be substantiated. Special pleading subverts an assumption of existential import.
This variation occurs when the interpretation of the relevant statistic is "massaged" by looking for ways to reclassify or requantify data from one portion of results, but not applying the same scrutiny to other categories.