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Notes -
This is an example of how results based on "controlling for confounders" are inherently dubious for complicated fields like social science. Fundamentally the researchers are coming up with a list of potential confounders (which must be legible across many individual cases, available to the researchers, etc.) and assuming that anything left after they're controlled for must be whatever signal they're looking for. I recommend this SSC post as a classic example of this, in which a study on the impact of bullying controls for bullies targeting unpopular disadvantaged kids using the Bristol Social Adjustment Guide. In this case this is what they controlled for:
This misses nearly all the details of the case. They count the raw number of official "applied aggravators" but not what those aggravators are. They count the number of prior convictions but not their severity, the number of mitigating circumstances and number of defenses but not what those are or how convincingly they are argued. They check whether the victim was held hostage for some reason but not other similar specifics (chosen controls tend to be arbitrary and vary widely across studies on the same subject). The people making the decision have all the details that a set of controls can't possibly encompass, and we know the controlled factors differ by race, yet any systematic difference in their decisions is assumed to be a product of racial discrimination rather than everything they didn't control for.
Imagine a study trying to determine if the date of birth on a birth certificate is a biased indicator of age. Group 1 is stereotyped as being older than Group 2, does this influence the date written down when they're born? Naturally the study controls for age, with a multiple-choice question to choose an age range ("[B]: 20-29 years old"). They find that, while Group 1 does pick older age ranges, even after you control for age [B] respondents in Group 1 have an earlier date of birth than [B]s in Group 2. In fact, a later more sophisticated study outright asks for age, and finds that 25 year olds in Group 1 have an earlier birth date than 25 year olds in Group 2. Needless to say, this is a perfectly expected result even without any birth-certificate bias.
In other words "race" and "number of mitigating circumstances" correlate strongly enough that if they didn't put "mitigating circumstances" in their model any difference in sentencing from mitigating circumstances would be assumed to be due to racism. Naturally they don't consider whether the same thing might be happening with factors they didn't control for.
Interestingly their conclusion calls the variation not explained by their model "extra-legal and social factors". I don't think it's really "extra-legal factors" when the jury makes decisions using methods more complicated than "count up the number of applied aggravators".
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