Taking a statistical mean in no way effects the individual's experience. It inflicts nothing on the subjects. It simply states what it is; the mean.
If you're interested in an individual's experience, then, as I said, you don't need any statistics at all, you only need look at the data. You only use statistics if you want to look at the aggregate. Since you want to use statistics, then you have to look at the aggregate, and the mean value for your baseline is 'some racism'. That this is nonsensical when applied to individuals is my point.
Further, using a statistical mean to define your baseline leads exactly to the state of declaring non-victims to be expectional and needing a label to explain why they don't fit the statistical baseline -- hence the emergence of privilege as a term. But when you look at individuals again, this quickly becomes meaningless because you have victims and not victims. If you insist on using your statistically determined mean and exceptions to the individuals, you end up with the silliness of labeling those that are not victims as privileged to be not victims. That's fundamentally my point -- that kind of analysis doesn't lead to truth, and in fact obscures truth. It's actively harmful.
The lawyers vs. partners thing, for example. (pulling numbers out of my butt for the sake of an example) It if on average 10 out of every 100 lawyers reaches the level of partner and the distribution of White to Black lawyers is 50/50, but 8 out of every 10 partners is White, that's a very significant thing to look at. One would presume that, all other factors being equal, the distribution of partners would also be equal; 5 out of 10. If study of that data shows an inequity and that inequity is addressed, that in no way inflicts racism upon the Whites in the group.
That's statistics, in application.
Yes, it's a very basic application of statistics. And it is suggestive, but statistics can never, ever show causation. What you've done is substitute people for a parameterization of people -- you've simplified them to black or white. You've then run analysis based not on people but on your parameter of people, and found something. That may be useful (and, in this case, I'd agree bears more investigation), but you've lied to yourself if you think the result that is true for your parameterization is also true when you consider real people. That's the lie buried in statistics. It's only useful if you remember to treat it as a dog that bites.
But, all that said and agreed to, your example isn't comparable to the issues of whether or not being white is a privilege, and no amount of statistical jargoning will end up with it being rational to it a privilege to not be a victim. In your case above, the white people that take the positions of blacks that are unfairly discriminated against are not privileged, the blacks instead are victims. That you can squint and pretend that their is some kind of extra benefit to being white doesn't hold with the actuality is that it's not one side having more, it's one side getting less.
I'm not arguing that racism doesn't exist, or that it doesn't manifest in ways that superficially appear to favor whites. I'm instead arguing that such a thing isn't a white privilege, it's a harm against those discriminated. When you isolate to zero sum games, like your lawyer example, one person losing must equal another person winning. But the driver here is making people lose through racism, not making people win through existing.
It's pretty simple to flip the narrative on that little item. It's not relative immunity from a negative; it's a higher chance of a positive outcome. THAT is privilege
You realize that fails pretty quickly. If I have four aces in a poker hand, am I privileged? Perhaps if I position myself to perfectly receive a cross in front of the goal (soccer reference), am I privileged? Maybe I work hard and go to school and get a degree, does that make me privileged?
I note that you seem to be not shot today. Does that make you privileged over people that have been shot?
My answer to all of these rhetoricals (because I believe it to be in good faith to provide an answer to a rhetorical) is: no.
My underlying and unwaivering point is that it is not a privilege to not be a victim.