The applicable quote I heard once is “while you are presumed innocent, the system is designed to convict you”. I think I heard that on some random YT video I’ve seen through the years.
I don't think there's a good way to measure that. If you go by conviction rate, it's something like 75% +/-10% depending on jurisdiction and grading. Then you'd have to adjust for the 2-10% of wrongful convictions for the incarcerated. Then adjust for the people who commited a crime but were not convicted, but I haven't seen stats on that.
Even if we all agree that minimizing type I errors (false positives) is of paramount importance, the optimal design of the system depends heavily on the true positive rate at the top of the funnel.
Your 2-10% wrongful conviction rate matches the rate capital defendants are legally found to have been wrongfully convicted[3]. They're a good subset to focus on because they're the cases get the most resources and attention, and are the only category of defendants who regularly get volunteer lawyers for postconviction review.
But that can't prove that the system doesn't wrongfully convict at a higher rate. If public defenders are underfunded that will reduce their ability to prove wrongful convictions, for example. Note that a successful postconviction petition is much harder without a good record established by the original trial counsel. The Glossip case is a good example of how "innocence is not enough" to get exoneration.
(Your stats are also off by a bit. The average state conviction rate is around 80%, but there's way more than 10% variance. California is up at 94% while Florida is at 55%. [1] Meanwhile the feds are all the way up at 99.6%. [2]
[1]: Table B-1 on https://www.paperprisons.org/statistics.html
[2]: https://www.doarlaw.com/blog/2021/04/what-you-should-know-ab...
[3]: https://www.pnas.org/doi/pdf/10.1073/pnas.1306417111
Edit: I forgot cite 3
Getting a verdict overturned based on procedural issues isn't as easy as popular culture makes out. You have to show both that your rights were violated and that no reasonable jury could have possibly found you guilty if your rights weren't violated. Simply having signed statements from your jurors that they wouldn't have found you guilty if they knew what the prosecutors covered up isn't sufficient, for example.
(And it wouldn't "almost certainly" lead to a tossed conviction. The defendant would have a chance but not a guarantee at getting a new trial. See the comment you replied to for details)
It’s definition is here: https://deathpenaltyinfo.org/stories/criteria-for-inclusion-...
It includes acquittal or dismissal of charges after the original conviction was tossed. But that does not imply actual innocence. For example, if a key piece of evidence is excluded because of an unconstitutional search that could lead to acquittal or dismissal of charges.
The innocence thing isn't just death row. There are groups who have helped people who are not on death row, mostly using DNA. The majority of the people they help are not on death row. Sure, it could be higher. The point was that there is already what I would consider to be a high wrongful conviction rate. In my own experience, I think the wrongful conviction rate for non-custody offenses is multiple times higher.
What I meant to say is that death penalty eligible defendants get better representation than pretty much everyone else. So their wrongful conviction rate should be lower than average.
In what circumstances is arresting someone necessary or even beneficial for society on the whole? There are costs both to the people in terms of booking & housing someone in jail, and to the individual as for most folks not regularly dealing with law enforcement being arrested is at least somewhat traumatic.