Here's all you need to know about federal habeas corpus review of state-court decisions. It comes from the transcript of the Supreme Court's oral argument in Berghuis v. Smith (available here at SCOTUSBlog).

Under the Anti-terrorism and Effective Death Penalty Act (AEDPA), federal courts reviewing state-court rulings for constitutional error are supposed to grant deference to the state courts' decisions, and not throw out those holdings unless they are -- not just wrong -- an unreasonable application of clearly established federal law. Courts have spent about fifteen years trying to parse out the intricacies and nuances of this language. Chief Justice John Roberts hit upon a very succinct and pithy distillation in the Berghuis argument.

The case involved the proper standard a court should apply to determine whether members of a particular minority group are systematically under-represented in jury pools for criminal trials. (Here is a nice overview from SCOTUSwiki.) A fair amount of the argument revolved around various statistics, and percentages, and methods of analyzing group representation, and whether the state supreme court used the correct test for assessing the prisoner's jury claim. Justice Stephen Breyer, in sort of a roundabout way, asked the state's lawyer a question about the absolute numerical difference versus the expected sample size (or something), and basically said he didn't want to get the math wrong and "write something, like, saying 2 and 2 is 6."

Chief Justice Roberts tied this circumlocution back to the governing statute:

[I]t's not that you are going to say: 2 plus 2 is 6. I suppose, under AEDPA, all you have to do is say: 2 plus 2 is somewhere between 3 and 5, right?

And that's the bottom line in federal habeas. The state court, in ruling on someone's federal constitutional rights, can say, in essence, that "2 plus 2 is somewhere between 3 and 5," and a federal court cannot (or at least should not) overturn that decision, even when it acknowledges that 2 plus 2 is clearly 4 and the state court's didn't get that right. Now, you can debate the wisdom -- and even the constitutionality -- of that policy, and you can certainly debate how well the federal courts abide by that dictate, and you can debate whether the state court in the Berghuis case even managed to get in the right ballpark. But you'll never see a more cogent summation of the rule.