TwoDeep3
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What the stats do, or should do, is make it clear that the lack of big game success isn't a function of the overall QB play. And they highlight that Eli Manning--two rings and all--wouldn't have those rings if he didn't have the support from his pass defense, either.
Whether those obvious facts change the minds of average fans who are unhappy with Tony Romo, or not, isn't relevant. You're right that there are always going to be people who believe things based off of insufficient data, or off of drawing the wrong conclusions from the available data. All you can really do is point it out to them. If they don't change their opinions as a result, they were never going to, anyway.
What you think it should or should not do ignores what it actually does.
The stat indicating the interceptions when throwing to one receiver versus the others seems to indicate the receiver is at fault.
But that doesn't prove that issue at all. It's still conjecture.
And it is this reason why I believe stats prove what the stat gathers wants to prove, but isn't empirical and doesn't settle anything.