This was actually something I have been keeping an eye out for a while now. They have broken down each team using their own ranking system to give the statistical odds of making the playoffs. Basically... this is as close to "mathematical chances" as we can get until being mathematically eliminated.
Carolina Panthers: 0.2% chance of making the playoffs.
Only Buffalo at 0.0% chance has a lower ranking. The good news? It's based off our stats, which if you consider the first 5 games an aberration then you're not going to believe this anyway. The bad news... It's probably the most in-depth analysis of statistical likelihood you're going to find.