The sporting world's reaction to the Arizona Cardinals' Super Bowl berth has been marked by a fun combination of bafflement and condescension. The media has consistently treated the Cardinals like Red China, refusing to acknowledge their right to exist even as their power grew.
The New York Post had a typical take, likening the Cardinals' victory to a violation of the laws of physics:
The sentence that always connected "Arizona Cardinals" and "losers" now must be rewritten, or at least revised. The sun continues to rise in the east and the laws of gravity still apply but some absolutes are no more.Heck, even Cardinals QB Kurt Warner has bought in, noting in his press conference that he "want[ed] to say Arizona Cardinals and Super Bowl in the same sentence", as though putting those two thoughts together in the past would have resulted in total protonic reversal.
at left: Warner, dressed for his offseason job as an evengelical exorcist.
The media is pimping this meme for two reasons. First, it gives them a chance to bloviate about the tradition gap between the Cardinals and their more august opponents, the Pittsburgh Steelers. Second, it lets them fill some time talking about the "historic" nature of the Cardinals' appearance in the big game.
But this meme has it all wrong. To the extent that the Cardinals have defied rational expectations, they've done it through their years of failure, rather than their month of success.
To show how, we at the GRBG will stoop to using math. This is ordinarily a dangerous path for us, as we last took a math class in 1995, and passed that class only through the grace of our TI-82 graphing calculator. Luckily, we think that the math in this instance tops off at simple division, so we feel good about our chances.
at right: our collective left brain.
We are now in year 43 of the Super Bowl era. This is the first time that the Cardinals have made the big game meaning they have gone 1 for 43 in Super Bowl appearances (See? Told you the math part would work out OK). There 16 teams in each NFL conference. Assuming, then, a completely random distribution of results, which the NFL's structure tries very hard to generate, a team should now expect to make a Super Bowl once every 16 years, on average. Historically, the odds were even more favorable, because there were fewer teams.
So how likely is it that the Cardinals would have made at least one Super Bowl in the 42 years before the '08-'09 season? The math gets ickier here, but our calculations (reproduced below for math dorks) figure that there was a 95.5% chance the Cardinals would have made the Super Bowl before now.
In other words, the remarkable thing here isn't that the Cardinals finally made it this year. It's that they somehow managed to f#$% it up for so long in the past. The press guys had 42 years to talk about how remarkable the Cards were, and you never heard a peep. But now that their results have finally started to become less remarkable, it's all that the media can do to keep from pitching over sideways in shock.
Because math was involved, we'll give this meme a 4 on our 10 point scale. But remember, every time you hear a story about how this Cardinals team is remarkable, know that it was the 42 previous teams that were the true standouts.
Math time. We took a weighted average of the number of teams in a conference over the years, and found that it came out to about 14 (rounded for ease of usage). So the chances of a team winning at least once in 42 trials would be:
1 - ((13/14)^42) = .95571
Obviously there are some assumptions in here you could tweak, but for a back of the envelope job, we're OK with it. If you want real math, go to Football Outsiders. Poindexter.