A Logical Look at What Happened in the Carolina vs Arizona Game

The Carolina Panthers, played in the toughest division in the NFC, the NFC South.  The Arizona Cardinals played in the easiest, the NFC West.  The Panthers completed a 12-4 season.  The Cardinals were 9-7.  The Panthers were 8-0 at home.  The Cardinals were 3-5 on the road.  The oddsmakers in Vegas decided that this was good enough to favor the Panthers by 9.5 to 10.0 points.

Result - Arizona beats Carolina 33-13

What Happened?

Jake Delhomme threw a career-high 5 INTs.  That was unexpected.  A shocker.  But, how unexpected was it, really?

Let's take a look at some #s.

First, what are the chances of winning a playoff game, when a QB throws X interceptions?  Here are the stats:

0 INTs - 184-51, a winning percentage of 0.783

1 INT - 140-112, a winning percentage of 0.556

2 INTs - 54-117, a winning percentage of 0.314

3 INTs - 17-76, a winning percentage of 0.183

4 INTs - 1-27, a winning percentage of 0.036

5 INTs - 0-11, a winning percentage of 0.000

6 INTs - 0-3, a winning percentage of 0.000

These are based on all playoff games in the Super Bowl era.  The data is courtesy of Cold Hard Football Facts.

As I have shown before, a QBs likelihood of throwing interceptions has been decreasing over time (based on the increasing value of that component in the QB Rating).  So, if one were to look at this season's regular season stats, I'm sure this table would look even more skewed.  (I don't have 2008 game by game data handy).  The point is still the same - throw INTs, and you dramatically reduce the likelihood that your team wins.  The fact that someone threw 5 picks is actually quite irrelevant.  Once you throw 2 picks, you're likelihood of winning is dramatically reduced, and it's less than 1 in 5 if you throw 3.

Ok fine, so let's look at both QBs in this game Jake Delhomme and Kurt Warner.   According to the table below, in Jake's career (including prior post season games), he had never thrown 5 INTs in a game.  However, he had thrown at least 2 INTs in a game 22% of the time, and at least 3 INTs in a game 6% of the time.  What's perhaps most interesting is that Kurt Warner had thrown at least 2 INTs in a game 28% of the time, and 3 INTs in a game 12% of the time.  

So, what does this all mean?  We need to look at the second table (see below the first table for the analysis).

According to this table, based on the likelihoods shown in the previous table there was an 18% chance that at least one of the QBs in this game was going to throw at least 3 INTs (see the last column in the table below).  That's a about 1 in 5.  That's much higher than I would have thought.  That's actually a higher likelihood than both QBs finishing the game having thrown 0 INTs.  Now admittedly, the likelihood that it was Delhomme and not Warner that was going to throw the 3 or more INTs was 2-to-1 against (given at least 1 QB would throw at least 3 INTs).  But the fact is, there was a pretty good chance that this was going to be a game where at least 1 QB threw multiple INTs.  Heck, there was about a 1 in 14 chance that at least 1 of them was going to throw 4 or more INTs - again, much higher likelihood than I would have thought (and you too, I'm guessing).

So there you have it.  An unexpected result.  Certainly.  But not that unexpected.  What should also be clear is that if you throw a pick, you're chances of winning reduce quite significantly.  And for each subsequent one, the odds of winning decrease exponentially.  After 3 picks, it's lights out.