Short Yardage Conversion Rates: 2009-2015

Thanks to football outsiders' Scott Kacsmar, we have some data for NFL conversion rates over the last 7 years.  While looking at these rate alone is helpful and allows Scott to draw the reasonable conclusion passing is a bad yet popular choice in short yardage situation, we might benefit from being able to visualize the variance on these estimates.  To this end, I constructed the Wald 95% confidence intervals for each of those estimates by year:

First let's look at the one-yard-to-go situation, broken down by down and type of play:

With the exception of the suspiciously low non-QB run rate in 2011 (p = 0.001 compared to neighboring years), we can clearly see that running has been better than passing over the past 7 years of historical data in one-yard-to-go situations.  What about two yards to go, you ask?  Here are the comparable charts with the run data aggregated for 4th and 2 (the sample was too small otherwise):

The size of the confidence intervals illustrate that teams are passing more often than running in 3rd and 2 situations.  We see a similar trend in the 4th and 2 situations.  

Just looking at this data, it's tempting to conclude that we should always go with a QB run, but I doubt one can really compare QB runs and non-QB runs without being able to differentiate between a full yard to go and merely inches.  The problem is that we may be comparing apples and oranges if QB sneaks are more likely in the inches situation, as those would be more likely to convert.  This is a bit of a soapbox issue for me as researchers (in medicine and sports) will often do a retrospective analysis and erroneously conclude a causal relationship, when it may merely be a correlative one.