# The curious case of the 2-yard line

A lot of discussion has been going on (including some in this blog) on whether teams should start going more often for a two-point conversion after a touchdown.  While it seems that with last year’s PAT kick rule changes the benefits of going for 2 after a touchdown are more clear, little attention has been given to the actual play calls – i.e., pass versus run – for the two-point conversion. What triggered the analysis that follows is my anecdote observation that most two-points conversions are pass plays, while “regular” plays from the 2-yard line are not! So I set out to examine whether this discrepancy is a statistical fact – or just a biased impression using data from the past 7 regular seasons (2009-2015).

In particular, for every two-point conversion attempt I compute the fraction of passing play calls.  One should expect that this fraction should be statistically identical with the fraction of passing plays from the 2-yard line during the course of a game.  We present these fractions in the following figure.  We also present on the same plot the fraction of passing play calls for the snaps that required only two yards to be covered regardless of the field position.

It is obvious from these results that passing plays are prefered for the PAT cases as compared to other plays from the 2-yard line or snaps that need to cover 2 yards for a new set of downs (and this difference is statistically significant).  This is not clear why. The situation encountered in the PAT 2PT conversion is the same as a “regular” play from the 2-yard line; cover 2 yards and you get a score.  A  difference is that the one score is worth 6 points while the other only 2.  The other difference is that the PAT is only one try, while during the game you might have multiple tries to achieve the goal and this might impact the play calling and strategy.  To examine that I computed the fraction of passing plays as a function of the down count.

As we cans see for the first couple of downs, running is the majority of the play calls.  However, as we move to 3rd and 4th down passing takes over! Overall, still passing is chosen approximately 48% of the times (as compared to the  70% in the two points conversion).  I find this rather interesting.  It seems that once the tries left to cover the two yards are fewer (e.g., two-point conversion, 3rd and 4th down) teams turn to passing! I am certainly not sure why…

Finally, I analyzed the data on a per-team basis.  I understand that for some teams there are few data points for two-point conversion attempts but nevertheless we can still get some intuition (standard errors should be presented in both axis but this would certainly make the figure unreadable..).  For visualization purposes we focus on the plays from the 2-yard line (from the first figure we can see that there is no statistical difference between these plays and the snaps at any part of the field with 2 yards to go). In the following figure for each team we present its passing fraction for the two-point conversions and for the regular snaps from the 2-yard line.

As we can see most of the teams are above the y=x line, which means that they make more passing plays in the two-point conversion rate than expected.  There are a few teams that are consistent in the two situations – Rams, Cardinals, Vikings, Saints and Broncos – while there are others with major discrepancies – e.g., Giants, Steelers 49ers and Texans.  Hopefully, this season more teams will attempt for two-point conversions and we will collect more data to understand this behavior better!