He's a Super Bowl champion and MVP, a two-time NFL MVP, and master of the hail mary. Although many of his statistics are remarkable, one of his most unique skills is his ability to provide his offense with opportunities by utilizing free plays, which are generated when the defense commits one of a few penalties. If the defense is called for offsides, lining up in the neutral zone, twelve men on the field, or illegal formation, the offense has a 'free play' in which they can run a play and then either decline the penalty and take the yardage gained by the play, or accept the penalty yardage if that provides greater benefit. On such occasions, the offense usually attempts high-risk, high-reward plays because there is no real penalty for mistakes; even if the play results in a turnover, for example, that result will be negated as the offense can simply choose to accept the penalty and replay the down.

It's not obvious, though, whether Aaron Rodgers' ability to draw and utilize free plays contributes in a meaningful way to the outcomes of his offense. In order to determine how much free plays contribute to Rodgers' offense, first I had to establish whether the Packers under Rodgers actually get more yards off of free plays than other offenses. (Spoiler alert: they do). The first graph shows the distribution of free-play yards by each offense across the past five seasons.

However, this isn't the whole picture. It's possible that although they draw more free-play yardage, this yardage is negligible in the context of an entire game, or an entire season. Looking at the data a little further, there are two important things to note: firstly, that the yards off of free plays are concentrated in just a few games, and secondly, that free plays have the greatest impact on third-and-short situations. The second graph shows the average likelihood of converting on third down at each yardage distance, as well as the likelihood of converting when a free play is drawn.

The great conclusion of all of this was that free plays make a significant difference in a few games each season for the Packers. Here are a few games in which free plays made a measurable impact, projecting the score over the course of the game with and without free plays. (Sorry, this one wasn't designed for mobile.)