Of course it would be nice if complex problems boiled down to a single number; recall the days of high school math. Sadly, the real world is never that simple. That does not, however, stop us amateur sports enthusiasts and even some actual professional sports analysts from using simple decontextualized tally metrics as evidence for assigning superlatives to players or teams.
At a party for Super Bowl 46 featuring the New England Patriots and the New York Giants, someone argued to me that the Patriots defense ranked 31st (out of 32 teams) in total yards allowed (TYA) and thus were a horrible defense and would single-handedly lose the super bowl to the reawakened Giants offense. It’s true that the New England Patriots’ defense did indeed essentially tie for worst with the Green Bay Packers for TYA with 6577 and 6585 yards, respectively in the 2011 regular season. I’m definitely not a Patriots fan, but I felt that this accusation based entirely on TYA was a little unfair. There I was, caught in a very rare moment in defense of Boston sports. I waved my hands and posited that in some cases TYA is biased against high scoring offenses since the defenses are playing conservatively to preserve the lead and eat up time. This isn’t a new thing, mind you, I just haven’t ever actually seen a plot of this to test this hypothesis.
Consequently, I set out to see how many yards each NFL defense allowed as a function of the relative score. My tentative hypothesis was that some of the high scoring teams would have defenses with high TYA where a large chunk of those yards were forfeited when the team was leading by at least two scores.
Disclaimer: I am not a sports analyst or in any way a football strategist. I do not claim that this graphic is the most informative or accurate way of ranking defenses. My priorities for this project were to (a) practice parsing sports data with Python (this is my first Python project of any kind), (b) make a good friend eat some crow, and (c) further stigmatize the use of TYA as the sole piece of evidence for ranking defenses. TYA for sure has some value, but it should bow down to other metrics that incorporate scoring, probability of allowing points, take-aways and game context. Errors: I did not credit defenses for yards after take-aways either by fumble or interception. This failure is mostly due to my fear of parsing text from human-constructed sentences. Data Sources:hosted.stats.com
These distributions are Yards Allowed by Lead (YAbL). The x-axis consists of 3.5 point interval bins centered at 0 and extending from -28 (a deficit of more than 28 points) to +28 (a lead of more than 28 points). On the y-axis are the cumulative number of yards allowed by each defense in those relative score bins.
As expected, it is clear that defenses on teams with highest-scoring offenses give up a significant number of their yards when in the lead by more than one possession. The four highest-scoring teams in the 2011 regular season were, in order, the Green Bay Packers (GB), the New Orleans Saints (NO), the New England Patriots (NE) and the Detroit Lions (Det)[espn.com]. All four of these teams finished 23rd or worse in TYA. The YAbL plots confirm that GB and NE especially give up most of their yards when preserving a two-possession lead. My rationalization for this is that teams switch strategies to play with a prevent defense when preserving a significant lead. In a prevent defense, teams are looking to prevent quick scores and take time off of the play clock at the cost of allowing long drives with many plays. So this strategic decision is one contribution to the right-heavy YAbL we see for these teams. The other contribution is the simple fact that these defenses are playing a disproportionate number of drives with a lead. With this data alone, it is impossible to determine how many extra yards are forfeited from switching to a prevent defense. I suspect that if GB and NE were playing on teams with weaker offenses and thus playing in closer contests, their TYA would decrease a little bit. I do not claim nor believe that either team’s defense is all that great; indeed they appear to be fairly average or below average in tie-game situations.
Detroit on the other hand performed poorly in single-posession games and games where they are down by more than one score. Despite having a powerful offense at times, scoring an average of almost 30 points per game, the defense struggled to preserve the lead. More information is needed to accurately compare their distribution to other teams, but on the surface they appear to play on par with defenses like Tennessee and Miami, who were without strong offenses and were not in playoff contention.
The more dominant defenses stand out and correlate well with TYA. Pittsburgh, Miami, Baltimore, San Francisco and Houston were almost always playing with a lead and yielded few yards regardless of their situation. In these cases, TYA paints a reasonable portrait of the effectiveness of these defenses.
Tall and narrow distributions centered at zero don’t provide much information about the defense, but they do tell a story about the kind of games these teams play. It’s fitting, I suppose, that both drama-riddled New York teams play in noticeably tight games, either up or down by a single score with roughly equal frequency.
In general, defenses allowing the fewest yards are indeed elite and effective defenses. However, some of the teams allowing the most yards are unfairly slandered as being defensive sieves; these defenses give up many of their yards when already leading by two or more possessions. The added value of these YAbL plots is relatively minimal and are mostly useful in discriminating high TYA defenses that actually stink vs those whose numbers are inflated by context. Finally, the YAbL distribution plots are at least as informative as TYA and can in some cases provide useful contextual information. I’ll continue to work on this kind of analysis to incorporate different normalization options, scoring outcomes, and interactive features for users to more efficiently compare defenses. It’s possible that a similar distribution will have some valuable information and can be incorporated in written analyses with sparklines [here], so users have instant visualization without having to look at a separate figure.