AbstractAny drive's scoring chances increase as the offense moves down the field, but exactly what impact an additional X yards gained provides is not generally known (or at least not commonly discussed). In this post I've charted out a team's scoring chances for a first-down situation at any point on the field. In addition to a dramatic increase in touchdown percentage for all drives that have a first down within 10 yards of the end zone, there is a leveling off in the fraction of drives ending in touchdowns right outside of this zone. While the root causes of these features are not made clear by this analysis, they may be due to the necessity for different offensive and defensive tactics near the endzone.
IntroductionAs a team drives down the field, excitement naturally builds. Each first down brings them closer to the end zone and a touchdown. At least, it should. How much does each first down improve your chances of scoring, and are there any parts of the field where having a first down closer to the goal line doesn't help matters?
DataTo obtain the necessary data I queried my copy of the Armchair Analysis database for all plays in the first three quarters. I ignored the final period so as not to bias the results with desperation drives from teams attempting a late rally. I then used a python script to find all first-down plays and the end result of the drive they occurred on.
This resulted in 63182 first downs over 17164 scoring drives. Roughly 60% of these plays were on touchdown drives, while the rest were on series that resulted in field goals (I completely ignored safeties, for the record). This uneven distribution is unsurprising, given that TD drives generally cover more of the field (and thus generate more first downs) than FG drives.
ResultsA plot of how likely a drive is to end in points as a function of field position is shown in Figure 1. It shows the fraction of scoring drives that result from a first down at a given yard line, with the opponent's end zone denoted by zero. Errors were determined via bootstrapping, and due to the sheer number of samples in this data set they are small.
|Figure 1: On any given drive, having a first down at a given point on the field is plotted against the probability of the drive ending with a score.|
As expected, the likelihood of scoring any points increases monotonically (aside from a couple of bumps and wiggles most likely due to statistical fluctuations) from the offense's end zone to the other team's goal line. On a team's own side of the field the relationship is linear, with a field position boost of ten yards resulting in roughly a 10% increase in scoring probability.
Once you cross midfield, however, the odds of scoring take a distinct upturn. Looking at the data split into the different types of scores (red and blue points in Figure 1) shows that this uptick is the result of field goals, which makes some sense given that a team starting at the 50 only needs a couple of first downs in order to be in field goal range.
Inside the opponent's 30, the percentage of drives ending in field goals levels off because the offense is already within field goal range — getting additional yardage doesn't make you more able to attempt a field goal. The likelihood of ending the drive with a touchdown, however, continues to increase.
After a leveling off between 10-20 yards away from the opposing team's goal, the TD percentage rockets upwards for first-and-goal situations at the expense of field goals. Ultimately, a first-and-goal at the 1-yard line gives the offense an 85% chance of scoring a touchdown and an almost 95% chance of getting any points.
Discussion and ConclusionsIt's somewhat surprising to see the dramatic increase in TD% when the offense is within the opponent's 10-yard line. This implies that there's something different about that last 10 yards — either it becomes significantly easier to score a touchdown (doubtful; I think the opposite is probably true), or teams are more likely to go for it on all four downs when they're so close to scoring. It's also possible that there's a psychological shift, providing a boost of adrenalin to the offense. A full investigation of these possible explanations is beyond the scope of this post, but might be worth revisiting in the future.
Of further note is the lack of improvement in a team's touchdown chances inside the red zone but outside the 10-yard line. This is in stark contrast to the dramatic ramp-up of TD% once a team reaches a first-and-goal scenario. While the TD% in this region stagnates, however, FG% increases correspondingly, leaving a smooth increase in the total scoring probability.
On it's own, the leveling off of the touchdown percentage wouldn't be inconsistent with random statistical fluctuations, such as the apparent increased scatter in the total scoring percentage around the 50 yard line. But the consistency of the feature around the opponent's 10-yard line, along with the corresponding increase in the frequency of field goals, indicates that this phenomenon is real.
So it seems like there is indeed a bottleneck effect when a team gets ~15 yards away from a touchdown, likely due to the difficulty of getting a first down very close to the goal line. This bottleneck disappears once a team gets into a first-and-goal situation, possibly the result of a team's increased willingness to go for it on fourth and goal. So the next time your team has to settle for a field goal when they had first-and-10 from the 12, take a small comfort in knowing that they weren't in quite as good of a spot as it seemed.
--A huge shout out to Kenny Rudinger for noticing that my preliminary results for this post were obviously in error, allowing me to sort out the bugs in my analysis code *before* subjecting my boneheaded mistakes to public scrutiny.