In Week 1 last year, Tom Brady connected with Wes Welker for a 99-yard touchdown against the Dolphins. In an effort to determine whether teams actually protect the ball better as they approach the goal line, we recently looked at 1-play fumble and interception probabilities (also known as transition probabilities from our Markov model). Out of all our absorption probabilities, only fumble, interception and touchdown really make sense to examine on a 1-play basis across downs. Punts and field goals almost always occur on 4th down (turnover on downs always occur on 4th down) and while a safety can occur on any down, they occur extremely infrequently.
In 2011, 37.7% of all offensive touchdowns occurred on 1st down, 33.0% on 2nd down, 25.0% on 3rd down and 4.3% on 4th down. This makes logical sense as there will be more 1st downs than 2nd downs, more 2nd downs than 3rd downs, and so on. But, how does down affect the probability of scoring a touchdown on the next play? Do teams take (and successfully convert) more shots downfield on 1st down than later in the drive?
While distance-to-go is an important variable in determining whether teams aim for the end zone, for simplicity sake we will be looking at all distances-to-go grouped together. A team is obviously more likely to go for a 1-play TD on 2nd-and-1 than 2nd-and-7 (5.6% of 2nd-and-1 plays result in touchdowns versus only 2.6% of 2nd-and-7 plays).
To further test the notion that down does not affect the probability of scoring a TD on that play, we can estimate 1-play TD probability based on down, distance-to-go, and yard line.
Here are the regression results with p-values:
When 4th down is included, all three variables are significant. The negatives signify that a team is less likely to score a TD on one play as down, distance-to-go and distance from the end zone all increase. Yet, when we remove 4th down from the equation, the p-value for down jumps to 0.2730, demonstrating that it is not a significant variable in determining 1-play TD probability except on 4th down. Similarly, if we try to estimate 1-play TD probability just using down but not including 4th down situations, the R-squared value is 0 (and p-value for down is 0.878). Again, this reinforces the notion that down is not a significant factor in 1-play TD probabilities.