## 1-Play Touchdown Probability

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).

Upon first glance, other than on 4th down when teams are more likely to kick field goals and punt, the down has almost no effect on 1-play TD probability. There is a little noise between the 5 and 15 yard line, but that could just as easily be explained by random variation.

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.

Keith Goldner is the creator of Drive-By Football, and Chief Analyst at numberFire.com - The leading fantasy sports analytics platform.  Follow him on twitter @drivebyfootball or check out numberFire on Facebook

### 3 Responses to “1-Play Touchdown Probability”

1. Anonymous says:

It looks like around midfield 4th down takes a slight up tick over the rest of the downs. Teams in desperation mode throwing up a Hail Mary?

2. Daniel says:

Nice post, Keith. I'd be interested in looking at the goal line area a little more closely. On the opponent 1-2 yard line, it appears that 3rd down has a slightly higher rate of touchdowns. This could be random noise or it could be due to the fact that 3rd down is 'do or die' and teams make more of an effort to score.

If this is the case, I would also expect to see a higher rate of turnovers and plays for negative yardage ('bad plays'). If the rate of bad plays is not higher, teams may be wise to treat all first and second downs near the goal line as if they were third down.

Thanks again for the solid post. I'm looking forward to more applications of the Markov model.

3. Unknown says:

I agree Daniel that the 3rd down numbers from 15 yards and in are interesting, though I find the significant difference around the 10 yard line to be the most interesting aspect. My gut tells me that teams are throwing more on 3rd down than 1st and 2nd when in the red zone, which is skewing the numbers to a higher TD %, and as you suggest, perhaps a higher turnover % as well.

If I am correct, then this highlights another aspect of over-conservative play calling by NFL coaches, where they are calling sub-optimal plays on 1st and 2nd down in the red zone, and that the "optimal" TD% is likely shown by the 3rd down numbers on the graph.