# To go or not to go…? (for 4th down)

Fourth down decisions certainly create a lot of chatter, especially when your team loses – after all we all love to be backseat drivers. Coaches are certainly hesitant going for it at fourth down situations (similar to the 2-point conversion VS PAT kick decision).  While at times this is indeed the “best” decision, going for it is beneficial more often than what coaches think – or at least what they appear to think based on their decisions. In my recent paper to be presented in the workshop for Machine Learning and Data Mining for Sports Analytics I analyzed the fourth down decisions through mean field approximation using play-by-play data from the last 7 NFL seasons.  A disclaimer is that this analysis is an average analysis and does not consider factors such as game situation, which can dramatically alter the decision making.

When there is a fourth down decision to be made there are three options:

• go for it
• punt
• attempt a field goal based on the team position on the field

Going for it has the potential to keep the drive alive and eventually get 6 points, i.e., a touchdown.  However, failing to convert leads to a turnover and the opponent starts their following drive at the yardline where the turnover was committed. This means that the starting position itself might provide a better chance for them scoring (either a field goal or a touchdown), while the failed conversion might have cost 3 points from a field goal.  All of these need to be accounted when deciding whether to go for it or not.  Let’s start with each component individually.

Fourth down conversion rate: I first analyzed the success at converting fourth downs based on the yards needed for getting a first down.  As one might expect as the yards-to-go increase the success rate decreases.

However, one of the problems with these results is the fact that the fourth down success rates are calculated based on the observed attempts in the last 7 NFL seasons.  This biases upwards the average conversion rates, since coaches go for the conversion when they “feel” the situation is just right (or in special situations – e.g., trailing with a few minutes left in the final period).  Furtheremore, the variance is high since there are only few observations for yards-to-go greater than 5.

Field goal success rate: Another information needed for deciding on fourth down situations is the success rate of a field goal attempt as a function of distance.

As one might have expected the field goal success rate is a decreasing function of distance.

Drive success and starting field position:  The starting position of a team can impact the success of the drive. At each kick-off teams attempt to go for a touchback, which give the ball to the opponent at their own 20 (starting this season this will be their own 25).  In general the average starting point for a drive is not much different than this.  So the baseline probability of success for a drive can be thought of as the one for staring field position the own 20.  The following figure presents the fraction of drives that ended up in a touchdown, field goal or punt/turnover for each starting field position.

Based on these results it is obvious that turning the ball on downs can potentially impact the probability of success for the opponent’s drive.

Putting everything together

By combining the above results -we leave the details to the paper for the interested reader – we can obtain a cheat-sheet for the fourth down decisions. In the following figure the cheat-sheet is parametrized by the distance to the goal line and the yards-to-go for a first down.  Yellow color corresponds to a go-for-it decision, while a blue color represents a punt (or attempt field goal depending on the distance to the goal) decision.

The actual output of the analysis is the expected point benefit from attempting a fourth down.  In the above figure we have just quantized this decision to 1 and -1 depending on whether the expected benefit is positive or negative respectively.  One thing to observe is that once in the red zone teams should always make use of all of their 4 downs and should not settle for a field goal (we will come back to this in a while).  As we can see there is some “noise” in the data (e.g., while when you are at your own 40 and have a 4 and 1 situation the decision is go for it, this is not the case when you are at your own 39!) since we have not smoothed them out.

Limitations

The analysis above does not come without limitations.  First and formost the fourth down success rate is biased as alluded to above. Also the mean field approximation does not account for special situations (mainly related with the point differential and the time remaining on the clock).  It only considers the objective of maximizing the points scored.  However, one can certainly see that the decisions from the above chart are not always optimal with respect to winning a game.  For instance, consider the case where a team is trailing by 2 points and is at the red zone with one minute remaining and faces 4 and 1.  It is obvious that the optimal decision in this situation is to attempt a field goal.  In general, one of the factors that need to be incorporated in similar cheat-sheets is the variability of the decisions.  In particular, the expected net point gain is positive for a large number of the situtations presented in the figure.  However, the standard error for the fourth down conversion rate is 4.7% while for the field goal is only 0.42%. Finally, in our analysis we have not accounted for skilful punters that are able to pin the ball deep in the opponent’s territory  (e.g., own 5-10 yard line).  This impacts the success probability for the upcoming drive (see “Drive success and starting field position”).