Cowboys Film Study: 4th Down Attempts and Game Theory
The Cowboys attempted just 11 plays on 4th down last season, converting on only four of them (36.4%). The average distance-to-go was 2.64 yards, although eight of the 11 plays were either 4th and 1 or 4th and 2.
Despite converting on only four of the plays, the Cowboys gained an average of 6.72 yards-per-play on fourth down. This was due to three outliers–big plays of 53, 19, and 14 yards.
Despite the short distance-to-go on the majority of the 4th downs, Dallas passed the ball on seven of them (63.6%). All of their conversions came on passes, meaning they were 0-for-4 when running on 4th down.
This lack of success when running on 4th and short could be a problem for the Cowboys if it prompts offensive coordinator Jason Garrett to call even more passes in short-yardage situations. While Dallas had more success passing during 4th and short last season, this was simply due to a small sample size.
In reality, offenses tend to pass far too frequently in short-yardage situations. The graph to the left, provided by Advanced NFL Stats, shows the conversion percentages of teams on 3rd downs in various situations. Of course 4th down plays are different, but no so much so that we cannot draw meaningful conclusions from the comparison of the two.
In 3rd and 1 situations, offenses obtain a 1st down on 70% of runs, compared to just 58% of passes. In fact, running the ball on 3rd down actually yields the most success (in terms of achieving 1st downs) up until 3rd and 5. Surprisingly, passing the ball never becomes significantly advantageous over running the ball in any situation up through 3rd and 10.
The reason behind this has to do with game theory. If defenses were to remain in their base personnel regardless of the down and distance, running the ball in medium-to-long yardage situations would be generally unsuccessful. Since defenses substitute their nickel or dime personnel and dial up a play designed to defend a pass, however, offensive coordinators could increase their 3rd and 4th down conversion rates by calling far more runs in those situations.
Another way to look at it is that the play-calling of other offensive coordinators around the league affects that of Garrett. The two are not independent of one another. Running the ball on 3rd and short-to-medium is the optimum strategy not because of anything inherent in the game of football, but because of the play-calling of other offensive coordinators. If other OCs suddenly started calling a bunch of 3rd and 4th down runs, defenses would adjust, perhaps making passing the ball in those scenarios the optimum strategy.
Now, we should not only factor in conversion rates, but also big play percentages. For example, while we would love to see the Cowboys’ 36.4% conversion rate on 4th down plays increase, it wouldn’t be advantageous if it increased (even moderately) at the cost of losing big plays. The plays of 53, 19, and 14 yards which the Cowboys obtained on 4th downs were momentum-builders which often led to quick scores.
Thus, the run/pass balance on 3rd and 4th and short is a delicate thing. Yes, you want to convert the play for a 1st down, but obtaining a 1st down is not the only goal. Sometimes, it is advantageous to bypass high-percentage 1st down plays for medium-percentage plays which could result in a quick touchdown.
We talked about this quite a bit in our study of 2nd and 1 play-calling. In those situations, when offenses possess downs left with which to work, it is optimal to open up the playbook and take a shot down field. On 4th down, however, there is no room for error. While obtaining a 1st down is still not the only goal, it is much more important than it is on 2nd and 1.
Let’s return to the Cowboys’ 4th down play-calls. We have said that game theory suggests teams should run the ball more in 3rd and 4th and short situations. One of the reasons that Dallas may have failed in 4th and short last year was they tried to get too fancy with their play-calling. Of the 11 plays on 4th down, an incredible seven of them were out of the Shotgun formation. The Cowboys might benefit from simply lining up in a run formation and pounding the rock on 3rd and 4th and short.
Of course, we believe the ‘Boys should generally go for it (much) more often on 4th down. NFL coaches are incredibly conservative and slow to adjust to new information.
Take a look at the graph to the right. Notice that, no matter your position on the field, it is almost always smart to go for it on 4th and 1 or 2. In fact, the graph shows that it is even the best strategy to go for it on situations such as 4th and 10 at your opponent’s 35-yard line or 4th and 5 at their 10-yard line.
Plays like these–4th downs in your opponent’s territory–are crucial to a team’s win expectancy. Of the Cowboys’ 4th down plays in 2009, only one of 11 was in their own territory. Two of them were 4th and goal situations (and particularly memorable ones at that)–one at Denver and the other versus San Diego. The results of both plays (an incomplete pass and a zero yard rush) directly affected the outcome of both contests.
Nonetheless, the ’09 failures of Dallas on 4th down should not affect their willingness to go for it in the same situations in 2010. Many people use outcomes to justify choices, but that can lead to poor decisions. Instead, good decisions are ones that maximize the probability of a wanted outcome. A sample size of just 11 plays is too small to draw meaningful conclusions, meaning the Cowboys would be wise to take league-wide statistics into consideration–leading them to go for it more often on 4th down, particularly with power runs in short-yardage situations.