Nine Yards is Enough - Why NFL Receivers and Running Backs Should Stop Shy of the First Down

Can NFL teams win more games by instructing the ball carrier to stop short of the first down?

The First Down

This year marks the one hundredth anniversary of the National Football League. The game has undergone many changes, although statistical analysis of strategy has been something of a late starter. A good chunk of that history expired before a serious discussion of punting strategy. To this day, some armchair statisticians are driven to distraction by sub-optimal fourth down decision making. 

In this post I go after another sacred cow - the first down. I'm going to argue that players are, perhaps unwittingly, making a mid-play strategy error on the first down that is materially impacting their chance of winning the game. Their sin isn't a lack of aggression this time, but too much. It may sound strange, but they are finding their way to the first down marker too often.  Yes, that's right. Teams are mistakenly securing too many first downs.

What should they be doing instead you ask incredulously? Not securing first downs? 

Exactly! They should not take the first down on the first down, unless they can get some extra yards in the process. 

The Choice

Now I may be wrong about this, but from my casual observation of American Football I could swear that commentators, fans and coaches alike uniformly encourage their players to lunge, stretch, hurdle or bulldoze their way across that last yard in order to move the chains. Getting the first down is a motherhood issue. It is to be applauded. For example, how often do we see a wide receiver break the imaginary yellow plane in acrobatic fashion, often one arm outstretched, as they careen out of bounds? 

Using data from the 2009-2013 NFL seasons we shall investigate this "decision" (or perhaps we should call it a non-decision). It is a decision made every time a receiver decides to put their body on the line in order to get to the first down marker. To be clear, we are only talking about decisions made on the first of four downs. Readers unfamiliar with NFL may wonder about the terminology. The "first down" refers to both the first of four attempts to advance ten yards, but also refers to the act of achieving said ten yard advance, thereby resetting the down count. 

At the outset I add the caveat that a decision is only made when a player with the ball is certain they cannot achieve more than ten yards (or maybe eleven) in advance of the line of scrimmage. Obviously a player in full flight would be silly to pull a jump stop one yard short of the first down markers. But there are plenty of situations that arise when it is abundantly clear that no extra yardage will be achieved. 

In choosing to complete the first down, or not, the ball carrier is determining which of these two outcomes will ensue.  

1. Second down and one yard. 
2. First down and ten yards (but with line of scrimmage one yard further down the field). 

The second possibility seems to be the strongly preferred option, given two seeming advantages:

• The play is advanced one yard
• The team will have one extra down

However, there is one big disadvantage. The number of yards required for the next down reset will be ten, rather than one. In this post I want you to look at it from a different perspective. You're probably going to get that first down anyway. It might as well be further down the field. 

Yards in a Possession 

It's our duty to convince the NFL offensive coordinators that first downs aren't always a good idea. Actually, some certainly appreciate this already, based on initial reaction to this post - though some thought it was borderline unethical to stop one yard shy. The real challenge is convincing players. They must do what might not come naturally. Or rather, they must not do what does come all too naturally. They must resist the urge to make that extra effort when in fact, it is counter-productive to their team's winning chances. Save that first down celebratory dance for when it really helps. 

Simple logic has a funny way of helping players build muscle memory. As it happens, the reasoning is easy to grasp once we have established an upper bound on the value of possession relative to yards. That's the only part that might be considered somewhat complex - yet even a naive analysis might suffice. Since teams drive 35-40 yards on average, a possession can't be worth more than about 40 yards. 

Points in a Yard

Some people might find the above rationale for "a possession is worth less than forty yards" to be suspicious. I wouldn't like the findings to depend on it, so I'll offer you another way to arrive at roughly the same answer - albeit requiring just a little more effort. We ask a different question. How many points is a yard worth? By this, I refer to a yard of field position, assuming we are on the first down. 

Of course, of course, of course ... the value of a yard depends on this and that. I'm not going to get into endgame analysis or special situations, nor the value of the clock when one team is ahead. I shall be content with somewhat typical field and game position, which, if you prefer, can be assumed to occur in the first three quarters of a relatively even game (that is, not so lopsided that one team has significantly diverged from a strategy that roughly speaking, maximizes mean points scored). 

As an aside: here is an illustration of why points per yard may vary even under benign settings. Suppose we are in field goal range on the third down. The value of a yard is reasonably represented by the slope of the blue line in this plot I stole from a 538 article on punters (thanks Benjamin Morris). The plot shows the probability of a successful field goal. Since the slope clearly varies quite a lot, so does the value of a yard on third down when, let's assume, we must take the field goal. The value of a yard on first down will include a kind of average of these results, somewhat smoothing out the differences in slope, but we will still have differing values of points per yard. 

This kind of variation shouldn't deter us. I will be lazy and borrow from our good friends at Advanced Football Analytics from where our next plot is taken. This particular analysis is the work of Brian Burke, and it shows a value function derived from a Markov Model for football. With some caveats, this really is the real value of field position and it takes into account the possession after this one, and the possession after that, all the way to the end of the game. 

As an aside, look closely and you will see the field goal effect (the varying marginal value of a yard) as we get to the red zone. At first it wiggles up, representing the relatively small benefit of getting closer when your kicker is highly likely to make the kick. Then, the expected points drop faster. You also see effects when touchdowns have high probability - albeit in the other direction since 1 yard means all the world when a team is 2 yards from the end zone. 

These are curiosities but certainly not essential to our analysis. The beautiful thing about a value function is that it rolls the future back to the present, making our analysis very simple (my attempt at a lay introduction to value functions is here, for anyone who may be interested. I use golf, baseball and chess instead of football). In case you are wondering, that's how the values can go negative. This isn't a plot of average points in the current drive.

Here's an example of reading the plot. Notice that the intercept occurs at 85 yards approximately. This means that a Herculean punter who can always pin an opposition to their own 15 yard line when punting from their own 15 yard line would be a handy asset. A team transferring possession in this manner has, according to this plot, lost absolutely nothing. 

In the absence of a physics-defying punter, we can use the plot to draw conclusions that are more reasonable. For example, let's say we read off 66 yards (i.e. our own 34 yard line) corresponding to +1 point on that plot. We are +1 points because we have possession. That's how my eye reads it, anyway. Now imagine we punt it to our opposition. They start their next play on their own 34 yard line after an entirely plausible, if unspectacular, net punt of 32 yards. So now they are +1 points. Net, we have lost 2 points.

Or perhaps the punt is better. They start at their own 20 instead, corresponding to an expected 0.5 points per possession. Net, we have lost 1.5 points. I put it to you that a possession is worth not more than 2 points, or perhaps a tad more, but not much more. You get the idea. 

Similarly, we can read the value of a yard. You can see that if we are not near the red zone then it takes about 60 yards to go from 4 points to zero. This means about 15 yards per point. Put those together and you see that a possession is worth about 30 yards - with the caveats above - and probably not much more. The 30 yard estimate seems small, don't you think? Well then, make it 40. 

If you worry this might not apply to college football, by all means refer to this analysis by Saiem Gilani. I think you will find that the relationship between yards and possession is pretty close to what I postulate. Gilani cites the history of this kind of work, going back to Virgil Carter's paper in 1971. 

3rd and 1

Armed with the seeming fact that a possession is worth no more than 40 yards, and probably considerably less, we turn to the 3rd down. We assume one yard remains. I could not find any study of third down and one situations so alas, I had to do a tiny amount of work myself (see the notebook which you can use to reproduce my database queries and rudimentary arithmetic). I was pretty lazy and used a CSV prepared by Den Dilday (Github homepage) containing all plays from the 2009-2013 seasons. I'm sure the skeptical reader will be able to enlarge the dataset should they wish to do so. 

We need to understand third and one for the obvious reason that an unsuccessful second and one play will probably leave us in that position (the astute reader will note there is a small chance of a loss on the play - but I will be recommending running plays where this effect is very small).  

What most interested me was the number of yards gained on a successful third and one play. That's a conditional average, not the average including unsuccessful plays that don't advance the line of scrimmage. When passing, this conditional average gain is 12.75 yards. When rushing, the average gain is 5 yards.

Aside: this is a pretty large discrepancy and it suggests that teams might consider passing on third and one more often than they do. Passing plays are only successful 61% of the time, versus 72% when rushing (and I am led to believe, 80% for quarterback sneaks - though that was not in the data I had). An 11% chance of lost possession corresponds to only a few yards, according to our analysis above. And this gets swamped by the massive 7.75 yard differential when passing. Teams should run passing plays on third and one! 

Third an 1 strategy is certainly interesting, but the only thing we need to take from this analysis is that successful third down and one results in an advance of field position of 5 yards even if you choose to run the ball. And by the way, a rushing play has a 72% chance of success, when it is 3rd and 1. 

2nd and 1

When we look at 2nd and 1 plays, rather than 3rd and 1, we find that the rushing play percentage goes even higher - up to 80% chance of making at least 1 yard on the play. The average number of yards gained, assuming success, drops slightly (down to 4.73 from 5.0). This isn't surprising. The defense doesn't have quite the same incentive to kill the one yard gain. A larger number of small gains bring down the average yards achieved assuming at least a one yard advance.  

(Another aside: the differential between passing and rushing yards gained decreases, as compared to the 3rd and 1 differential. Successful passing plays lead to only 6.5 yards of gain on average, compared with 7.75 for passing on third down. The data suggests that the natural urge to pass on second and run on third might be working against the better interest of teams. But these are sidebar discussions for another time).  

All we need for our analysis is the following "facts". 

• If you tell your team to rush on 2nd and 1, and then again from 3rd and 1 (should that be necessary) then you will have a 94.5% chance of getting the first down and only a 5.5% chance of being "forced" to punt. 
• With the same 94.5% probability, you will advance an average of 4.75 yards, give or take.

Perhaps it is already apparent why sometimes, you don't want those chains moved. 

Take 2nd and 1, or 3rd and 10? It ain't close. 

Finally, the moment of truth has arrived. Our star receiver takes a catch at the nine yard line. Flat footed, he turns to see a defensive player bearing down at great speed. Risking a season-ending injury he can, most certainly, dive forward with outstretch hands and make the hero play - securing the first down. Alternatively, he can casually step out of bounds, leaving his team at 2nd and 1.  

Or perhaps a tight end has broken one tackle and staggers toward the first down marker dragging a defender who has grasped his leg. Should he break the plane or voluntarily stop his progress, if he knows he won't get any further?

For a potentially controversial topic the calculus is alarmingly easy. Our team, starting at 2nd and 1, will get the first down anyway 94.5% of the time. But what is more important is that our team will advance field position in the process, by an average of almost 5 yards. This means that the first down will take place four yards further into enemy territory than it otherwise would. Four yards (or even 3.75) is not to be sneezed at. And this assumes rushing, which may not be optimal on 3rd and 1, as we have discussed. 

We can now frame the decision in terms of implied yards per possession. The wide receiver's lunge suggest that a 5.5% chance of losing possession is more important than 3.75 yards of field position. He is wrong! Since 5.5% is roughly 1 in 18, this means that possession must be 17 times more important than 3.75 yards. The receiver implies a value of possession of 17*3.75=63.75 yards ! But as we have seen, there is no way in God's green football field that a possession is worth 64 yards. It is closer to half that number. 

A century of football strategy out the window? 

It gets worse. Interestingly, going for the first down isn't even worth it if you get to the 11 yard line. The calculus would then read 2.75*17=46.75, which is still way too high a value (in yards) to put on possession. We have to get to the 11.5 yard line to get something closer to a sensible value of yards per possession (38.25). So the moral of the story is, unless you think you can advance two yards past the first down, take a knee. 

About me

Hi I'm the author of Microprediction: Building an Open AI Network published by MIT Press. I create open-source Python packages such as timemachines, precise and humpday for benchmarking, and I maintain a live prediction exchange at www.microprediction.org which you can participate in (see docs). I also develop portfolio techniques for Intech Investments unifying hierarchical and optimization perspectives.