Anyone who has looked at the 4th down strategy chart above knows that going for it on 4th and 1 (trying to convert) is ALMOST ALWAYS the optimal play. While the multi-part series of posts (Part 1 can be found here) that culminated in that chart explained the thinking behind it, it occurred to me that we didn’t actually lay out the numbers.

So here is the theory, using the concept of expected points, of why it’s usually best to go for it on 4th and 1, from nearly ANY spot on the field. Remember that when I use expected points, I’m piggybacking off the work done by Brian Burke at AdvancedNFLStats.com (expected points).

The overall thesis is: Possession in an NFL game is EXTREMELY valuable, and NFL coaches voluntarily surrender it far too often. With just 1 yard to gain, the odds are heavily in the offense’s favor of gaining a first down and keeping the ball. Despite this, “common” strategy calls for giving the ball away in these cases. This is wrong.

Basically, we are combining what we know about the probabilities of converting 4th and 1 with the expected point values of each yard line. By doing so, we can come up with the actual expected point trade-off for each punt/go-for-it decision. Put more simply, just how valuable is “field position” gained by punting on 4th and 1?

Before I get to the good stuff, I want to make one caveat very clear. I’m using NFL averages to compute the following values. Obviously, most teams deviate from the league average to some degree. However, if I can show that all NFL teams, in aggregate, should be more “aggressive” on 4th and 1, then it’s a fairly small step to then apply it to the Eagles specifically. I just have to acknowledge that there is, in fact, another step there.

First, we need an expected success rate. Using this site, which I cited for our 3rd down play-selection/game-theory discussion, we can see that over the past 10 years, all 4th and 1 plays have been successful 66.5% of the time. Below is the output. The 66.5% is simply the weighted average success rate.

Second, we need to know just how much field position can be expected to be gained by a punt. Using ESPN’s stats, we can see that last year, the median NET punting average was approximately 41 yards (between 41 and 42).

So we have our building blocks:

– Teams are successful at converting 4th and 1 yard 66.5% of the time.

– By choosing to punt, teams can be “expected” to gain approximately 41 yards of field position.

Now let’s look at expected points and put those two things in context. Here is a graph showing the expected value of a first down at each yard line.

Unsurprisingly, the expected value of a first down increases towards 6 points as you get closer to the goal line. By itself, though, this chart isn’t overly helpful. However, we can use this chart to gauge the value of an average punt in each spot.

Let’s look at the scenario of a 4th and 1 at the offense’s own 9 yard line (the worst possible field position at which this can occur). Simplifying things, there are 3 potential outcomes.

– Punting, which we will assume results in the opposing team taking possession at the 50 yard line (41 yard kick).

– Going for it and converting. Here, to keep things easy, we’ll assume the offense gains just 1 yard, the minimum needed to gain a 1st down.

– Going for it and failing, the result of which gives the opposing team the ball at the 9 yard line.

Applying the success rate and expected points we saw above, we come to the following values for each scenario:

– Punting is worth -2.04 points, which is the expected value of a 1st down at the 50 yard line (for the other team, hence the negative).

– Going for it and gaining 1 yard is worth -0.21 points, which is the value of a 1st down at the 10 yard line. However, this only has a 66.5% chance of happening, which we’ll adjust for in a moment.

– Going for it and failing is worth -4.83 points, which is the value of a 1st down for the OTHER team at the 9 yard line.

Using the 66.5%/33.5% success odds, we can calculate the expected value of going for it, that is the expected value WITHOUT KNOWING if you will succeed or fail.

Converting: -0.21 * .665 = -0.14

Failing: -4.83 * .335 = -1.62

Combined: -1.62 + -0.14 = -1.76

See why that’s a big deal?

Given a 4th and 1 at your own 9 yard line, an average punt is “worth” -2.04 points, while going for it (with average success) is “worth” -1.76.

Going for it is worth 0.28 points MORE than punting.

Hopefully one example was enough, so rather than continue, I’m just going to give you a chart. Here is the expected value of both punting and going for it at each yard line (between the 9 and 50), assuming a 41 yard punt, a 1 yard gain if converting, and league average success rate when going for it.

So there you have it. As you can see, going for it is more valuable than punting regardless of field position. As I said at the top, with just 1 yard to gain, the odds heavily favor the offense, yet they don’t seem interested in taking advantage of it.

Giving up possession of the football, regardless of whether it’s the result of a TO or punt, is bad. It looks like teams are underrating the degree to which punting the football is a negative play. They also seem to be under-appreciating the odds of converting in 4th and 1 situations. As a result, “common” NFL strategy is far from optimal, leaving an opportunity for a forward thinking team to gain a significant advantage over the rest of the league.

Obviously each of these assumptions needs to be tweaked for individual teams. However, if the league, overall, should be going for it a lot more often in 4th and 1, then by definition, many teams should going for it more often. Here are some quick adjustments that result in “going for it” more often, with the reciprocals being adjustments that should result in punting more often:

Bad Punter – Go for it more often (lower net punting average)

Good Offense – Go for it more often (higher expected value of a first down)

Bad Defense – Go for it more often (value of OPPOSING team’s possession after a kick is higher)

Someday, we’ll see a team take advantage. I think Chip Kelly will be more aggressive than average (closer to optimal), but far from as “aggressive” as he should be. Hopefully, after developing a successful track record and some credibility, he’ll have the stones to implement strategy like this more fully.