These days in the NFL, the most obvious situations such as 4th and 1 and 4th and short near midfield are now reliably attempted by all but the worst coaches. Of course, if you are reading this site you probably already realize that coaches should go for way more first downs than this.

This seminal study provided the framework for fourth down decision-making which we will use here, along with a convenient chart describing when teams should go for it. The chart suggested a strategy still far more aggressive than what teams use today. It is worth re-visiting fourth down strategy as the game has changed since the 2000-2008 sample:

2000-2008 | 2020 through Week 6 | |

Pass yards per play | 6.01 | 6.64 |

Rush yards per play | 4.14 | 4.39 |

Net penalty yards per penalty | -0.42 (favors defense) | 0.82 (favors offense) |

Total points per game | 42.3 | 51.4 |

Net yards per punt, punts between 20-40 yard line | 37.4 | 43.7 |

Average starting field position following kickoff | 28.1 | 24.8 |

Conversion %, 3rd and 8 to 11 (average 9.29 to go both periods) | 31.7% | 35.6% |

The higher conversion rate of third downs, higher overall scoring, and better kickoffs (meaning fewer points are lost on the ensuing kickoff after scoring) would seem to favor a more aggressive strategy on fourth down. However this is offset by better punts and the fact that better offense makes kicking off after scoring worse. In addition, 2020 is a special year in that scoring is up almost six points per game compared to the year before even as special teams performance has remained largely the same. Given there are forces acting in both directions it is not a slam dunk that teams should be more aggressive given these changes, and perhaps the coaches are right. We will now find the net impact of these changes to fourth down strategy.

We will focus here only on 4th down decisions between a team's own 20 and 40 yard line. In the below charts and graphs we will split outcomes into high (over 46) and low (under 43.5) total situations to allow the reader to compare 2020 football to the 2000-2008 environment; however, underlying calculations are based on regressions using all games.

In addition, we will only study situations in the first three quarters and eliminate situations where there are less than five minutes left in the second quarter. We will assume that net yards per punt and kickoff are fixed at the 2020 averages. We will limit our sample to games since 2016, where the kickoff rules were changed to the current version.

Finally, since there is almost no sample of teams going for fourth and long, we will assume that fourth down conversion rate is the same as what third down conversion rate was in similar situations. This may or may not be true; there are great arguments to be made for both a higher and lower conversion rate on fourth down relative to third. The one situation where there is a good sample of past plays, 4th and 1 versus 3rd and 1, doesn't show much of a difference.

To start, we consider the impact of game total and spread on the key metrics that influence the fourth down decision: net next points scored by ball location between a team's own 20 and the opposing 20 yard lines (and the subsequent EPA of the drive after considering the points lost to the ensuing kickoff when that team scores), conversion percentage, and yards gained past the marker on conversion.

**Expected Points Added by Field Position**

We begin with net next points scored (positive if the offense scored next, negative otherwise) by yards from a team's own goal, for all drives starting at 1st and 10 at a given yard line:

The difference between the two groups is barely perceptible, and overall, the high total games only average about 0.25 points per drive more for a given spot on the field. But this makes sense, as assuming an average of 24 drives per game this results in a difference of six points per game which is 2/3 of the nine-point difference in totals. The other three points come from high total games having more drives as well as the average position of the ball on the field being closer to the opponent's goal line.

Expected points added depends not only on the current drive, but also the resulting kickoff; when a team scores, they have to give the ball to the other team, and this usually has a negative point expectation. The chart above, confirmed by a regression model of all drives starting between the 20 and 40 that also adjusts for the spread and total of the game, gives us an average value of 0.89 points for an opponent starting on the 25 yard line in a high total game and 0.60 points for an opponent starting on the 25 yard line a low total game. Subtracting these values from drives that had a positive (offensive) score and adding them to drives with a negative (next score by the defense) score we arrive at the following chart of EPA per drive by yards per own goal:

Due to the higher yards per play and conversion percentage, drives on a team's own half of the field are worth more in high total games than in low total games. However, due to the kickoff adjustment, as the ball crosses about the other team's 40 yard line, the net EPA converges to the point that low total drives are worth slightly more. The per-drive benefits of a higher scoring environment decline as a team moves down the field, due to fewer remaining plays for offensive skill to be expressed, the red zone, and teams kicking too many field goals. As the kickoff remains the same, this causes a deep drive in a high-total game to be worth relatively less.

While the above chart may prove unsatisfying we can verify the slope of EPA versus total (and spread) through regression modeling. Because the relationship differs in different parts of the field we use three separate regressions, a poor man's splines, one for drives from 20 to 40 yards from the team's own goal line, one for 40 to 60, and one for 60 to 80:

20 to 40 | 40 to 60 | 60 to 80 | |

Intercept | -1.95 | -1.08 | 0.187 |

Yards from Own Goal | 0.0574 | 0.0507 | 0.0482 |

Spread of Team with Ball | -0.122 | -0.097 | -0.061 |

Game Total | 0.031 | 0.016 | -0.003 |

Note that the game total basically only matters for drives between the 20 and 40; the slope of game total is around 0 if the team has the ball on the opponent's half of the field. From the standpoint of a fourth down decision, if a team punts from their 20 to 40 yard line, the ball will almost always end up on the other team's 20 to 40 yard line. What this means is that when a team goes for the fourth down and gets it, while their drive will be worth more in a higher total game, they also would have gained more in a high total game by pinning the other team further back when punting.

However, when the team does not get the first down, they don't lose any more EPA than they would in a low total game. When keeping the ball they get the benefit of a higher scoring environment, but when losing the ball, the models suggest the other team does not get any benefit. This means teams lose less from not making it on fourth down relative to the times they keep the ball. This slightly favors a more aggressive strategy.

**Third (Fourth) Down Conversion Rate and Yards Gained Past the Marker by Game Total**

We now move on to 3rd down conversion rate by game total. As one would expect conversion percentage is higher across all yards to go situations in higher total games:

On average, third downs are converted about 6% more often in the higher total games. To estimate third down probabilities across all totals and yards-to-go situations we can set up the following logistic regression, for all third down attempts made with between 2 and 14 yards to go between the 20 and 40:

Intercept | -0.654 |

Yards to Go | -0.143 |

Spread of Team with Ball | -0.0175 |

Game Total | 0.029 |

The relationship between conversion percentage and game total can be visualized in the following graph:

Finally, we can account for the extra yards gained past the marker, when teams convert the third down, as well as yards gained or lost when teams fail to convert. From regression modeling, when teams get a first down on third down, they average 3.87 + (yards to go) * 0.194 + (game total) * 0.096 yards past the marker, while when they don't get it, they average (yards to go) * 0.321 - 2.16 net yards.

As an example, given a third and 10 with a game total of 50, a team would average 10.6 yards past the marker the times they got the first down for an average gain of 20.6 yards. While past fourth down analysis has ignored these extra yards this 10-yard difference is worth nearly 0.6 additional points the times the team gets the first down and makes going for it on fourth and medium-long more attractive.

**Putting it all Together**

We now have all we need to find the break-even conversion percentages, and hence correct strategy by game total and spread for a given fourth down situation. Punting is the easy part: we assume a 44 yard net punt, which will result on the ball ending at 100 minus the current yard line minus 44 yards from the opponent's goal line. Using the EPA equation above we get:

EPA(Punt) = - (-1.95 + (100-current yard line - 44) * 0.0574 + (-0.122*Spread of the Other Team) + (Game Total) * 0.031)

To slightly simplify the math of going for it we will ignore the net yardage the times the team does not get the first down, since this is very close to 0. Using the EPA equations above, we arrive at the following equation:

EPA(Go For It) = (Value of 1st and 10) * (Probability Team Gets First Down) - (Value of Other Team's 1st and 10) * (Probability Other Team Gets a Stop) =

(-1.95 + (current yard line + 3.87 + (Yards to Go) * 0.194 + (Game Total) * 0.096) * 0.0574 + (-0.122)* (Spread of Team with Ball) + 0.031 * (Game Total)) * (Expected Conversion Percentage, Given Game Total and Spread)

- (0.187 + (100-current yard line) * 0.0482 + (Spread of Other Team)*-0.061 + (Game Total) * (-0.003)) * (1 - Expected Conversion Percentage)

There are too many dimensions here. To simplify things, let's assume that every game is a pick'em and every 4th down decision starts at the 28 yard line. We can then show the net points gained or lost, (EPA(Go For It) - EPA(Punt)), by distance and game total:

Teams should go for it when the yards-to-go line above for the game total on the x-axis is greater than 0. For a total of 41, the cutoff is around 4th and 2, which is in line with the Burke work which was based on a sample with an average total of 41. But higher totals change the equation considerably. In games with a total of 56, not uncommon in today's NFL, teams should be going for it on 4th and 10 on their own 28, and even in a typical game this year with a total of 50, the cutoff is around 4th and 7.

Note also the extremely high point values on short yardages in the higher total games. In old-school football, other than on 4th and 1 punting was never a huge mistake, because even when going for it was right, it was very close. However, punting on 4th and 2 in a game with a total of 50 is almost a full point worse than going for it, and further down the field or in higher total games there are even worse situations where coaches punt on a regular basis. It is easy to leave a field goal or worse on the field in games like these.

While field position would seem to matter, starting at the 40 or the 20 rather than the 28 barely makes any difference to the lines above. While giving up the ball is less (or more) bad, punting is less (or more) good, and it ends up being largely a wash. But past the 40, reduced net yardage on punts as well as reduced EPA losses when missing the conversion attempt shifts the equation further in favor of going for it.

Perhaps more surprising is the case of a seven-point favorite rather than a pick'em game, where the above chart is also nearly identical. Across typical fourth-down situations a seven-point favorite will get the first down about 4% more often, other things being equal, so we would expect going for it to be favored. However, punting is also much better for big favorites. By punting, they force the other team to drive the length of the field (almost) 100% of the time, and as the EPA equations above showed, EPA slopes much higher with team strength when teams have to drive the full length of the field (0.122 points per point favored between a team's own 20-40 vs. 0.061 on the other team's 20-40) as there are more plays for skill difference to be expressed before the next scoring event. This means that fourth-down strategy does not depend much on team strength, as the increased conversion probability offsets the increased gain big favorites see from punting.

Finally, of all drives in games with a total over 46 that involved a first and 10 starting at between the 35 and 50 yard lines (the type of drive that would result from converting a 4th and medium at the 28), 17.4% ended in a punt or field goal with 4th and 3-5 to go and another 7.3% ended on a punt or field goal on 4th and 1 or 2. A very rough estimate is that in a game with a total of 50 the first type of mistake is worth about half a point and the second type of mistake is worth nearly a full point. This means that teams can gain about 0.15 additional points per drive by going for it on subsequent situations, adding further to the break-even probabilities above, at least until the other team figures out they should go for it more often as well.

**Summary**

In the new higher-scoring NFL where offensive holding is rarely called, but marginal defensive penalties are never missed, teams are leaving tons of points on the table on fourth down. Most of the gains come from teams converting in medium to long-yardage situations far more often than in the dark ages of football when totals were in the 30s and low 40s.

As with the "shift" in baseball, where it turns out traditional defense is actually close to correct, and is certainly correct against right-handed hitters, my belief is that traditional strategies usually converge to near optimal and in football the conservative fourth down strategy was also correct for a long time. Totals in earlier decades were rarely above the low 40s and according to this analysis punting is usually right in those games, although as net punting yardage was also lower in those decades, it was probably at least right to always go for 4th and 1. The coaches of today learned to coach during this time, and hence learned a strategy that was right then, but is wrong now.

Analytics or not, it is inevitable coaches in high-total games will now find that the real "loss aversion" is in giving up the ball for free, since the way football is now, the other team usually drives right back down the field following a punt. We already see this in college football, at least among the coaches that have to be smart to win, rather than outspending smaller schools for the best players, and trends from college always flow to the NFL over time.