AFA continues its partnership with the Harvard Sports Analysis Club. The following analysis originally appeared on HarvardSportsAnalysis.org

In the 94-year history of the National Football League over 14,000 games have been played. And in every game but two a punt has occurred (the recent Packers-Bears game in Week 4 was one of these rare occurrences). It seems as if these events that occur so often in the NFL have been left unstudied. How much is a punt actually worth in the NFL and who are the best at doing it?

To do this, I looked at over 3,000 punts from the last five seasons (Advanced Football Analytics has data through Week 12 for the 2013 season) using the AFA play-by-play database. After controlling for all punts that were blocked or fumbled by the punt team, I was able to create a new stat that I called “effective punting distance” which was simply the difference between the starting field position (yrdline1) and the resulting field position after the punt and return attempt (yrdline2). While this stat doesn’t perfectly measure a punter’s ability—there are confounding factors such as the quality of the punting team’s return coverage and the skill of the returner—it should be a more telling metric than simple punting distance. Effective punting distance accounts for punts that are not returnable, such as touchbacks, out of bounds, fair catches, and punts downed by the coverage team while penalizing punts that give the receiving team a return attempt.

This first scatterplot plots the relationship between yrdline1 and yrdline2, the starting and ending points of a punting play. The scatter seems to show a diminishing marginal return to effective punting distance when approaching the goal line, which confirms the intuition that punters attempt to finesse their kicks as they get nearer the goal line.

Scatterplot of NFL Punting Yards

The next graph shows the average resulting field position vs. the starting field position across the entire league. Because of very small sample size for punts occurring beyond the 35-yard line, I’m only showing punts from the 35 and beyond. In addition, I have fitted a third degree polynomial line to better approximate the true curve. This smooth polynomial regression line is what I will use to calculate the league average at each yard line instead of the jagged line connecting the sample means at each data point.

Smoothed Plot of NFL Average Punting Yardlines

Now that we have a good representation of the league average punter, we can find a way to show the difference between a good punter and an average one. The next picture is a very arbitrary, theoretical representation of what a bad punter (green), average punter (blue), and good punter (red) look like. This graph also shows that when punters move farther away from the goal line, the difference in their skill level becomes more pronounced.

NFL Punters Stratified by Skill

It is also possible to think about this relationship mathematically where the integral of the league average punting function minus the theoretical individual punting function indicates punter skill level, which we could find by fitting another third degree polynomial regression line. This method would give us the punter’s yards above average, however this isn’t necessarily the best way to evaluate punting ability.

Since every marginal yard does not have equivalent value, it will make more sense to evaluate a punter’s ability in terms of expected points above average. An expected points framework allows us to find the expected value of a possession starting from a specific yard line. A league average punter would typically punt from his team’s 20-yard line to the opponent’s 37-yard line yielding an expected point value of 1.25 for the upcoming possession. If the punter can instead force the opposing team to start from their own 20 instead, the ensuing possession only has an expected value of .34 points. In my model, the punter is then credited with the difference in expected point values, meaning this punt was .91 points above league average.

The histogram below shows the distribution of punt expected values centered at zero (a mathematical certainty). The graph is also heavily negatively skewed with a skewness statistic of -3.87. This makes complete sense, as the vast majority of punts are caught with little return, but some will be returned for touchdowns.

Histogram of Expected Points Added Over Average

Now we can see which punters make the biggest difference over average in expected point value. The table below shows the total expected points over average contributed by a punter over the last five seasons, with a minimum of 20 punts attempted. Over the last five seasons, the punter who has most positively impacted his team has been Thomas Morstead of the New Orleans Saints with 11.03 points added over average. On the reverse side, we have the poorest punters in the NFL through 2011, including Jason Baker of the Carolina Panthers. On average, each punt he took cost his team .46 points compared to a league-average punter.

What should be striking here is that Morstead has only been able to add 11.03 points over four seasons and most of the 2013 season, equivalent to 2.32 points over average each season. For comparison, the average NFL team scores 371.85 points a season. Football Outsiders estimates that in 2013, Peyton Manning was able to contribute 2,475 yards above average at quarterback, which is worth approximately 160.6 expected points above average.

It is also worth noting that NFL teams currently have a difficult time evaluating and paying punting talent appropriately. For example, the highest paid punter for the 2014 season is Mike Scifres of the San Diego Chargers who is earning \$3.25 million this year (corresponding to a \$4 million cap hit) but producing results below the league average. Even if teams starting evaluating punters correctly, the marginal benefit a team could expect from signing a top punter is not worth nearly the current market cost.