By Pranay Varada, Elliot Chin, and Praveen Kumar
In recent years, the running back has become one of the most interesting and controversial positions in the NFL. Over the past few years, we’ve witnessed a devaluation of the position, with many teams opting not to pay running backs big money as they get older. This offseason alone, star running backs like Saquon Barkley, Derrick Henry, and Joe Mixon were given no choice but to change teams. Reflecting a changing landscape of positional value across the age spectrum, not one running back was taken in the first 45 picks of the draft.
But it’s not all doom and gloom. Christian McCaffrey had an MVP-caliber season for the 49ers, Kyren Williams had a breakout rookie season for the Rams, and Raheem Mostert led the NFL in rushing touchdowns at age 31. Clearly, though, these players are very different from one another, even if they all play the same position. That led us to ask the question: how could we group running backs into different types? And how do these different types of backs attain – or fail to attain – success?
The Data
To answer this question, we turned to Stathead’s football database. We gathered all player-seasons for running backs since 2018 (the earliest year with advanced rushing statistics) and set thresholds of 10 games played and 50 rushing attempts made. In total, we looked at 387 running back seasons over the past six years. For each running back, we considered both their rushing and receiving stats, including:
- Age
- Games played
- Rushing attempts, yards, and yards per attempt
- Targets and receptions
- Receiving yards and yards per reception
- Yards before and after carry
- Yards before and after catch
- Average depth of target (air yards divided by targets)
- Rushing first downs and touchdowns
- Receiving first down and touchdowns
- Broken tackles, rushing and receiving
- Drop percentage
This gave us a wide variety of data to use for our analysis.
The Process
To investigate the different types of running backs, we used principal component analysis, or PCA. PCA allows us to derive the most important information from datasets that contain many variables.
The PCA process starts off by centering all variables at zero and scaling them to the same range, so that they can be compared to each other by the same standards, and the average point becomes the origin. Then, one can compute the first principal component, the line that best approximates our data following a least squares method. Each observation is then projected onto this new line to get a coordinate value along the line. The same process is repeated for each subsequent principal component. To maximize interpretability, we focused our analysis on the first two principal components. Projecting all of our data onto these two components yielded a means of visualizing each running back’s 21 data points on a simple coordinate grid.
To actually group the running backs, we used a technique called k-means clustering, which essentially finds k points in the coordinate space for which points are grouped together if they are closer to one of these points than any of the others. This produces k clusters, grouped around their mean. We chose to group the running backs in our dataset into five clusters, enabling us to look at several different types of players.
Visualizing the Data
This plot shows the five different clusters produced by PCA and k-means clustering. Labeled running backs are randomly selected from those that played at least 16 games in a season.
First, to understand what the different clusters represent, we can look at the coefficients of the principal components:
The first principal component appears to have almost entirely positive coefficients, suggesting that it is correlated with both rushing and receiving prowess, more strongly with receiving. The second principal component, meanwhile, has positive rushing coefficients and negative receiving coefficients. Thus, we can think of the bottom right quadrant as having running backs who are both productive rushers and receivers, while players further up on the plot are even stronger rushers but with more limited receiving potential. Note also that both principal components have slightly negative age coefficients.
Now, we can analyze the individual clusters.
Cluster 1 contains mainly low-usage, inefficient runners with average receiving capabilities. Dolphins running back Salvon Ahmed is a prime example of this type of player, as is Latavius Murray, who has made five appearances in this cluster since 2018, the most of any player.
The players in Cluster 2 are slightly higher usage, many of whom are cogs in running back committees. Gus Edwards, Zack Moss, and Rashaad Penny are good examples of Cluster 2 backs. They’re more reliable than the backs in Cluster 1, but aren’t going to be very dominant.
Cluster 3 isn’t as uniform as some of the other clusters, but it seems to be characterized by aging or lower-usage backs with pass-catching upside. Nyheim Hines has made more appearances here than any other player. Alvin Kamara has been here for his past three seasons in the league after starting out in Cluster 5, and he’s matched in appearances by D’Andre Swift.
Cluster 4 is home to the best high-usage pure runners. They’re not going to offer too much on the receiving end, but they do a lot of what they do best: run the football. Derrick Henry is the archetype of this cluster – he’s been here in every single one of his eligible seasons since 2018. Nick Chubb, James Conner, Josh Jacobs, and Joe Mixon are also perennial Cluster 4 backs.
Cluster 5, meanwhile, contains the best high-usage pass-catching backs in the game. Christian McCaffrey dominates this cluster, with appearances in all of his eligible seasons since 2018. McCaffrey maxes out the first principal component more than anyone else. Austin Ekeler has been here a few times, along with the aforementioned Kamara; Saquon Barkley also started his career out here.
So it seems initially that Clusters 4 and 5 tend to be the class of the league. Next, we test this theory.
Where the Best Backs Lie
Using the principal component map, a natural question is whether the players that max out the two dimensions of running back success are the same ones that garner All-Pro plaudits at the end of the season. Using the list of first-team All-Pro running backs from 2018 to 2023, we plotted these players’ coordinates in context to take a look at this:
Clearly, we can see the All-Pro running back selections match up pretty well with our principal components. Considering the wide variety of stats and tape All-Pro voters have access to, it’s interesting that we can narrow all of this data to just two numerical dimensions and still have a good idea of who the best running backs are every year.
Still, looking at the unlabeled points, there have been a few notable snubs over the years. In 2019 alone, Nick Chubb, Chris Carson, and Ezekiel Elliott all performed similarly to running backs who were named first-team All-Pro, but were not selected. In 2021, Najee Harris put up All-Pro stats as a rookie, landing him in the company of Elliott and Todd Gurley’s 2018 seasons and Christian McCaffrey’s 2023 season. Look for 2024’s All-Pro running backs to land somewhere along this diagonal axis of running back superiority.
Looking to the Future
When a player is “developing,” “breaking out,” or having a “slump,” what does that really mean? Terms that fans and commentators use to refer to player performance over time are inherently multidimensional, and therefore differ from player to player. James Cook, for example, had the prototypical sophomore break-out season, rushing 148 more times in 2023 than 2022 at a slight efficiency loss. Christian McCaffrey, meanwhile, has always been a bellcow but rushed for a career-high yards-per-attempt upon joining the San Francisco 49ers. But the space of player development is not just two axes of production and efficiency: Ravens RB Gus Edwards doubled his rushing attempts in 2023 while also quadrupling his number of touchdowns as he cemented his role as the lead goal-line back. Jets RB Breece Hall saw a similar trend with growing receptions outpacing rushing volume.
How might we analyze, therefore, how players are expected to perform over time? Aging curves are a standard metric in sports analytics, first pioneered in baseball, and predict how the average player’s performance will evolve as they age. But aging curves only operate in one dimension, usually involving a player’s WAR or a similar holistic metric. To expand upon aging curves, we introduce “aging trajectories,” in which we use a learned vector field to represent the predicted trajectory of a player’s career in multidimensional space. With aging trajectories, we can evaluate how running backs of different archetypes—pass catchers, bell cows, situational backs—change over time, and whether the play styles of running backs differs as they age.
To create aging trajectories, we trained a gradient boosting model on the first two principal components of a running back’s performance in a given year, with the goal of predicting the principal components of said running back’s performance in the subsequent year. Later, to assess how trajectories vary with age, we added in raw age with no principal component parameterization, so that we could assess the impact of age on predicted trajectories.
A key use case of aging curves is to assess how development occurs at different ages. Therefore, we recalculated principal components without age as an input, and used the first two principal components and age to predict a running back’s next-year performance with a gradient boosting model. Overall, this produced only a small change in the actual calculated principal components, while allowing orthogonality of inputs in order to isolate age. Below, we show learned vector fields for players at ages 20, 24, 28, and 32.
To highlight the differences across ages, we show the difference between the learned vector fields for age 20 and age 28 running backs. Clearly, older running backs show a much stronger regression towards the mean while younger running backs are comparably more likely to improve their stats in subsequent years. This is in line with the intuition from aging curves in football and other sports.
These vector fields can be used to create aging trajectories for different player types, which we demonstrate below. Darker points indicate the beginning of trajectories at age 20, while lighter points indicate trajectories approaching age 30. Interestingly, certain attractors appear as fixed points where different running back archetypes converge to end their careers. Many aging running backs, for example, end with slightly a negative first principal component value and slightly positive second principal component value, indicating a low-volume role restricted to the ground game.
Ultimately, aging trajectories can help better understand how players change in a more nuanced manner. However, looking at the graph above, the trajectories can clearly be overfit to specific running backs. This is especially true when dividing careers into discrete years; a continuous path through the vector field may be better at predicting a running back’s true trajectory. Future adjustments such as larger sample size and better smoothing of the learned vector field could provide more realistic estimates for player development.
Feature image from NFL.com
