Descriptive Model of Injury Duration in the NFL
Introduction
The surge in sports-related injuries, particularly lower-leg injuries, has raised questions about the safety and long-term health implications for athletes. In the NFL, where players endure intense physical demands, these injuries not only impact individual careers but also influence team performance and league dynamics. Alarmingly, recent studies and anecdotal evidence point to a potential culprit: the increasing use of artificial turf in professional stadiums. Artificial turf, while cost-effective and durable, has been criticized for its harder surface and reduced shock absorption compared to natural grass, potentially contributing to a heightened risk of lower-body injuries. This issue has captured widespread attention, fueling debates about player safety and the evolving priorities of modern sports organizations.
Understanding the factors that influence injury duration is essential to addressing these concerns. This study seeks to identify the key variables—such as playing surface, player-specific characteristics, and game conditions—that determine the number of weeks NFL players miss due to injury. By rigorously analyzing injury data, this research aims to shed light on the role artificial turf may play in prolonging recovery times while uncovering other critical influences on player wellness. Given the NFL’s commitment to prioritizing player health, the findings from this investigation could inform policy decisions regarding stadium infrastructure, training practices, and injury prevention strategies.
Data
The data for this study were derived from the rosters, injuries, schedules, snap counts, and players tables in the “NFL Verse” R Package (index) . The rosters & players tables offers detailed player metadata, including physical attributes like height and weight, as well as career-specific details like rookie year and draft position. The dependent variable, weeks included on the NFL’s Official Injury Report, was sourced from the injuries table. Snap counts were aggregated from the snap_counts table, providing a breakdown of players’ contributions across offensive, defensive, and special teams plays. The schedules table suppied game-level metadata, including game conditions (surface type, temperature, wind), team performance, and home versus away dynamics. These tables were combined using their composite keys into a single table, with each row representing a single player’s season-wide metrics. See the below table for the full list of variables analyzed in this study.
| Variable | Description |
|---|---|
| [Dependent] weeks_on_injury_report | Number of weeks which the player appeared on the NFL’s injury report |
| age_at_beginning_of_year | Age on January 1st of the given season |
| height, weight | Reported height & weight of player |
| rookie_year, entry_year | Year the player entered the NFL |
| team | A team the player played on during the given season. |
| position | A position the player played during the season |
| jersey_number | The most frequent jersey number the payer wore during the season |
| count_home_games, count_away_games | Number of games the player was on the roster for, split by home & away |
| snaps_on_grass_surface, snaps_on_synthetic_surface | Number of snaps the player played on natural grass vs synthetic turf |
| snaps_indoors, snaps_outdoors | Number of snaps played in indoor stadiums vs outdoor stadiums |
| offensive_snaps, defensive_snaps, special_teams_snaps | Number of snaps played, broken down by offensive snaps, defensive snaps, and special teams snaps |
| avg_game_temp, avg_wind | The average temperature and wind speed of the player’s games that season |
It is important to note that, while weeks_on_injury_report is a proxy for weeks missed in a season due to injury, there is a key difference. A when a player has an injury which is anticipated to last longer than 4 weeks, they are placed on the “Injury Reserve” and, as such, are not reported on NFL’s injury report. This means that time missed due to particularly devastating injures will not be captured in the weeks_on_injury_report variable.
There were null values and imperfect joins in our data set, which were treated either by omission (assume missing completely at random), or by imputation. See a the data issues and mitigation below.
To limit researcher degrees of freedom, this study is split into an exploration data-set, which contains 1,582 rows of player metrics for the 2022 NFL season, and a confirmation data-set, which contains 1,654 rows of player metrics for the 2023 NFL season.
Visualizations
Correlation Plot
From the coorelation plot we find that, dispite being reported seperately in our data, Rookie Year & Entry Year are perfectly correlated. Age is very highly inversely coorelated with Rookie Year and Entry Year, and thus we will use Age to represent the idea of age & years played in our study, and omit Rookie Year and Entry Year. Total Snaps is highly correlated with the Count Home & Away Games Count of Home & Away Games are highly correlated with each other. As a result, we will omit Home Games & Away Games from our study and use Total Snaps (and it’s derivations) to represent the idea of play time. While it is interesting to see jersey number, when treated like a metric (though it is more appropriately represented as a category), is moderately correlated with height and weight, likely due to the fact that there are ranges of jersey numbers for a given position, and different body types are more prevalent in different positions. Jersey number, however, will be omitted from this study as it has little descriptive value.
Variable’s Distributions
By viewing the distributions of the variables for this study, we find that our dependent variable, weeks_on_injury_report, is right skewed with what appears to be an exponential distribution. Other interesting findings include all snap variables appear to have exponential distributions as well. Height, weight, and age have roughly normal distributions with some skew
Modeling
Assumptions: Large Sample Ordinary Least Squares
As we have over 1,000 samples in both our exploration and confirmation data-sets, we will use the Large Sample OLS assumptions and assess significance of our confirmation data-set using robust standard errors.
Independent & Identically Distributed
The independence assumption in linear regression states that the observations (i.e., injury duration data for each player) are independent of each other. This means that the injury duration of one player should not influence or be influenced by another player’s injury duration. Independence may be violated as, for example, if a starting quarterback is injured for long duration, then the secondary quarterback is more likely to experience injury, due to the fact that they will play more snaps thus exposing themselves to more opportunities to become injured. We can assume, based on the fact that each sample represents an NFL player, and our population is NFL players, that our samples are identically distributed. Despite the aforementioned potential violation of independence, this model likely still has descriptive value.
A Unique Best Linear Predictor Exists
Histograms do not indicate infinite variance in any of the variables in this study, so there is finite covariance and therefore a BLP exists. There are multiple variables which are potentially co linear, for example total_snaps = snaps_indoors + snaps_outdoors. When modeling, we will omit one of the colinear variables from the model to ensure a unique BLP exists.
Model Specification
Our strategy for model specification is the following, we will start with a coefficient-only model & determine which transform of y captures the most variance by R2 and adjusted R2 values. From there, we will incrementally add features, assessing the R2 and adjusted R2 for non-trivial improvements. Features which improve the model based on these metrics will be kept, features which do not will be omitted from future models. The final model will be validated using the 2023 season’s data for confirmation, and features will be tested for significance using the robust standard error.
For these models, given the weeks_missed_due_to_injury exponential distribution, we will use the log of weeks_missed_due_to_injury as our dependent variable. Note that not all model comparisons will be displayed in this report due to page limitations, however the code is available (hidden) in the .rmd file.
##
## ================================================================================================
## Dependent variable:
## ---------------------------------------------------------------------
## log_weeks_on_injury_report
## (1) (2) (3)
## ------------------------------------------------------------------------------------------------
## total_snaps 0.001***
## (0.00004)
##
## snaps_on_grass_surface 0.001***
## (0.0001)
##
## snaps_on_synthetic_surface 0.001***
## (0.0001)
##
## Constant 0.674*** 0.192*** 0.194***
## (0.018) (0.024) (0.024)
##
## ------------------------------------------------------------------------------------------------
## Observations 1,582 1,582 1,582
## R2 0.000 0.297 0.302
## Adjusted R2 0.000 0.296 0.301
## Residual Std. Error 0.723 (df = 1581) 0.607 (df = 1580) 0.605 (df = 1579)
## F Statistic 666.165*** (df = 1; 1580) 341.553*** (df = 2; 1579)
## ================================================================================================
## Note: *p<0.1; **p<0.05; ***p<0.01We find that total snaps (2) describes more variance than the intercept-only model (1). Knowing whither the snaps occurred on grass or synthetic does not explain sufficiently more variance than simply modeling for total snaps (2), as evidence by the minor increase in R2 and adjusted R2, and the reduction in the F-statistic between model (2) and (3). Even if we accepted the small increase of R2 and adjusted R2 as sufficient, fact that the calculated coefficients are the same for total_snaps = snaps_on_grass_surface = snaps_on_synthetic_surface = 0.001 indicates that breaking down snap count by surface type provides no additional descriptive value than total_snaps alone.
This same analysis was done with breakdowns by offense/defense/special teams snaps, and by snaps indoors vs outdoors, we find the same minuscule increase in R2 and adjusted R2, and equivalent values of coefficient, as such they will not be considered in future models. The addition of age into our model moderately improves R2 and adjusted R2, indicating more variance is described when age is included in our model. The inclusion of weight & height reduces our adjusted R2, providing evidence that these variables are primarily capturing noise and should be omitted from future models.
When position is added to the total_snaps + age model, the R2 and adjusted R2 further increases, indicating more variance has been captured. Finally, when average wind and average game temps are added, there is a reduction in R2 while adjusted R2 remains constant.
Model Results
We have determined via our exploration that the most descriptive features to predict the log of weeks on injury report are: Total Snaps, Age at the Beginning of the Year, and Position. Finally, we will run this model using our confirmation set, the 2023 season’s data, and validate whither the selected features are still significant based on their robust standard errors. We will use a significance level of 0.05 to determine significance.
##
## t test of coefficients:
##
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.8041e-01 1.4667e-01 -2.5936 0.009582 **
## total_snaps 1.1296e-03 4.7307e-05 23.8775 < 2.2e-16 ***
## age_at_beginning_of_year 2.7398e-02 5.6446e-03 4.8537 1.327e-06 ***
## positionDB -1.5896e-01 5.0505e-02 -3.1474 0.001677 **
## positionDL -1.0594e-01 5.6473e-02 -1.8759 0.060840 .
## positionK -2.3860e-01 9.2225e-02 -2.5872 0.009762 **
## positionLB -1.4667e-01 5.2353e-02 -2.8015 0.005146 **
## positionLS -4.1603e-01 8.3321e-02 -4.9931 6.575e-07 ***
## positionP -7.4622e-02 8.9014e-02 -0.8383 0.401972
## positionQB -3.6162e-01 7.7736e-02 -4.6519 3.552e-06 ***
## positionRB 2.9161e-02 6.5355e-02 0.4462 0.655514
## positionTE -1.1899e-01 6.4066e-02 -1.8573 0.063454 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Interpretation
In the case of a log-linear model like ours, a small change in the independent variable leads to a percentage change in the dependent variable. Note that the reference category for position is wide receiver, and as such the intercepts for all positions must be compared against wide receivers.
| Predictor | Intercept | Interpretation (Everything else held equal…) |
| total_snaps | 0.0011 | an increase of 1 snap corresponds to an approximate 0.113% increase in weeks on the injury report. |
| age_at_beginning_of_year | 0.0274 | for each year of age, the weeks on the injury report increase by about 2.74% |
| positionDB | -0.1590 | players in the Defensive Back position are expected to spend approximately 15.90% less time on the injury report compared to wide recievers |
| positionDL | -0.1059 | there is not sufficient evidence to indicate that Defensive Linemen and Wide Recievers experience a different ammounts of time on the injury report |
| positionK | -0.2386 | players in the Kicker position are expected to spend approximately 23.86% less time on the injury report compared to wide recievers |
| positionLB | -0.1467 | players in the Line Backer position are expected to spend approximately 14.67% less time on the injury report compared to wide recievers |
| positionLS | -0.4160 | players in the Long Snapper position are expected to spend approximately 41.60% less time on the injury report compared to wide recievers |
| positionP | -0.0746 | there is not sufficient evidence to indicate that Punters and Wide Recievers experience a different ammounts of time on the injury report |
| positionQB | -0.3616 | players in the Quarterback position are expected to spend approximately 36.16% less time on the injury report compared to wide recievers |
| positionRB | 0.0292 | there is not sufficient evidence to indicate that Running Backs and Wide Recievers experience a different ammounts of time on the injury report |
| positionTE | -0.1190 | there is not sufficient evidence to indicate that Tight Ends and Wide Recievers experience a different ammounts of time on the injury report |
In conclusion, for the NFL’s 2023 season we found that the older players are, and the more snaps players played, the longer you are likely to spend on the injury report. We found that, for the same age and number of snaps, Running Backs and Wide Receivers will spend the most weeks on the injury report, while Quarterbacks and Long Snappers will spend the least number of weeks on the injury report.
While we did not confirm our initial suspicion that playing more snaps on artificial turf leads to an increased frequency of injury, this could be because of a couple of factors. (1) As discussed in the data section, long-duration injuries, such as ACL tear, will put players on Injury Reserve, omitting them from the NFL Injury Report which this model predicts. (2) This model included all injury types, upper and lower body, where upper body injury likelihood and duration, we suspect, are not impacted by the playing surface. For a future iteration of this study, the injuries considered should be limited to lower body injuries, and the Injury Reserve should be included for a more accurate proxy for “weeks missed due to injury.”