Penalty Yards Awarded for Defensive Pass Interference in the NFL are Unjustified

I watch way too much college football, but I have a limited interest in the NFL. I will watch NFL games featuring Lamar Jackson, Deshaun Watson, the Jaguars with Fournette and Josh Allen, and the Chief’s offense—when those games are actually available in my viewing area. Blackouts are one of myriad reasons a person might develop a distaste for the NFL (e.g., stadium costs, handling of violence against women, ticket costs, nonguaranteed contracts, obstructing the publishing of concussion problems, treatment of retired players, and Roger Goodell). In full disclosure, I loathe how defensive pass interference (DPI) penalties are enforced in the NFL, the topic of this post. Regardless, I am specifically curious if the yardage granted by an enforced DPI call in the NFL is justifiable statistically.  

Longtime POTH readers know I am an aspiring defensive back. Hence, I will typically be biased against many DPI calls, but I recognize that DPI does genuinely occur. My concern about DPI enforcement in the NFL is that it is a spot foul. The offensive team is awarded a first down at the yard line where the DPI was committed. It thus assumes that the receiver would have caught the pass were it not for the DPI. A spot foul 10 or 15 yards down field seems reasonable to me, but 30 or 40 yards seems like far too much field position to simply gift the offense on what may or may not have been a catch if there were no PI. In other words, it is unfair to award the offense, say, 40 yards because of DPI given that one of several events could have led to an incompletion if there were not DPI. My thesis is that NFL DPI penalty yardage becomes increasingly unjustifiable as the spot of the foul gets farther from the line of scrimmage. But, I don’t know that and that’s why I’m exploring the matter. 

any act by a player more than one yard beyond the line of scrimmage that significantly hinders an eligible player’s opportunity to catch the ball

I needed play-by-play data. It had to include depth of target, the distance from the line of scrimmage to the yard line where the pass is caught or comes closest to the targeted receiver. I found nothing in the open-source arena but ArmchairAnalysis does provide a sample of their thorough NFL charting data, which I used. Specifically, it is a sample of about 4013 plays from two weeks in the 2019 NFL season. Of those, about 2430 are passing plays. I removed 82 throwaways, 157 sacks, and 11 spiked balls, because these events preclude a pass to a receiver.  This left 2180 passing plays eligible for analysis. 

First, I compared the completion % of the 2273 passing plays that were not sacks, which is 65%, to the NFL average % for all other weeks in 2019 (through week 12), which is 63.8%.  This way we can assess if this sample of passes is somehow dissimilar from passes in the remainder of the season. It was not, χ² = 1.49, p = 0.22, 95% CI [0.63, 0.67]. 

Figure 1. Top panel shows distribution of completions (magenta) and incompletions (brown) by depth of target. Bottom panel shows completion % by depth of target (dotted black) and estimated probability of completion by depth of target (green).

Figure 1 shows the raw completion percentage by depth of target (dotted black) and the estimated probability of a completion when accounting for random variance due to defense and targeted receiver (green).¹ The farther a targeted receiver is from the line of scrimmage, the less likely the pass is to be completed. Indeed, this provides some support for my thesis that awarding a first down at the spot of the DPI is increasingly unjustifiable when the depth of target is farther and farther from the line of scrimmage. This is because passes targeted farther down the field are simply less likely to be completed.

Figure 2. Expected yards per pass attempt by depth of target (dotted black) and the expected yards when controlling for random variance due to defense and offense units (orange).

Another way to frame the issue is in terms of yards per attempt (Y/A). That is, how many receiving yards are expected on a pass to a given depth of target. Y/A is a widely used measure of passing efficiency. Figure 2 shows the Y/A by depth of target (dotted black) and the expected Y/A when accounting for random variance due to defense and offense (orange).  This provides additional support for my thesis that awarding a spot foul for DPI is increasingly unwarranted when the DPI is farther from the line of scrimmage. For example, a target of 32 yards down field is expected to gain only 15.9 yards. This might seem odd because 15.9 is less than 32, but Y/A accounts for the probability of the pass being completed. Again, passes target farther down field are less likely to be caught thus a spot foul is less justifiable.

Summarily, this exploratory post yields evidence suggesting that the penalty yards awarded for DPI in the NFL are unwarranted. Although some random variance was accounted for in the models, the major shortcoming is that other factors that affect completion percentage and receiving yards were not accounted for in the analysis. This includes factors such as QB pressure, pass coverage, field position, score differential, and others. Nevertheless, the results demonstrate that, by being a spot foul, the penalty yards awarded to the offense following a DPI (with an uncaught pass) in the NFL are incommensurate with the yardage that would be expected given the depth of target. We here at POTH have no delusions that the enforcement of penalty yardage for DPI will be subject to change. Likewise, we are not anarchists; we respect the game and know that parameters are needed to standardize competition. However, we do feel it necessary to present evidence that directly contradicts any notion of rules designed to ensure a fair game that is decided on the field, by the players.

1 Computed using GLMM specifying a binomial distribution. Depth of Target is fixed effect, with defense and targeted receiver as random effects. QB and offense were considered as random effects but were essentially null and excluded from the model. The model explained about 12% of the variance in completion %. Depth of Target was significant, reducing the log odds of completion by -0.059 for each one yard from the line of scrimmage.

2 Computed using LMM. Simple linear regression had R2 = 0.108 and a smooth regression line had R2 = 0.11, so I used a linear model for simplicity. Depth of Target is fixed effect, with defense and offense as random effects, each with a random intercept for depth of target. The model explained about 18.4% of the variance in A/Y. Depth of target was significant, increasing the A/Y by about 1.03 yards for every three yards of depth of target.

Hand Size, Arm Length, and Drop Rate among NFL Receivers

Although it is not evident here, I have been exploring the influence of physical attributes on in-game performance in gridiron football. Physical attributes include anthropometrics such as height and weight as well as assessments of athleticism such as the 40-yard dash and standing vertical jump. In this post I focus on hand size and drop rates in NFL receivers. By receivers I refer broadly to any eligible pass catcher; specifically, WRs, TEs, and RBs. 

At least one other author has examined the influence of hand size on WR performance. Joe Redemann at numberFire explored relationships between hand size, several standard statistics, and “a player’s contribution to his team”, NEP, across multiple seasons. A mild relationship between hand size and catch rate (receptions / targets rate) was discernible (r = .17). Ultimately, Redemann demonstrated that the performance of elite WRs was relatively unrelated to hand size whereas a stronger—but still mild—relationship evidenced between the performance of ordinary WRs and hand size. 

We should expect then to find that larger hands predict in fewer drops. We should also expect a minimal reduction in drops offered by larger hands. We shall extend the analysis by including TEs and RBs in addition to WRs. 

NFL Combine data were procured from NFL Savant and passes dropped were extracted from Sporting Charts. Drop data were gathered for WRs, TEs, and RBs from the 2009-15 seasons. Combining Combine and drop data yielded 604 player-seasons from 238 players without checking for spelling inconsistencies between the two data sets. As regular readers know, I am lazy, so I pressed onward with this sample. Player height and arm length were included because of my intuition that doing so would better isolate the effect, if any, of hand size by isolating the effect of atypically large hands given medium or small stature. 

Table 1. Targets, Drops, and Anthropometrics for NFL WRs, TEs, and RBs, 2009-15

	Totals			Medians
	Seasons	≥ Median Targets	Players	Handsize	Arm Length	Height	Drop %	Targets
RB	123	65	63	9.25	31	71	0.051	28
TE	103	52	42	9.875	33.125	77	0.046	35
WR	378	194	133	9.25	32.1	73	0.043	67
TOTAL	604	311	238
MEDIAN				9.375	32	73	0.045	53

Table 1 displays basic information about the players within our sample. Medially, TEs presented with the largest hands and, for the included seasons, WRs dropped fewer passes while being targeted more frequently. Thus, position should be accounted for in the analysis. Also, we will need to account for season to season variability within players. 

I constructed several models. For each model, the count of drops for each player-season was the dependent variable (actually, the rate of drops, or, drops / targets). Hand size, arm length, height, and position were predictor, independent, or explanatory variables—whichever jargon you prefer. Players were included as a random effect to account for each player’s variability in drops between seasons. Random effect also means that the models are constructed accounting for the differences between players that we are not measuring in this analysis; for instance, a factor as relevant but complex as coverages faced or as esoteric as blood type. 

Three models were constructed. Excluded here, there is a table at the bottom of the page with pertinent model data.

• The first model included all 604 player seasons. In short, increased hand size predicted fewer drops; being a WR decreased drops.
• The second model included 311 player seasons from 127 players who accumulated ≥ median targets at their positions. Again, larger hands and being WRs predicted fewer drops. Interestingly, greater arm length predicted greater drops.
• In the third model, I included all 604 player seasons while accounting for whether ≥ median targets were accumulated in a given player-season (via dummy coding). Again, being a WR and having larger hands predicted fewer drops.
  

Figure 1. Expected Drops by hand size for NFL receivers.

For convenience, the p-values for hand size in models 1, 2, and 3 were .07, .05, and .10, respectively. So, the statistical significance of hand size in explaining drop rates hovers slightly above the conventional cutoff of .05.  But how does hand size actually impact drops? Probably minimally, as can be seen in Figure 1. Arm length and height held constant, for WRs, 3 inches of greater hand size equates to about 1 less drop per season; for RBs and TEs 3 inches of greater hand size equates to about half a drop per season.

Why though would greater arm length predict more dropped passes in the group of receivers targeted at or above the median? It might be a spurious finding, but, perhaps players with longer arms drop errant passes at the fringes of their catch radii, passes beyond the range of players with shorter arms. 

Alternatively, RBs are known to exhibit the highest drop rate. Likewise, consider that RBs are often catching passes coming out of the backfield where more defenders may be lurking; perhaps RBs are targeted with more less accurate passes due to their being a check down or hot receiver targeted when the QB is hurried; or by releasing from his blocking assignment into the flats, knowing a pass is coming, and having to reorient his body to catch. The process of reorienting with multiple proximal defenders might be more difficult for larger RBs, with longer arms. Unsurprisingly then, within each position, only for RBs is the raw correlation between drop rate and arm length appreciable—although this may be the result of small sample sizes:

• WR: r = .014, p = .805, n = 315
• TE: r = .133, p = .311, n = 60
• RB: r = .369, p = .004, n = 58
  

Summarily, the effects of hand size and subsequently arm length on drop rates in NFL WRs, TEs, and RBs were examined in this analysis. Although the effect of hand size was in a significant range, the ecological impact of hand size is irresolute because, with all else held constant, 1 inch of hand size was worth about 1/3 of a drop per season for WRs. Additionally, if you are managing NFL offensive personnel and you rely on RBs in your passing game, the present results suggest it may be advisable to cultivate a smaller RB with shorter arms to specialize in pass catching.

Technical supplement. For GLMMs 1-3

Variable	Fixed-Effects
	Estimate	SE	z	p
Model 1: AIC = 2216.4		Player Var & SD = .039, 0.197
Intercept	-2.940	0.085	-34.400	0.000
Hand	-0.065	0.036	-1.790	0.073
Height	-0.002	0.056	-0.030	0.978
Arm	0.067	0.051	1.330	0.185
TE	-0.113	0.142	-0.800	0.425
WR	-0.172	0.093	-1.840	0.066
Model 2: AIC = 1298		Player VAR & SD = .037, 0.193
Intercept	-2.974	0.101	-29.350	0.000
Hand	-0.0840	0.0422	-1.990	0.047
Height	0.112	0.064	1.760	0.079
Arm	0.028	0.067	0.420	0.674
TE	-0.239	0.166	-1.440	0.149
WR	-0.199	0.111	-1.790	0.074
Model 3: AIC = 2207.2		Player Var & SD = .039, 0.197
Intercept	-2.786	0.094	-29.570	0.000
Hand	-0.058	0.035	-1.670	0.095
Height	0.070	0.049	1.430	0.153
Arm	0.003	0.054	0.050	0.960
≥ Median Targets	-0.199	0.059	-3.410	0.001
TE	-0.131	0.137	-0.960	0.340
WR	-0.189	0.091	-2.090	0.036

Note: R v3.3.1 console used for analysis. The glmer function within the lme4 package was employed in the GLMM. A Poisson distribution was specified; a negative binomial distribution yielded essentially identical results but the models did not converge. Data and R code available upon request, of course.