This was presented at CASSIS 2018.

1. The Passing Skill Curve in the
NFL
@kpelechrinis
The Cascadia Symposium on Statistics in Sports
August, 2018

2. Pass-First League
• NFL is a clearly pass-first league today
• Passing is overall more efficient
• During the 2014-2016 regular season:
• EPA/passing play: 0.25
• EPA/rushing play: 0.06
Winston-Cabot-Sagarin model

3. Pass-First League
• NFL is a clearly pass-first league today
• Passing is overall more efficient
• During the 2014-2016 regular season:
• EPA/passing play: 0.25
• EPA/rushing play: 0.06
Winston-Cabot-Sagarin model
4x more efficient

4. Pass-First League
• NFL is a clearly pass-first league today
• Passing is overall more efficient
• During the 2014-2016 regular season:
• EPA/passing play: 0.25
• EPA/rushing play: 0.06
Winston-Cabot-Sagarin model
4x more efficient
Just pass all the time

5. Pass-First League
• NFL is a clearly pass-first league today
• Passing is overall more efficient
• During the 2014-2016 regular season:
• EPA/passing play: 0.25
• EPA/rushing play: 0.06
Winston-Cabot-Sagarin model
4x more efficient
Just pass all the time

6. Everything in moderation!
Cleobulus of Lindos, 6th century AD

7. Passing Skill Curves
• Inspired by Dean Oliver’s skill curves for basketball players
• Efficiency – vs – utilization
• Efficiency is a monotonically decreasing function of utilization
B. Skinner, “The Price of Anarchy in Basketball”, JQAS 6:1, 2010

8. Passing Skill Curves
• NFL play-by-play data from 2014-2016 seasons
• Passing utilization: fraction of offensive passing snaps over all offensive
snaps
• We exclude punts, field goals and kickoffs
• Passing efficiency: mean expected points added per passing (per team/game)
• WCS model adjusted for opponent
• K. Pelechrinis, W. Winston, J. Sagarin, “Evaluating NFL plays: Expected Points Adjusted for
Schedule” (stop by the poster)

9. ρ=-0.35 (p-value < 0.001)

10. Passing Skill Curves
• The above controls for the passing defense (through the adjustment of
expected points)
• However, the relationship does not control for:
• Overall passing ability
• Overall rushing ability
• Use a regression model

11. Passing Skill Curves
• Dependent variable: Mean πEPA,i per passing play in game i
• Independent variables
• Passing utilization ui
• Offense’s passing rating πrtg
• Mean rushing EPA per play ri
• Interaction term between ui and ri

12. • Passing efficiency is still negatively correlated with utilization
• The extent of this correlation is tied to the team’s rushing performance
• The total utilization-based component for the efficiency is then: 𝜋"#$
%
=
− 0.85 + 0.67 ⋅ 𝑟1

13. Rushing and Passing Interactions
• Basically if a team runs the ball well (larger ri), the relationship between
passing efficiency and utilization is less negative
• For example, with r=0.65 (the maximum rush EPA observed in our dataset in a game),
the corresponding total regression coefficient is -0.42
• For r = -0.73 (the minimum rush EPA observed in our dataset in a game), the
corresponding total regression coefficient is -1.34

14. How much should we run?
• Obviously a complex question
• However, passing in 100% of the snaps is certainly not going to cut it
• Even though passing efficiency can still be higher than rushing efficiency when u à 1
• The objective of a team is to have the appropriate mix of passing and
rushing plays that maximizes the efficiency on a per-play basis
• Regardless if this play is a pass or a run
max
%∈[8,:]
𝑢 ⋅ 𝜋"#$ + 1 − 𝑢 ⋅ 𝑟
𝑤ℎ𝑒𝑟𝑒, 𝜋"#$ = 0.81 − 0.85 ⋅ 𝑢 + 0.99 ⋅ 𝜋BCD − 0.59 ⋅ 𝑟 + 0.67 ⋅ 𝑟 ⋅ 𝑢

15. EPA(u*) = 0.22
EPA(1) = -0.03
EPA(0.75) = 0.14
Average passing
Great passing
EPA(u*) = 0.34
EPA(1) = 0.21
EPA(0.75) = 0.31
Bad passing
EPA(u*) = 0.13
EPA(1) = -0.28
EPA(0.75) = -0.05

16. Reverse Causality
• Running more does not necessarily cause
passing be more efficient
• Teams that trail in the fourth quarter might
turn to passing à bias
• We have repeated the same analysis using
the utilization over the first three quarters
only
• Still negative correlation (slightly weaker)

17. 0.00
0.25
0.50
0.75
1.00
-1.0 -0.5 0.0 0.5 1.0
Expected Points Added per Rush
OptimalPassingUtilizationu*
p -0.25 0 0.25
EPA(u*) = 0.19
EPA(1) = 0.08
EPA(0.75) = 0.15
Average passing
Great passing
EPA(u*) = 0.36
EPA(1) = 0.31
EPA(0.75) = 0.35
Bad passing
EPA(u*) = 0.09
EPA(1) = -0.16
EPA(0.75) = -0.02

18. Other EPA models
• One of the problems with expected point
models is that there are several different
ones
• Repeated the same analysis with nflWAR
(install nflscrapR if by any strange chance
you haven’t yet!)

19. Where do we go from here?
• There is more to the story than just that passing is more efficient
• We are confined by what we observe and this can lead us to make unsupported
conclusions
• Sometimes extrapolations beyond the observed ranges can be tricky and dangerous
• This analysis tells us that there some interactions between passing and
rushing but not why and what is the underlying mechanism
• We have treated rushing as constant
• Rushing efficiency (or lack thereof) might also be a function of utilization