July 25, 2025
Effort is intangible and subjective
Currently no objective measure of effort exists in the NFL
Idea: previous research has explored professional soccer players reaching theoretical max acceleration capacity1
Goals:
Improve estimation of individual acceleration-speed (A-S) profiles using statistical models
Assess how frequently players operate near or exceed their physical limits as a proxy for effort
Game, play, player data from Weeks 1-9: 136 games
Player tracking data: each observation is a frame in 10 fps
Pre-processing:
Filtered to running plays where a running back (RB) is the ball carrier
Trimmed each play to frames between handoff and end of play
Derived directional acceleration
Gives no credit to low speed points
Unrealistic theoretical max speeds - not comparable to soccer
Penalizes players for being athletic
Does not differentiate between acceleration and deceleration
Average frame-level effort for each player
\[ \Psi_i = \begin{cases} \frac{1}{1+d_i} & a_i\geq 0 \\ \frac{1}{2}\cdot\frac{1}{1+d_i} & a_i<0 \end{cases} \quad \implies \quad \text{Effort} = \frac{\sum_{i=1}^n \Psi}{n} \]
Conclusions
A-S-based effort alone does not explain performance
Metric quantifies how often a player comes to his acceleration frontier
Limitations
Metric does not fully account for game context
Personalized A-S curves make cross-player comparison difficult
Future work
Applying metrics to wide receivers
Another way to validate effort metrics?
EPA model: random forest using predictors available only at time of handoff
Game context
Home field advantage
Quarter
Down
Score differential
RB characteristics
Speed
Directional acceleration
Weight
Positional coordinates of RB on field
Nearest defender characteristics
Speed
Directional acceleration
Angle with the RB
Distance to RB
Play context
Yards to go to a first down
Yards to go to the endzone
Number of blockers in front of the RB
Number of defenders within 5 yards of the RB
Offensive formation
Run concept