# Reducing Concussion Rates on Punts by Incentivizing Fewer Punt Returns

We analyze the differences in concussion rates between returned and not-returned punts. We show that the **concussion rate on returned punts is 7 times higher than on non-returned punts**. 
Because of this, **we propose two rule changes that incentive teams to reduce the number of returned punts**. 

(1) If the returner completes a “fair catch”, the ball is spotted 5 yards closer to the kicking team’s end zone (favors return team). 

(2) If a ball is punted out-of-bounds on the fly, the ball is spotted 5 yards farther downfield (or half the distance to the goal of inside the 10 yard line; favors punt team). 

These rules incentivize both the punt and return teams to behave in ways that will reduce the number of returned punts, without requiring any fundamental changes in the game (e.g. blocking, tackling, formations, etc.). 

We analyze their impact on the game, and *we provide evidence (via a simulation study) that they will reduce concussion rates*. Our simulations indicate that even with **conservative assumptions, the concussion rate on punts can be reduced by up to 37% under our proposed rule changes**. 

Our proposals are in line with prior league rule changes to incentive fewer kickoff returns (move kickoff location up 5 yards, move touchback spot up 5 yards). Additionally, they are extremely simple to implement, requiring minimal education of league, team, and player personnel.


## How our Proposals Reduce Concussions 

The goal of our proposed differences is to incentivize teams to not return punts, as we have shown through the data, that returned punts have 7 times the concussion rate of non-returned punts (see following figures created through notebook kernel: https://www.kaggle.com/kpelechrinis/the-yinzers-base). 

![Image](http://www.pitt.edu/~kpele/concussions-rate-aggr.jpg)

![Image](http://www.pitt.edu/~kpele/concussions-rates-nfl.jpg)


This incentive be achieved by returning teams benefiting from calling more fair catches, and kicking teams benefiting from punting out of bounds. 
We show through analysis of Win Probability Added (see kernel: https://www.kaggle.com/ryurko21/the-yinzers-win-probability-impact-of-rules), that punting teams gain win probability added by punting the ball out of bounds under rule #2, while return teams gains win probability added from completing a fair catch under rule #1. 
Furthermore, under rule #2 we expect more punts to be punted towards the sideline. 
We have modeled (see Figure 3 in notebook kernel: https://www.kaggle.com/kpelechrinis/the-yinzers-base) the concussion likelihood of a returned punt as a function of the distance from the closest sideline that the punt returner received the punt, and our results indicate that this probability reduces as the punt is received closer to the sideline. 
Therefore, even if a punt is attempted to be returned, under rule #2 the punts are expected to be received closer to the sidelines on average and hence, exhibit less likelihood of a concussion occuring. 





## Concussion Rates as a Function of the Distance from the Closest Sideline 

In order to find the relationship between concussion rates on returned punts and the distance between the location where the punt was received and the sideline we built a logistic regression model (kernel: https://www.kaggle.com/kpelechrinis/the-yinzers-base). 
Our response variable $Y$ is binary and captures whether there is a concussion observed during a specific punt return play or not as a function of a set of covariates $\mathbf{x}$ (i.e., $Pr[Y=1|\mathbf{x}]=\dfrac{1}{1+e^{-\mathbf{a}^T\cdot \mathbf{x}}}$). 
We use a single covariate for the model, namely, the distance between the location where the punt was received and the closest sideline. 
The latter is calculated using the NGS data provided and the following code (see kernel: https://www.kaggle.com/kpelechrinis/the-yinzers-base). 
The logistic regression model trained (see following figure created through the notebook kernel: https://www.kaggle.com/kpelechrinis/the-yinzers-base) indicates that *the likelihood of a concussion for a punt return that was received closer to the sideline is smaller as compared to the same likelihood when the punt is received closer to the middle of the field*. 

![Image](http://www.pitt.edu/~kpele/sideline-d-concussion.jpg)

## Impact of Rule Change on Win Probability

By using a win probability model we developed (details are provided at kernel: https://www.kaggle.com/ryurko21/the-yinzers-win-probability-impact-of-rules), we analyze the impact of the rule changes on the win probability added from punts. 
As we can see in the figure below (for more details, analysis and results on win probability added see kernel: https://www.kaggle.com/ryurko21/the-yinzers-win-probability-impact-of-rules) the **proposed rule changes incentivize both teams to behave in ways that will reduce the number of returned punts**. 
In particular, the win probability added from a fair catch for the return team is positive from the perspective of the return team as compared to the current rule, while the win probability added from an out-of-bounds punt as compared to the current rules in negative from the perspective of the return team and hence, positive from the perspective of the kicking team.

![Image](http://www.pitt.edu/~kpele/wpa_distr_impact.jpeg)


Again, reducing returns punts translates to **reduced number of concussions sustained**. 


## Estimating the Impact of Rule Change on the Number of Concussions via Simulation

We are also interested in obtaining an estimate of the impact of our rule change on the number of concussions per 1,000 exposures (i.e., per 1,000 punts). 
The key parameters of the simulation attempt to capture the impact of the rule changes on the behavior of the teams. In particular, we consider two variables, namely, (i) the percentage reduction in returned punts $r$, and (ii) the average shift $s_d$ of the punts towards the sideline. 
For each pair of ($r, s_d$), we simulate punts and estimate the number of expected concussions per 1,000 exposures. 
During every simulation we first decide whether a punt will be returned or not based on the base rate of return in the data and the simulation parameter $r$. 
If a non-returned punt is simulated, a concussion is observed during this simulated punt with a probability equal to the concussion rate for non-returned punts. 
If the simulated punt is returned, we bootstrap the distances from the sideline from the NGS punt dataset and shift the punt according to the simulation parameter $s_d$. 
In particular, the shift is sampled from a normal distribution with average $s_d$ and standard deviation 7 (which is equal to the standard deviation of the distances from the sideline for the punts returned in the data). 
Once the distances are bootstrapped we use the logistic regression model to estimate the probability of a concussion for each returned simulated punt. 
The following figure provides a visualization of the simulation process, while the simulation code and results presented following are generated via kernel: https://www.kaggle.com/kpelechrinis/the-yinzers-base. 

![Image](http://www.pitt.edu/~kpele/simulation_machine.png)


In general, our results indicate that more punts towards the sideline (higher shift $s_d$) lead to fewer concussions per 1,000 exposures, while higher percentage decrease in the returned punts (higher $r$) further reduces the concussion rate. 
Our simulations consider a wide range of scenarios, from very conservative (blue line) to more optimistic (yellow line). 

![Image](http://www.pitt.edu/~kpele/injuries_per_1000punts.jpg)

While we cannot know how teams will react to these rule changes, the outlook is promising:

1. **With a conservative estimate of 5% reduction in returned punts and a slight shift of the punt of 2.5 yards towards the sideline, there would be a 7% reduction in the concussion rate**. 

2. **With a more optimistic estimate of a 20% reduction in returned punts and a large shift of the punt of 10 yards towards the sideline, there would be a 33% reduction in the concussion rate**.

If we also account for the inherent uncertainty of the estimated rates, **a conservative lower-bound on the concussion rate (r=5%) would lead to a 37% reduction of a concussion rate**. 

![Image](http://www.pitt.edu/~kpele/con_rates_bounds.jpg)


## Discussion

### Muffed punts

As with any change, unintented behaviors might be triggered. In our case, potential unintented consequences could include: 

1. The punt returner attempts to make a difficult fair catch to gain the 5-yards incentive, when under the current rules he would let the punt to land and be downed
2. The rate of muffed punts could increase

So we are interested in examining whether muffed punts have higher concussion rates. 
As we can see from the following figure (produced from notebook kernel: https://www.kaggle.com/kpelechrinis/the-yinzers-base) overall, muffed punts have high concussion rates, **but** only when the punt was NOT signaled for a fair catch! 

![Image](http://www.pitt.edu/~kpele/muffed_punts.jpg)

In particular, there were **no concussions sustained on muffed punts that were signaled for a fair catch** in the dataset.

### Will There be a Reduction in Punt Distance? 

We analyze this in detail in kernel: https://www.kaggle.com/ryurko21/the-yinzers-directional-analysis. 
In summary, we analyzed the punts based on their direction and distance from the line of scrimmage and we did not find any statistical evidence that there will be any drastic change. 
In particular, as we see below punts kicked on non-extreme angles have roughly equal net yards as those kicked straight ahead. 


![Image](http://www.pitt.edu/~kpele/punt_direction_length.jpeg)


### Why not Make Changes in the Touchbacks too? 

Touchbacks have low concussion rate as well. Incentivizing more touchbacks could potentially further reduce the overall concussion rates. 
However, **punts that can *become* touchbacks are fewer** (e.g., punts from a teams own 30 yard line cannot realisticall result to a touchback on a fly). 
Furthermore, adding a rule change for the touchbacks can **add confusion to fans, officials and the clubs**.

### Why Not Do Away With Punts Altogether? 

We are not in favor of drastic changes to the game. Our proposals are in line with prior changes to kickoff rules: we provide incentives to make punt plays safer, while avoiding eliminating punts altogether. 
If punts are eliminated, ball placement on a change of possession would be a contentious and challenging subject. And not to mention that punts are exciting plays that fans enjoy and can impact games (especially for Eagles fans: http://www.nfl.com/videos/nfl-game-highlights/09000d5d81d06fc3/Can-t-Miss-Play-Jackson-s-walk-off-punt-return)

# Summary/Conclusions

We provide data-driven evidence that: 

1. Almost all concussions on punts occur on returned punts
2. Concussions are less likely on returned punts received closer to the sideline
3. The punting team has incentive to punt the ball out-of-bounds
4. The return team has incentive to call for a fair catch

Therefore we expect:

1. More punts will be kicked out-of-bounds (and hence, fewer punt returns, and thus, fewer concussions)
2. More in-bounds punts will result in fair catches (and hence, fewer punt returns, and thus, fewer concussions)
3. More in-bounds punts will be kicked toward the sideline (and hence, reduces rate of concussions sustained on returned punts)
4. Our proposals are easy to understand and easy to implement (Minimal effort required to educate referees/officials, players, coaches and teams)
5. No fundamental changes to the game required (No confusing rule changes dictating} how players can tackle and limits fan confusion and negative sentiment towards rule changes)