Abstract
          NFL teams are constantly figuring out how to gain advantages, changing kickoff strategies over the years. Teams are debating whether they should take a touchback or return the ball. Research has shown that teams make strategic decisions on kickoffs based on the risk vs reward and how it is going to impact their field position. To research this I used NFL kickoff data from the past 10 years, created a model, and looked at probabilities. I found that there is a correlation between return yards and kickoff variables. Fumbles are more likely than touchdowns on a given kickoff and depending on the team, they must decide whether they want to take that risk.
Introduction
          The game of football is a sport that is evolving every single day. Teams are always looking at how to gain an advantage. Special teams and specifically kickoffs are a part of the game where teams have been investigating to try to get this step ahead. In the game of football, kick returns are pivotal parts of the game that can swing any game one way or another, having a significant impact on the course of a game. A successful kick return, either for a long return or a touchdown not only can provide a team with great starting position or points, but it can also give a team with a spark of energy. Kickoffs add an extra layer of strategy to the game and present teams with difficult decisions on how to approach them.
          I wanted to take a deeper dive into kickoffs and the optimal strategy after years of watching kickoffs and thinking if I would have made the decision that the teams did in those situations. The most recent case of this was in the 2022 AFC Divisional Playoff game between the Kansas City Chiefs and Buffalo Bills. This was an intense back-and-forth game that ended up going to overtime. After going up by 3 with 13 seconds left in the fourth quarter, the Bills decided to kick the ball out of the back of the endzone, not forcing the Chiefs to use any time off the clock. The Chiefs were able to get into field goal range and kick a game-tying field goal in those 13 seconds. The Chiefs ended up winning in overtime. After that, I wondered if the Bills should have made the Chiefs use time off the clock and if that would have changed the outcome of the game.
          For my project, I wanted to analyze NFL kickoffs to see whether return teams should return the ball or if they should opt for a touchback. Kickoffs are a very risk versus reward-play for both teams, so what do the numbers say about those risks versus rewards? I wanted to see how different factors such as where the returner starts his return and how far the ball is kicked impact return yardages.
Literature Review
          There have been different research and studies conducted on the NFL to identify the optimal actions for both teams during kickoffs. Multiple factors go into the decision of what to do during those events. Kickoffs, punts, and special teams in general have a big impact on the outcome of a football game. Maximizing these plays is of the utmost importance for teams. In the research done on this, there have been many common themes investigated such as strategy, field position, risk vs reward, rules, expected points, and more.
Strategy:
          Strategy is a big part of any play, especially on kickoffs and punts. Deciding what to do to put your team in the best spot. In an article by John D Urschel and Jun Zhuang in 2011, they take a deep dive into NFL coaches, their strategies on kickoffs, and how they affect the outcome of a game. They examined the choice of kicking an onside kick versus kicking it deep and the choice of taking a touchback or running it out. They found that during the 2009 season, there were 267 games and 2592 kickoffs. 18 of those kickoffs were returned for touchdowns. 98% of the kickoffs were deep and only 2% of them were onside kicks. The success rate of the surprise onside kicks was greater than expected but not statistically significant. They also investigated the average start position of the teams and their mean points scored on those possessions. In this paper, they found that coaching strategies on kickoffs were “inconsistent with the notion that coaches have neutral preferences over risk and loss” (Urschel and Zhuang 2011). 
           Teams all develop unique strategies to help them gain an edge. The Detroit Lions did this in 2019. A study by Jeremy Reisman in 2019 looked at kickoffs during the season. The Lions kicked it short on most kickoffs not wanting to give the 25 yards of field position. During one game against the New York Giants, they had seven kickoffs. They kicked it short all seven times and six out of the seven times the Giants were unable to return it to the 25-yard line. During the 2019 season, 29 of 32 NFL teams just kicked the ball out of the back of the endzone for touchbacks more than 50% of the time. During the period that this data was observed for the Detroit Lions, they ranked ninth in kick return average allowed (21.1) and they also gave their defense the third-best starting field position. 
           In a project done by Rahul Amara, Sohum Shah, and Rohit Tanikella in 2022, they looked at the numbers behind the strategies of punt returns. They first looked into misfielded punts. The facts that go into a misfielded punt are, the “motion of the returner prior to making the catch, the maximum height of the ball during the punt, the proximity of the nearest gunner” (Shah 2022). From their data, they saw “nearly 10 times more misfielded punts [occurred] on where a fair [catches were] not called” (Shah 2022). As can be imagined the gunners were much closer to the returner on misfielded punts than those that weren’t. The median distance the gunner was to the returner on a clean catch was 10.1 yards and the distance the gunner was to the returner on a misfielded punt was 5.6 yards. They also found that if a return becomes riskier, the chance of a misfield increases, and the yards gained on return decreases. In conclusion, they found that “If the returner is running to catch the punt, he should think first to call fair catch … If the nearest gunner is within 5 yards of [the returner they] should always call for a fair catch … It is ill advised to field a ball that [a returner] has to run across the field to catch” (Shah 2022).
           There are many other different strategies teams use on special teams to gain an advantage. An article by AFCA Insider in 2021 discusses the strategy of directional punting and how it is utilized. It breaks down the field into different zones and the strategy in the direction that the punter will kick the ball based on the position of the field. The punter is always trying to maximize their hangtime and distance. A lot of coaches will implement strategies like this and more. In an article by Jeffery May in 2022, he discussed a strategy that the Raiders implemented that had not been seen before. They would hold the ball on the kickoff tee to allow the kicker to get under the ball to get more hang time on their kicks. They believed this would help them gain an edge. Similarly, in two different articles discussing strategy, two hall-of-fame coaches, Bill Belichick and Bill Parcells were looked at. In football, it is hard to have two of the same situations. It is important to play to the teams’ strengths so if they aren’t good at a particular thing, they should try to hide it as much as possible. This applies to all areas of the game and can be important when looking at special teams, kickoffs, and punts (NBC Sports 2016). Situations in football games should be practiced every week. A team never knows when a certain situation is going to show up. It is so simple but teams forget to do this (Parcells 2022).
Field Position:
          In the game of football especially in the modern day, field position is something that is always discussed. Teams want to maximize their field position to score more points. This causes teams to shift their strategy to try and optimize their field position. Both the kicking team and the return team take this into account. In a 2016 article called Sending Kickoffs Through the Back of the End Zone is an Example of Poor Decision Making, Jonathan DeLong found that during the 2016 and 2017 seasons, 58.6% of the kickoffs were touchbacks. When the kicks were returned, 59.1% of the kicks were returned short of the 25-yard line. The average starting field position when the kicks were returned was at the 24.4-yard line. They found that from this data, a team has almost an equal chance of stopping the returner at or inside the 20 (34.3% of returns) as they did allowing them to pass the 25 (35.2% of returns). They also looked at the more extremes with teams having a 10.1% chance of stopping a runner inside the 15 and a 6.9% chance of letting them past the 40. The return team is also twice as likely to fumble the ball as they are to score a touchdown. In this paper, DeLong concluded that teams should kick it short.
          Penalties on plays have a big impact on field position as they can set a team back. On kickoffs and punts, this can especially hurt a team's ability to go down the field and score. In an article in 2020, Mark Simon looked into the impact of “lost yardage” on kickoffs and punts during NFL games. Lost yardage is essentially when a team returns a punt or kickoff but also commits a penalty on the return, therefore, bringing them back on the yardage that they gained from the return. It looked at the expected points from the return pre-penalty and post-penalty and how that impacted close games. It used data from the 2016 to 2018 seasons including the playoffs. This idea of “lost yardage” is big in kick returns because if teams constantly get penalties, it will put them in a bad field position to start their drives. If a team takes a touchback on the play instead, more than likely they are not going to be penalized and will just start with the given field position.
          In an article by Jack Brimberg, W. J. Hurley, and R.E. Johnson in 1999, they discuss the location problem of NFL punt returners and determine the optimal position of the returner for the most punts caught. They find that “Punts not caught result in an average loss of field position of 10-15 yards, depending on whether the playing surface is grass or artificial turf. Hence it is desirable to locate punt returners so they field the maximum number of punts.” (Brimberg 1999). Determining how and where to kick the ball has been looked at. In 2022, Claire B. Wichman modeled kickoffs and trajectories. She found that the kicks with the best results are kicked as close to the endzone as possible without going in and kicked high so that the ball is in the air long enough for the kicker’s teammates to travel down the field and stop the returner from advancing the ball.
Risk vs reward:
           Although kickoffs and punts don’t happen as much as offensive and defensive plays during the game, there is a lot of risk vs reward on kickoffs and punts. The momentum of the game can change on a single return. Players and coaches have to decide their chance of risk vs reward on every single kickoff and punt. In an article written by Football Outsiders in 2018, they looked at the risks and rewards of kickoff returns in the 2018 season. The study was inspired by Ty Montgomery who during the season on the Packers was told to take a touchback late in the game to give Aaron Rodgers a chance to drive the ball down the field for a game-winning score. Instead, Montgomery took the ball out of the endzone and fumbled the ball costing the Packers the game. The study tried to minimize the impact of penalties so they measured at different points to help take penalties out of the picture. During the 2018 season, the Jets led the league in average return yardage with 31.3 yards. Only 10 teams in total averaged a return that reached the 25-yard line or greater. Only 8% of all returns reached the 35-yard line or further. One of the biggest things about kickoffs and returns is the risk of turnovers. During the 2018 season, there was one returned touchdown and 3 turnovers. 
           In a project done by Elizabeth Grimes in 2022 called Predicting the Outcome of Kickoff Returns, she investigated kickoffs and returns. She looked into the factors that contributed to the most successful kick returns. This included looking at “what would make a returner decide to take the risk of attempting a kickoff return, and whether we can predict the ultimate starting field position of the next drive based on these factors” (Grimes 2022). She also broke it down player by player determining which players should elect to not take the ball out and those who should be based on predicted yardsPerTouchdown. Some factors that she calculated were DistanceToClosestCoverage, speedOfClosestCoverage, kickTeamWithin5, receivingTeamWithin5, netCoverage. For her results, she found that since kick returns are high-risk high reward plays, many players who returned the kick would’ve given their team improved field position if they opted for a touchback instead.  
Rules:
          The rules that are in place during kickoffs and punts heavily impact what teams and coaches can and can’t do. There have been many studies and articles written on the rules and the impacts of rule changes over the years. The touchback line has been brought from the 20-yard line to the 25-yard line. This has impacted the number of touchbacks since. An article written by NFL.com looked at the trend of touchbacks over the years and the effect on kickers' strategies. It talks about how despite the trend of touchbacks going up from a 41% touchback rate in 2011 to 61% in 2020, it has gone down to 57% in 2021. The reason for that is kickers kick it shorter on kickoffs. They show a heat map graphic in the article of kickoff location comparison between the two years. It shows that in 2021, fewer kickoffs landed in the endzone than in 2020. Kickoffs that fell short of the endzone increased from 23.4% in 2020 to 27.7% in 2021. Kickers have shown that they have changed their strategies to kick it short. The new rule changes have caused teams and kickers to find new strategies to better their field positions. 
           Another set of changes that have been put in place is surrounding onside kicks. Joey Pollizze in 2021 discusses this in his article looking at why the onside kick is not effective and needs to be removed. He looked at onside kicks during the 2019, 2020, and 2021 seasons. During the 2020 – 2021 season, 71 onside kicks were attempted with only 3 of them being successful. The success rate of the onside kicks was 4.23 percent. The success rate of that season was the lowest of any season in NFL history. The reason why onside kicks have become so challenging is the rule changes in recent years. The NFL has put in new rules that limit the number of players on each side. The season before that rule was implemented, the success rate of onside kicks was 21 percent. Onside kicks are supposed to be hard but multiple people around the league have come out and said that they don’t do much for the game. The success rates of them are too low. 
           The new rules caused more touchbacks but also caused teams to adjust. An article titled The Unintended Consequences of NFL Rule Changes by Satyam Agarwal in 2022 looks at how kickoff strategies changed after the new rule changes. In 2016 the NFL moved the starting line of a touchback from the 20-yard line to the 25-yard line. This caused more touchbacks but over time teams shifted their strategies to kicking the ball higher and shorter with a greater hang time. As a result of the shift in strategy, “the number of kickoffs that bounced before the end zone increased from 15% in 2015 to 24% in 2016” (Agarwal 2020). Also, the number of kickoff returns for touchdowns has declined. This article found that “Given that [teams] faced the risk of a long kickoff return, potentially leading to a return touchdown, kicking teams do not seem as risk-averse as football players are often said to be” (Agarwal 2020).
           The NFL has been changing the rules on kickoffs many times throughout the years. Due to recent studies and news coming to light about the issue of concussions and player safety, one of the places where that takes place is on kickoffs. The rule changed the touchback starting spot. Returning teams now have less of an incentive to take the ball out of the endzone (Bibber 2018). This has caused people to think of alternatives to get rid of the onside kick. Typically onside kicks only happen when the kicking team desperately needs the ball back. It is very hard for the kicking team to recover the kick. To give the kicking teams in need of the ball a chance, the NFL has had talks of adding a “fourth-and-15 from their own 25-yard-line” play that would take place instead of the kick. If the team converts the play, they would keep the ball (Patra 2023).
          The XFL is a football league that is pushing the boundaries with unique rules. In an article written by Peter Warren in 2023, he discusses some of these rules. Two of the biggest changes in rules on kickoffs are on the 4th and 15 alternatives and the positioning on kickoffs. The reasoning for the new rule is to give another option for teams looking to get the ball back instead of a traditional onside kick. Onside kicks have been known to have a low success rate. The XFL kickoff states “The kicker lines up at his 30-yard line, with the other 10 members of the kickoff team lining up at the opponent's 35 -- 5 yards away from the returning team. Only the kicker and one returner can move until the ball is fielded.” This has helped increase returns and minimize touchbacks while helping the injury risk (Seifert 2023).
Expected points:
          Expected points can help see the effects of different scenarios on the outcome of a game. Expected points is a metric that evaluates each play and determines how it impacts the offense’s likelihood to score. This can help on kickoffs and punt returns to see how different actions change the likelihood of scoring. In an article titled Assessing the Value of NFL Punt Returners, Ahmed Cheema in 2020 discusses the value of NFL punt returners and how they should be compared. It looks at expected points by position. It shows a graph at the beginning which shows the decrease in expected points the further away from the endzone that a team is. This makes sense. The expected points for a team based on field position varies based on how far they must go and a returner shaking one or two defenders can double and sometimes greatly increase the expected points for a team. It looked at all punts over the past 21 years as of 2020. In total, there were 35,578 punts. If a returner gained positive yards that increased the expected points and vice versa for negative or turnover plays. They also included fair catches in their analysis because even though the NFL doesn’t count them as returns, they can skew the data and inflate a returner's stats. On average the most expected win data points came around 0 and a little above 0 because of the fair catches. They ran a regression model and found that about 80.9% of the variation in aEPA can be explained by yards per punt return.
           There have been many different strategies on how to improve a team's chances to score and ultimately win. In an article written by Robert Simpson in 2022 called The Analytics Behind One Coach’s Very Aggressive Tactics, he discusses the strategy of one high school coach who never punted the ball and always attempted onside kicks unless they were up by 21 or more. That coach had a record of 216-29-1. To analyze this strategy the article uses Expected Points (EP) and Expected Points Added (EPA). In the NFL it is rare to see an onside kick outside the last few minutes of the fourth quarter of a game. Due to the low success rate of onside kicks, it gives little reason to try them. However, this article looks at onside kicks in college football where between 2014 and 2020, onside kicks were successfully recovered 23.8% of the time. In college football, the kicking teams have a -1.01 EP if they kick a touchback. They have a -2.93 EP if they fail an onside kick and a 2.68 EP if they successfully recover an onside kick. The difference between the touchback and failed onside kick is 1.92 EP which is the EP given up from failing an onside kick. As the article puts it “The amount of EP gained from a successful onside kick is the difference in the kicking team’s EP from recovery and the EP of the opposing team from failure, or 2.68 – (-2.93) = 5.61 EP gained” (Simpson 2022). In total a successful onside kick recovery is worth over 5 points while an unsuccessful onside kick is worth less than a 2-point deficit. To gain a statistical advantage teams would need to recover 25.6% of onside kicks.
           A lot of decisions can be evaluated on the shift in expected points. In an article by Keith Goldner in 2017, he investigates expected points and the relationship between that and location on the field. When looking at punts he talks about how the ability of the punter to pin the ball along with many other factors including weather, defense, and more have an impact on the decision on what to do. Every punt and situation is going to be different. 
Other Research:
           Kickoffs and punts can change the entire game. If the returner sets the offense up with great field position or in some cases scores a touchdown, it is a whole different game. But the returner could also ruin his team's chances with a muff or a fumble. There is a lot of risk versus reward with these types of plays. The advantage to a runner returning the ball is a long return and good field position. The risk is injury. “The NFL says a kickoff is five times as likely to cause concussions than a scrimmage play — and if the NFL acknowledges that something is dangerous, it’s probably really freakin’ dangerous” (Zeegers 2019) The NFL has changed a lot of rules to help prevent injuries on kickoffs. “According to Farmer, as early as 10 years ago, 76.4% of kickoffs during the season’s first month were returned. In 2019, nearly 75% of kickoffs go for touchbacks” (Zeegers 2019). Since concussions and CTE have become such a prevalent issue in the NFL, especially on high-traffic plays such as kickoffs, that has impacted the rules and strategy of these plays. Concussion rates have gone down since the new rules were implemented but so have the onside recovery rates (Haislop 2021).
           The values of punters have been looked at. The Harvard Sports Analysis Collective in 2014 did exactly this. They created a metric called “effective punting distance” which as they put it in the article is “the difference between the starting field position (yrdline1) and the resulting field position after the punt and return attempt (yrdline2)” (Harvard Sports Analysis Collective 2014). They found a diminishing marginal return to effective punting distance when approaching the goal line meaning kickers changed their approach and kick style when closer to the goal line to try to pin teams. An interesting thing that they found in this research is that as kickers got further and further away from the goal line, the skill levels of the kickers were more apparent.
Data Summary
          ​​​​​​​The dataset used to conduct analysis was one about kickoff data. This data was gathered using the “nflfastR” package in R which is an NFL data scraping package. I scraped play-by-play data from every NFL game from the past 10 seasons (2013-2022). Once this data had been scraped, I had to filter through all the data to find all the kickoff data and variables. The variable that I am interested in is return yardage. This is the number of yards the return man ran the ball on the kickoff. This number can take many different shapes from a positive to a negative to an N/A depending on the return or if the return man just took a touchback. Other variables that I had in this dataset include home team, away team, time of the game, kickoff inside twenty, kickoff in the endzone, kickoff out of bounds, kickoff fair catch, fumble, safety, touchdown, kicker name, kick returner name, return team, penalty, penalty yards, touchback, kick landing, and kick distance. This dataset includes data that is both continuous, string, and binary data. The continuous variables are ones like return yards and kick distance. The string variables are ones like the team’s name and game info. The binary variables are the ones like fumble, safety, and touchdown which are 0 if they didn’t happen and 1 if they did happen.​​​​​​​
Summary Statistics
          This is a table of summary statistics of some of the binary variables in my dataset. Most of the variables in my data set were binary variables. In total, there were 27,858 kickoffs that I looked at over the seasons I had scraped. Some interesting things to note here are that the majority of kickoffs resulted in a touchback and were not returned, 56.62% of them to be exact.
          More likely than not on a kickoff a team is going to elect to take a touchback. This strategy can be the result of many different things from not risking field position, not wanting to risk injury, not wanting to risk a fumble, and more. 19.19% of the kickoffs were in the endzone. Since during this period (2013-2022), touchbacks only happen in the endzone this would mean that the difference between the 19.19% of kickoffs in the endzone and the 56.62% of kickoffs for a touchback would have to be the percentage of kickoffs kicked out the back of the endzone for a touchback. This means that on 37.43% of kickoffs during this time frame, teams elected to kick the ball out of the back of the endzone and not give the return team a chance to decide whether they should return the ball or take a touchback. 
          This is a strategy of the kicking team as they always have the first choice of what approach they want to take. They could kick it in the field of play (endzone or in the yard lines) and the return team either takes a touchback or returns the ball forcing the kicking team to make a tackle. They could also just kick it out of the back of the endzone and not have to worry about any tackling. Like before with the decision of the return team, strategy comes into play for the decision of the kicking team. A kicking team may think they can pin the return team back or possibly force a fumble, but they also run the risk of a big play. 
          Three of the biggest risks vs rewards besides field position on a kickoff are fumble, penalty, and touchdown. Based on the summary statistics a fumble was forced on 0.62% of kickoffs. Fumbles were lost on 0.39% of kickoffs. Although both are small numbers there is always a chance. If a fumble was forced on a kickoff, the return team lost the ball to the kicking team on 63.59% of them. If a kick returner were to fumble it is more likely that they are going to lose the ball than recover it. Another way that a return team could be hurt is a penalty. Although none of these penalties can result in the team losing the ball, it could still hurt the return team’s field position to start their drive. A penalty occurred on 4.29% of kickoffs. A penalty was more likely to occur than a fumble which makes sense because any player can commit a penalty whereas only the player with the ball can fumble it. The third and final risk vs reward is a return for a touchdown. Unlike the other two, this is a reward for a return team and a risk for a kickoff team. Depending on the situation of the game, a kickoff return for a touchdown can flip the momentum of a game and sometimes can even decide the outcome of the game. Based on the summary statistics, there was a kickoff return of 0.28% of kickoffs during this time frame. Return teams were more likely to fumble the ball than score a touchdown. While this makes sense, teams must take this into account when determining their strategy on whether they should return the ball or take a touchback. On the flip side kicking teams need to use this in determining whether they should kick the ball short and allow for a return or just kick it out the back of the endzone for a guaranteed touchback
          This is a table of summary statistics of the continuous variables in my dataset. Like the binary variables, there is a count of 27,858 kick returns that I was looking at in this time frame. Return yards are the returns that a kicker returner gains after he catches the kick. The mean is 9.157 yards which is lower than we would typically think but this is skewed by all the touchbacks that have return yards of 0. When all the touchbacks were omitted, the mean of return yards was 22.84 yards. The big difference in means shows how many touchbacks there were and how big of an impact they had on the mean. The minimum of -19 yards was on a lateral play that did not work. The return start line had a mean start line of the 2.144-yard line. The max return start line of 69 and others around that area were the onside kicks. The minimum kickoff distance of -3 and others around this are also onside kicks. All of this data helps give some insight into strategies that teams have chosen to do as well as what they should do based on all of this information.    
Visualizations 
          This graph shows the average return start line of the return teams over the seasons in my data frame. There is a big change in the average return start line between the first three years in my data set (2013-2015) and the last seven years in my data set (2016-2022). There is a reason for this. After the 2015 season and before the 2016 season, the NFL changed a rule on the kickoff. This is shown by the red dotted line on the graph. They brought up the line where teams would begin their drive, if they elected for a touchback, from the 20-yard line to the 25-yard line. This gave the return team an extra 5 yards and better field position. As a result of this kickoff teams changed their strategies and started kicking the ball shorter, making sure that the return team could not take a touchback. If teams believed that they could tackle the returning player before the 25-yard line, then they would kick the ball short and allow for a return. After the rule change teams believed that they would take their chances in allowing for a return.
          This graph shows the return yards for all kickoffs in this data set that were not touchbacks. Since the majority of the kickoffs in this dataset resulted in touchbacks, I wanted to look at the kicks that were returned. I created a histogram with bin sizes of 10. The bin with the most amount of data was in the 20 range. When a kickoff is kicked to the 0-yard line it takes a return of at least 25 yards to justify not taking the touchback. If teams did not return the ball at least 20 yards then they would not be returning the ball much anymore. That is why we see the highest frequency around 20 yards as that is typically what happens on a kickoff that is returned. Teams return the ball to around the same area as a touchback would be. There is more data around 30-yard returns than 10-yard returns. On kickoffs, the kicking team has to run all the way down the field which takes some time. This can help explain why there would be bigger runs than shorter runs. The data on the right side towards 100 are the returns that resulted in a touchdown.
         This graph shows the touchback probability of kickoffs across all NFL teams during the selected season. In general, the trend was that over the years the probability of a touchback increased. There are some years such as 2021 where that wasn’t the case but as a whole, this is what we see. The 2013 season had the most amount of outliers with teams like the Kansas City Chiefs who took touchbacks on only 26.1% of their kick returns and teams like the Buffalo Bills who took touchbacks on 71.8% of their kick returns. The red dot shows the league mean of the probability of a touchback. The means are generally around the same as the median team during that season. The rule change after 2015 had an impact on teams taking a touchback.
Results
          These are the results of the model that I ran. I set return yards as the dependent variable and had return start line, kickoff distance, week, and drive as the predictor variables. I wanted to see if the distance of the kick or the spot where the player starts his return impacted how far the player will return the ball. I also wanted to see if the time of the game or the week of the season had any impact on the distance of returns.
           My model had three of the four predictor variables statistically significant. Those variables were return start line, kickoff distance, and week. This means that we have confidence that these variables have an impact on return yards. Return start line has a coefficient of 0.174 meaning that holding all else constant, if the return start line increased by 1 (the 1-yard line to the 2-yard line) the return yardage would decrease by 0.174. This makes sense because if a ball is kicked shorter, the kicking team will be able to reach the returner quicker and make a tackle. Kickoff Distance has a coefficient of 0.501 meaning that holding all else constant, if the ball is kicked 1 yard further, the return yardage would increase by 0.501. This makes sense in similar ways to the return start line as further kicks would result in the kicking team taking longer to reach the kick returner. Week has a positive coefficient meaning that holding all else constant, as the weeks increase, return yardages increase. Fatigue could have a role in explaining this as kickoff teams may feel the wear and tear more from running down the field and making tackles the whole season. The drive was not statistically significant but did have a negative relationship.
           This table shows the probability of a kick return for a touchdown based on where the return begins. For the first three zones from endzone to the 10 to 20, there was a steady drop in the probability. This could be explained because when the ball is kicked further there is more chance for a running start of the returner when the kickoff team reaches the player for a tackle. The probability does increase when it reaches 20 to 30 but that could be explained due to the small sample size. 30+ had a 0% probability due to a very small sample size and not having a touchdown in that range.
          This table shows the probability of a kick return that results in a fumble based on where the return begins. A fumble as we have seen before has a higher likelihood of occurring than a touchdown. This risk vs reward factors into each team's strategy on a kick return. What is interesting is that the probabilities of endzone and 0 to 10 are similar and the probabilities of 10 to 20 and 20 to 30 are similar, but the probabilities between those two groups are significantly different. The 10 to 20 and 20 to 30 probabilities are a little over 2 times higher than those of endzone and 0 to 10. This can possibly be explained by kickoff teams being able to reach the return man quicker when the ball is kicked shorter, allowing them to lay a big hit on the return man as soon as the returner catches it and gathers their thoughts. 30+ had a 0% probability due to a very small sample size and not having a fumble in that range.
Conclusions
          Should return teams elect to take a touchback and not risk a fumble or should teams return the ball with hopes of a long return or touchdown? Through analysis in running a regression and looking at probabilities, there is not one correct thing that should be done. It all comes down to strategy and risk versus reward. Statistically, there is more of a chance that a runner fumbles the ball, losing their team possession and a chance to score, than there is for a return for a touchdown. 
          Teams have shown changes in strategy over the years, especially because of new rules such as moving forward the touchback start line. Through the model, there appears to be a correlation between the start line and kickoff distance with return yardages. While these relationships are ones that we expect, the magnitudes of them play a role in the decision of whether to return or not. Also, depending on which week of the season the game is, factors into the decision on whether to return the ball or just take a touchback. Week having a positive statistically significant coefficient gives us some insight into how returns change throughout the season. As it gets deeper and deeper into the season, return yardages get bigger and bigger. Teams should consider this when making their strategy. When looking at the probability charts with the bin kickoff landing (return start lines), there is some interesting insight. The highest probability that a kickoff is returned for a touchdown is from a start in the endzone. While this may partly be explained by the sample size, there still does seem to be some truth to it. When the ball is kicked to the endzone, the kickoff team has further to run to try to reach and tackle the return man. This allows the returner to possibly reach top speed before the kicking players reach him, giving him more of a chance to evade the tacklers. If the ball is kicked around the 15-yard line, then the kicking team could reach the returner before he is able to make many moves. 
          The risk of fumbling the ball is higher than the reward of a touchdown. The probability of fumbling the ball is different based on where the player starts his return. If the ball is kicked shorter, then there is a higher chance of a fumble. An explanation for this could be if the ball is kicked shorter, the player who catches the ball has less time to react and get ready before a full-speed player hits him. This could be the reason why we see teams tell their special team players, who aren’t the returners, to take a fair catch or get down immediately when the ball is kicked short to them. Something that is interesting from the findings is that for a kick return that starts in the endzone, there is a higher chance of a touchdown than a fumble. This is the only bin where this is the case. This could factor into teams’ decisions knowing that the reward might be higher than the risk at this yardage. 
          Choosing the optimal strategy is something that happens on every single play during a football game. With kick returns, however, they are of the utmost importance because if a team picks the wrong strategy, then that could set them back or even end their drive before it even started. Every team has a different viewpoint on what they value more. If a team is willing to take the risk of a fumble for the reward of a touchdown, then they will return it every time. If a team is not willing to take the risk, then they will take a touchback. Kickoff personal as well as game situation also factor into this decision. If it is late in a critical game and a team absolutely cannot afford to lose the ball, then they should take a touchback and not take that risk. If a team has a return man like Devin Hester or Cordarrelle Patterson, two of the greatest returners ever, then they should take the ball out every time. 
          The decision to return a kick or take a touchback is a debate that every team is currently having. This debate will also continue to become more nuanced as the rules of football continue to change. During the 2023 season, the NFL introduced a new touchback rule. What this rule says is that a kick returner can take a touchback if he calls for a fair catch on a kickoff anywhere inside the 25-yard line. Essentially if the ball is kicked to the 10-yard line, then a player can call for a fair catch and the ball will automatically go to the 25-yard line without a return. This rule change is going to make it even harder for teams to decide their optimal strategy for years to come.
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