Empirical ProjectYou will complete an empirical project. This project must apply regression analysis to a question involving the role of women in the economy.The 20% will be allocated in the following manner:Proposal: 2%Data Description: 2%Output: 3%5-10 page write-up: 13%Empirical ProjectKristopher Cramer and Keyur JoshiTemple University IntroductionEvery Sunday, football fans watch their favorite football teams duel on the gridiron tocomplete one objective: win. The objective for every sport is to win, and there are specific traitsthat point to a winning team. The most obvious way winning is defined is by how many points ateam scores. A team’s winning percentage proves which team has more wins. However, topredict if a team will be successful is a more difficult task. The goal of this study is to determinehow significant third down conversion percentage is to achieving a higher winning percentage.Our hypothesis is that the more efficient a team is on third downs, the more likely the team willhave a higher winning percentage. The results of this study could be important for coaches toknow so they can focus their practice time on third down situations. This paper also givesfootball fans another way to look at how successful their team will be through efficiency andappreciate their coaches and players that much more. Previous to this paper, there has beenlimited research done on this topic. From what we found, there has only been one study on thirddown conversion. The theoretical model in our paper denotes winning percentage as thedependent variable, and we assume that all teams try to maximize win and efficiency. In order totest our hypothesis in our empirical model, we chose eight variables and ran them in a regression.After running tThe regression, the results showed a strong correlation between a team’s thirddown conversion percentage and their respective winning percentage. In this paper, we willdiscuss a brief background of the topic and its research. We will then look at the model tounderstand the data and the theory behind the research. Based on that data and theory, our resultsare presented and explained based on the numbers.2 Literature ReviewThis study, as stated earlier, is trying towill determine if third down conversion iscorrelated with winning. What this means is if a team that can convert on third down moresuccessfully than the other teams in the league will translate into a higher winning percentage, allelse equal. There has been one study that we found which worked with third down conversionpercentage. However, this study lacked a certain aspect which was resolved in our study. Thestudy is from the Journal of Quantitative Analysis of Sports. This study shows that third downconversion is indicative of efficiency of the offense. The study was conducted by three scholars;Ryan Cafarelli, Christopher Rigdon, and Steven Rigdon. The research was based on severaldifferent data points. They found that third down conversion rate was not useful in knowing ifthe team’s offense was efficient. The data they used was offensive rank, defensive rank, andyards to first down. They used models to show that an average team defense can stop certainNFL teams and the longer the distance to the first down the less chance to convert to a first down(Cafarelli, Rigdon, and Rigdon 2012). They did the same format for an average offense toconvert on an NFL defense, and the results were similar. The longer the distance is, the harder itis to convert. They feel that the conversion rate is a meaningless measure of an efficient offense(Cafarelli, Rigdon, and Rigdon 2012). The flaw with this study is that it does not take intoaccount several different data points which that affect the success. Also, their dependent variable,of offensive efficiency, does not translate directly to wins. This study uses offensive efficiency asthe end result, but offensive efficiency is just another measure used to see if it can translate towins.The notion of third down conversion rate’s being misleading or meaningless is alsobelieved by Brian Burke, a writer for The Washington pPost, and the creator of the website3 Advanced NFL Stats. He wrote an article for the Post, Third down conversion rate can misleadcoaches and fans. In this article, he acknowledges that third down conversion is stronglycorrelated with overall success.; hHowever, he believes that a team is better off converting onfirst or second down (Burke, 2012). He suggests that a team should try to avoid third downswhenever possible (Burke, 2012). He believes this to be true because third downs are isolatedopportunities for a ten-yard conversion rather than trying to set up for a “manageable thirddown” (which is third down and 1 yard to go) (Burke, 2012). He uses the Redskins as anexample, because at the time he wrote, the article the Redskins were at the bottom of the leagueon third downs, however their overall series conversion rate was at the current league average of68%. This number indicates the Redskins were converting on first and second down. Burke’sarticle is one of the reasons why this study’s regression included the variable first downs gainednot on third down (Burke, 2012). This study falls short of the main point to understand that teamswill not be truly successful if they cannot make the tough third down conversions. Those teamswho do are considered elite. Our research shows that there is a strong correlation between thirddown and winning percentage.ModelTheoretical ModelIn this study, success is defined as a higher winning percentage in the regular season. Inorder to maximize winning percentage, a team must be efficient, especially on third downs. Thisidea is much like firms’ in the business world wanting to maximize worker efficiency. Thetheoretical model assumes that 32 NFL teams maximize wins and holding other variablesconstant to determine if a team’s third down conversion percentage is correlated with how4 successful a team is. Due to this, it is expected that when the regression is run, the results shouldyield a correlation between third down conversion percentage and winning percentage.EmpiricalThe basis for this study was to extrapolate data which we can hold constant for all teamsto see if the third down conversion rate correlated to wins. This data that was found was later putthrough a regression with the computer program Stata. The data that we used for this was thetotal defense yards, strength of schedule, return yards on kickoffs, offensive yards, first downconverted not on third down, turnover differential, and long passes. The data for total defense,strength of schedule, returns yards on kickoffs, and offensive yards wasere extracted fromESPN.com. Statistics gathered from NFL.com consisted of turnover differential and the 20 pluspassing plays. The main statistics of third down conversion rate wasere downloaded fromFootball Outsiders. All three of these websites are considered to be credible. ESPN.com is apremier website for all sports -related stats. NFL.com is affiliated with the NFL and thus iscredible. The website for Football Outsiders is a credible source as it is affiliated withESPN.com. The statistics on Football Outsiders is known for more advanced forms of statistics,which go beyond the raw numbers.The reasons we included the variables were based on two reasons, the outcome of thestatistical analysis and intuitive thinking. The third down conversion and winning percentagewere the obvious choice as were the variables that were important to see if our assumptions weretrue. The other variables, such as team offense and defense along with strength of schedule, putinto perspective the team’s chances of making that third down conversion. The long pass tookinto account those deep plays that a team needed to complete. This was important because mostteams that take these deep passes of more than 20 yards are those that are trailing and need to5 catch up quickly. Now, this is not perfectly true as some teams have their offense set around bigplays but this can account for most basic reasoning.The data that needed to be calculated was the first down converted, not on third down. Tobegin, the total first downs in the season needed to be found. Taken with the third downconversion rate, the first down converted not on third down was calculated. The formula wastotal first downs minus quantity total first downs times third down converted. This gave the firstdown converted on all other downs except third down, which controlled how exactly how manythird downs were completed for a first down.In tThe initial stages of this paper, it had sixteen different variables. They included pointsper game, percentage third downs converted against defense, points per game allowed bydefense, return yards allowed, return touchdowns scored, return touchdown allowed, penaltyyards per game and field goals made per game. Some of the data did not relate to the study orwould not help show if the data was relevant. This included all those statistics on with points(PPG, PPG Allowed, and Field Goals) These statistics were taken out, as they are already knownto be correlated with winning percentage and would take away the possible effects of third downconversion on winning percentage. Also, it is obvious that those teams that scored more wouldimprove their win percentage. Therefore, we did not include them in our study. Some of the otherdata such as penalties had no correlation with or was not statistically significant and decreasedthe adjusted R-squared when we ran the regression. The first regression was originally ninevariables, but was reduced to eight when we ran the final regression. Finally, some of the dataseemed to be repeated. The total defense that we used can be said to include some of the effectsof third down completed against defense statistics. For that reason, the decision was to include6 the variable that encompassed more information than just a part of the defense. Based on theseimplications, some variables were taken out to reflect a more accurate picture.There are several strengths to this our data that was used. As the results will show, it ishighly correlated. It also shows the recent trend as it shows data for the past three regularseasons. 2011 statistics might be skewed due to thea lockout, as the offseason did not allow formuch practice time.There are several shortcomings to this study. Since only three seasons of data were used,the sample size was under 100 (sample size was 96). The other issue is with the strength ofschedule variable and data for strength of schedule for the previous year. For example, weneeded to know the strength of schedule for 2009 we used 2010 since 2010 was based on theperformance of the 2009 team. This however, did not account for team turnover, such as differentplayers or change of coaches. The other possible shortcoming in this study is a possible variablethat was not taken into account. There is a chance that a key variable was overlooked or deemedunimportant. These shortcomings do not make the results any less significant, but means theresults can be further improved. A further summary of the raw data is provided in the Appendix.ResultsTable 2WinningCoef.Std. Err.T-ScoreP>t[95% conf.Inteval]PercentageThirdconvtotaldefenseschedretydkoydsfirstnoton3tovdiflongpass_cons0.843814-0.00094-0.446380.0059130.0012240.0020160.009303-0.00269-0.077730.2991920.0003970.4710210.0048870.0007010.0009540.0012830.0013790.3483052.82-2.38-0.951.211.752.117.25-1.95-0.220.249138-0.00173-1.38259-0.0038-0.000170.0001190.006754.-0054331-0.770021.43849-0.00015480.4898260.01562610.00261720.00261720.01185240.00004660.6145656Table 37 SourceSSdfMSNumber of obs =ModelResidual2.631387910.9991816768870.3289230.01148596F ( 8,87) = 28.64Prob > F = 0.0000R – Squared = .Total3.63056958950.0382177248Adj R-squared = .6995Root MSE = .10717The results of the Ordinary Least Squares (OLS) regression showed that third downconversion percentage was found to be statistically significant at the t score of 2.82 p < .05. Inaddition, the correlation coefficient for third down conversions was found to be .843814.Theadjusted R-squared of this study regression was .6995. This number indicates that the results ofthis study are pretty accurate when predicting future outcomes on the basis of other relatedinformation as well as how well a the regression line fits the data. Since the highest value foradjusted R-squared possible is 1, .6995 indicates that the relationship between winningpercentage and third down conversion is fairly grouped around a best fit line. This result matchesthe study’s hypothesis that the higher the team’s third down conversion percentage, the morelikely the team is to win a game. These results make sense because the more efficient a team ison third down, the more first downs the team has. When they have more first downs, they areable to run more plays and establish longer drives. Being more efficient gives a team moreopportunities to score more points.The results of the regression also showed that a second variable, strength of schedule wasfound to be not statistically significant at the p <.05 level, although there was a negativecorrelation at .44. This result makes sense because the better the opposing team the harder it is8 to win a game, however the strength of the opposing team does not mean that much for it tomake a meaningful difference in a team’s winning percentage.ConclusionsBased on oOur findings, we would suggest that football teams should focus on their thirddown conversion percentage because it correlates with a higher winning percentage. Headcoaches and coordinators should stress to their players that efficiency on third down is veryimportant and a crucial part of the game. Teams should also try to draft and sign players who arebetter at gaining yards after catch or hard runners to push for the extra yard.Based on the results, third down conversion percentage is correlated with winningpercentage. When comparing our results to previous research, iIt appears our results differ fromBurke’s beliefs and the results of Ryan Cafarelli, Christopher Rigdon, and Steven Rigdon. WhileBurke believed there is a strong correlation between third downs and winning percentage, hebelieved that teams should be focused on first and second down (Burke, 2012). Because hebelieved this, we accounted for that variable in our regression and the result was a coefficient of .0020159 and a t score of 2.11. If he claims were to be true, the correlation coefficient should begreater, thus being more indicative of winning percentage.To say the least, oOur study is not perfect and there are ways to improve it. Possibleimprovements to our study could beare checking the variables over more than just three seasons.Our study only encompasses three seasons, which came out to 96 games. Also, it is very possiblewe missed an important variable. Our regression only included 8 variables based on the statisticswe thought were of importance to this study, which also kept our adjusted R square fromdecreasing. The inclusion of more variables should definitely be included. While this study is not9 totally conclusive and not perfect, it still shows a strong correlation between winning percentageand third down conversion percentage.There were some problems with presenting the regression results and one or two problems withinterpreting them, but, overall, I like what you did. The writing could use some attention.9210 ReferencesBurke, Brian. “Third Down Conversion Rate Can Mislead Coaches and Fans.” The WashingtonPost. The Washington Post, 10 Oct. 2012. Web. 06 Nov. 2012.<http://www.washingtonpost.com/blogs/football-insider/wp/2012/10/10/third-downconversion-rate-can-mislead-coaches-and-fans/>.Cafarelli, Ryan, Christopher J. Rigdon, and Steven E. Rigdon. “Models for Third DownConversion in the National Football League.” Journal of Quantitative Analysis in Sports8.3 (2012): 1-24. Print.11 AppendixTable 1: Summary StatisticwpctMeanStand.ErrorMedianModeStand.DeviationSampleVarianace0.5000.0200.5000.5000.1960.038ThirdDownConvertedTotalOffensiveYards0.384339.0000.0064.1590.3790.3330.0600.004336.650367.20040.7481660.371PPGTotalDefense21.8640.49122.10025.4004.81523.180340.3573.205339.350324.90031.399985.912%ThirdDownsConvertedAgainstDefensePPGAllowedbyDefenseStrength ofSchedule0.38322.0330.5000.0040.3650.0030.3830.39721.30020.8000.5000.4920.0413.5750.0250.00212.7820.001ReturnYardsGainedReturnsYardsAllowed23.3830.24623.30023.2002.4155.83223.5460.24923.45024.4002.4435.967ReturnTDsScored0.5210.0750.0000.0000.7400.547ReturnTDsAllowed0.521FirstDownsConvertedotherthanonThirdDowns186.3540.0742.1240.000186.7760.000#N/A0.72520.8120.526433.137PenaltyYards PerGame52.8310.97652.75043.1009.56191.411PassingPlays20+YardsGained47.9691.11647.00044.00010.936119.588TurnoverRatio-0.0211.0000.0001.0009.80196.063FGMadePerGame1.6390.0361.6001.4000.3570.128**Bold: data used in regression.12
Empirical ProjectYou will complete an empirical project. This project must apply regression analysis to a question involving the role of women in the economy.The 20% will be allocated in the following manner:Proposal: 2%Data Description: 2%Output: 3%5-10 page write-up: 13%Empirical ProjectKristopher Cramer and Keyur JoshiTemple University IntroductionEvery Sunday, football fans watch their favorite football teams duel on the gridiron tocomplete one objective: win. The objective for every sport is to win, and there are specific traitsthat point to a winning team. The most obvious way winning is defined is by how many points ateam scores. A team’s winning percentage proves which team has more wins. However, topredict if a team will be successful is a more difficult task. The goal of this study is to determinehow significant third down conversion percentage is to achieving a higher winning percentage.Our hypothesis is that the more efficient a team is on third downs, the more likely the team willhave a higher winning percentage. The results of this study could be important for coaches toknow so they can focus their practice time on third down situations. This paper also givesfootball fans another way to look at how successful their team will be through efficiency andappreciate their coaches and players that much more. Previous to this paper, there has beenlimited research done on this topic. From what we found, there has only been one study on thirddown conversion. The theoretical model in our paper denotes winning percentage as thedependent variable, and we assume that all teams try to maximize win and efficiency. In order totest our hypothesis in our empirical model, we chose eight variables and ran them in a regression.After running tThe regression, the results showed a strong correlation between a team’s thirddown conversion percentage and their respective winning percentage. In this paper, we willdiscuss a brief background of the topic and its research. We will then look at the model tounderstand the data and the theory behind the research. Based on that data and theory, our resultsare presented and explained based on the numbers.2 Literature ReviewThis study, as stated earlier, is trying towill determine if third down conversion iscorrelated with winning. What this means is if a team that can convert on third down moresuccessfully than the other teams in the league will translate into a higher winning percentage, allelse equal. There has been one study that we found which worked with third down conversionpercentage. However, this study lacked a certain aspect which was resolved in our study. Thestudy is from the Journal of Quantitative Analysis of Sports. This study shows that third downconversion is indicative of efficiency of the offense. The study was conducted by three scholars;Ryan Cafarelli, Christopher Rigdon, and Steven Rigdon. The research was based on severaldifferent data points. They found that third down conversion rate was not useful in knowing ifthe team’s offense was efficient. The data they used was offensive rank, defensive rank, andyards to first down. They used models to show that an average team defense can stop certainNFL teams and the longer the distance to the first down the less chance to convert to a first down(Cafarelli, Rigdon, and Rigdon 2012). They did the same format for an average offense toconvert on an NFL defense, and the results were similar. The longer the distance is, the harder itis to convert. They feel that the conversion rate is a meaningless measure of an efficient offense(Cafarelli, Rigdon, and Rigdon 2012). The flaw with this study is that it does not take intoaccount several different data points which that affect the success. Also, their dependent variable,of offensive efficiency, does not translate directly to wins. This study uses offensive efficiency asthe end result, but offensive efficiency is just another measure used to see if it can translate towins.The notion of third down conversion rate’s being misleading or meaningless is alsobelieved by Brian Burke, a writer for The Washington pPost, and the creator of the website3 Advanced NFL Stats. He wrote an article for the Post, Third down conversion rate can misleadcoaches and fans. In this article, he acknowledges that third down conversion is stronglycorrelated with overall success.; hHowever, he believes that a team is better off converting onfirst or second down (Burke, 2012). He suggests that a team should try to avoid third downswhenever possible (Burke, 2012). He believes this to be true because third downs are isolatedopportunities for a ten-yard conversion rather than trying to set up for a “manageable thirddown” (which is third down and 1 yard to go) (Burke, 2012). He uses the Redskins as anexample, because at the time he wrote, the article the Redskins were at the bottom of the leagueon third downs, however their overall series conversion rate was at the current league average of68%. This number indicates the Redskins were converting on first and second down. Burke’sarticle is one of the reasons why this study’s regression included the variable first downs gainednot on third down (Burke, 2012). This study falls short of the main point to understand that teamswill not be truly successful if they cannot make the tough third down conversions. Those teamswho do are considered elite. Our research shows that there is a strong correlation between thirddown and winning percentage.ModelTheoretical ModelIn this study, success is defined as a higher winning percentage in the regular season. Inorder to maximize winning percentage, a team must be efficient, especially on third downs. Thisidea is much like firms’ in the business world wanting to maximize worker efficiency. Thetheoretical model assumes that 32 NFL teams maximize wins and holding other variablesconstant to determine if a team’s third down conversion percentage is correlated with how4 successful a team is. Due to this, it is expected that when the regression is run, the results shouldyield a correlation between third down conversion percentage and winning percentage.EmpiricalThe basis for this study was to extrapolate data which we can hold constant for all teamsto see if the third down conversion rate correlated to wins. This data that was found was later putthrough a regression with the computer program Stata. The data that we used for this was thetotal defense yards, strength of schedule, return yards on kickoffs, offensive yards, first downconverted not on third down, turnover differential, and long passes. The data for total defense,strength of schedule, returns yards on kickoffs, and offensive yards wasere extracted fromESPN.com. Statistics gathered from NFL.com consisted of turnover differential and the 20 pluspassing plays. The main statistics of third down conversion rate wasere downloaded fromFootball Outsiders. All three of these websites are considered to be credible. ESPN.com is apremier website for all sports -related stats. NFL.com is affiliated with the NFL and thus iscredible. The website for Football Outsiders is a credible source as it is affiliated withESPN.com. The statistics on Football Outsiders is known for more advanced forms of statistics,which go beyond the raw numbers.The reasons we included the variables were based on two reasons, the outcome of thestatistical analysis and intuitive thinking. The third down conversion and winning percentagewere the obvious choice as were the variables that were important to see if our assumptions weretrue. The other variables, such as team offense and defense along with strength of schedule, putinto perspective the team’s chances of making that third down conversion. The long pass tookinto account those deep plays that a team needed to complete. This was important because mostteams that take these deep passes of more than 20 yards are those that are trailing and need to5 catch up quickly. Now, this is not perfectly true as some teams have their offense set around bigplays but this can account for most basic reasoning.The data that needed to be calculated was the first down converted, not on third down. Tobegin, the total first downs in the season needed to be found. Taken with the third downconversion rate, the first down converted not on third down was calculated. The formula wastotal first downs minus quantity total first downs times third down converted. This gave the firstdown converted on all other downs except third down, which controlled how exactly how manythird downs were completed for a first down.In tThe initial stages of this paper, it had sixteen different variables. They included pointsper game, percentage third downs converted against defense, points per game allowed bydefense, return yards allowed, return touchdowns scored, return touchdown allowed, penaltyyards per game and field goals made per game. Some of the data did not relate to the study orwould not help show if the data was relevant. This included all those statistics on with points(PPG, PPG Allowed, and Field Goals) These statistics were taken out, as they are already knownto be correlated with winning percentage and would take away the possible effects of third downconversion on winning percentage. Also, it is obvious that those teams that scored more wouldimprove their win percentage. Therefore, we did not include them in our study. Some of the otherdata such as penalties had no correlation with or was not statistically significant and decreasedthe adjusted R-squared when we ran the regression. The first regression was originally ninevariables, but was reduced to eight when we ran the final regression. Finally, some of the dataseemed to be repeated. The total defense that we used can be said to include some of the effectsof third down completed against defense statistics. For that reason, the decision was to include6 the variable that encompassed more information than just a part of the defense. Based on theseimplications, some variables were taken out to reflect a more accurate picture.There are several strengths to this our data that was used. As the results will show, it ishighly correlated. It also shows the recent trend as it shows data for the past three regularseasons. 2011 statistics might be skewed due to thea lockout, as the offseason did not allow formuch practice time.There are several shortcomings to this study. Since only three seasons of data were used,the sample size was under 100 (sample size was 96). The other issue is with the strength ofschedule variable and data for strength of schedule for the previous year. For example, weneeded to know the strength of schedule for 2009 we used 2010 since 2010 was based on theperformance of the 2009 team. This however, did not account for team turnover, such as differentplayers or change of coaches. The other possible shortcoming in this study is a possible variablethat was not taken into account. There is a chance that a key variable was overlooked or deemedunimportant. These shortcomings do not make the results any less significant, but means theresults can be further improved. A further summary of the raw data is provided in the Appendix.ResultsTable 2WinningCoef.Std. Err.T-ScoreP>t[95% conf.Inteval]PercentageThirdconvtotaldefenseschedretydkoydsfirstnoton3tovdiflongpass_cons0.843814-0.00094-0.446380.0059130.0012240.0020160.009303-0.00269-0.077730.2991920.0003970.4710210.0048870.0007010.0009540.0012830.0013790.3483052.82-2.38-0.951.211.752.117.25-1.95-0.220.249138-0.00173-1.38259-0.0038-0.000170.0001190.006754.-0054331-0.770021.43849-0.00015480.4898260.01562610.00261720.00261720.01185240.00004660.6145656Table 37 SourceSSdfMSNumber of obs =ModelResidual2.631387910.9991816768870.3289230.01148596F ( 8,87) = 28.64Prob > F = 0.0000R – Squared = .Total3.63056958950.0382177248Adj R-squared = .6995Root MSE = .10717The results of the Ordinary Least Squares (OLS) regression showed that third downconversion percentage was found to be statistically significant at the t score of 2.82 p < .05. Inaddition, the correlation coefficient for third down conversions was found to be .843814.Theadjusted R-squared of this study regression was .6995. This number indicates that the results ofthis study are pretty accurate when predicting future outcomes on the basis of other relatedinformation as well as how well a the regression line fits the data. Since the highest value foradjusted R-squared possible is 1, .6995 indicates that the relationship between winningpercentage and third down conversion is fairly grouped around a best fit line. This result matchesthe study’s hypothesis that the higher the team’s third down conversion percentage, the morelikely the team is to win a game. These results make sense because the more efficient a team ison third down, the more first downs the team has. When they have more first downs, they areable to run more plays and establish longer drives. Being more efficient gives a team moreopportunities to score more points.The results of the regression also showed that a second variable, strength of schedule wasfound to be not statistically significant at the p <.05 level, although there was a negativecorrelation at .44. This result makes sense because the better the opposing team the harder it is8 to win a game, however the strength of the opposing team does not mean that much for it tomake a meaningful difference in a team’s winning percentage.ConclusionsBased on oOur findings, we would suggest that football teams should focus on their thirddown conversion percentage because it correlates with a higher winning percentage. Headcoaches and coordinators should stress to their players that efficiency on third down is veryimportant and a crucial part of the game. Teams should also try to draft and sign players who arebetter at gaining yards after catch or hard runners to push for the extra yard.Based on the results, third down conversion percentage is correlated with winningpercentage. When comparing our results to previous research, iIt appears our results differ fromBurke’s beliefs and the results of Ryan Cafarelli, Christopher Rigdon, and Steven Rigdon. WhileBurke believed there is a strong correlation between third downs and winning percentage, hebelieved that teams should be focused on first and second down (Burke, 2012). Because hebelieved this, we accounted for that variable in our regression and the result was a coefficient of .0020159 and a t score of 2.11. If he claims were to be true, the correlation coefficient should begreater, thus being more indicative of winning percentage.To say the least, oOur study is not perfect and there are ways to improve it. Possibleimprovements to our study could beare checking the variables over more than just three seasons.Our study only encompasses three seasons, which came out to 96 games. Also, it is very possiblewe missed an important variable. Our regression only included 8 variables based on the statisticswe thought were of importance to this study, which also kept our adjusted R square fromdecreasing. The inclusion of more variables should definitely be included. While this study is not9 totally conclusive and not perfect, it still shows a strong correlation between winning percentageand third down conversion percentage.There were some problems with presenting the regression results and one or two problems withinterpreting them, but, overall, I like what you did. The writing could use some attention.9210 ReferencesBurke, Brian. “Third Down Conversion Rate Can Mislead Coaches and Fans.” The WashingtonPost. The Washington Post, 10 Oct. 2012. Web. 06 Nov. 2012.<http://www.washingtonpost.com/blogs/football-insider/wp/2012/10/10/third-downconversion-rate-can-mislead-coaches-and-fans/>.Cafarelli, Ryan, Christopher J. Rigdon, and Steven E. Rigdon. “Models for Third DownConversion in the National Football League.” Journal of Quantitative Analysis in Sports8.3 (2012): 1-24. Print.11 AppendixTable 1: Summary StatisticwpctMeanStand.ErrorMedianModeStand.DeviationSampleVarianace0.5000.0200.5000.5000.1960.038ThirdDownConvertedTotalOffensiveYards0.384339.0000.0064.1590.3790.3330.0600.004336.650367.20040.7481660.371PPGTotalDefense21.8640.49122.10025.4004.81523.180340.3573.205339.350324.90031.399985.912%ThirdDownsConvertedAgainstDefensePPGAllowedbyDefenseStrength ofSchedule0.38322.0330.5000.0040.3650.0030.3830.39721.30020.8000.5000.4920.0413.5750.0250.00212.7820.001ReturnYardsGainedReturnsYardsAllowed23.3830.24623.30023.2002.4155.83223.5460.24923.45024.4002.4435.967ReturnTDsScored0.5210.0750.0000.0000.7400.547ReturnTDsAllowed0.521FirstDownsConvertedotherthanonThirdDowns186.3540.0742.1240.000186.7760.000#N/A0.72520.8120.526433.137PenaltyYards PerGame52.8310.97652.75043.1009.56191.411PassingPlays20+YardsGained47.9691.11647.00044.00010.936119.588TurnoverRatio-0.0211.0000.0001.0009.80196.063FGMadePerGame1.6390.0361.6001.4000.3570.128**Bold: data used in regression.12
Empirical ProjectYou will complete an empirical project. This project must apply regression analysis to a question involving the role of women in the economy.The 20% will be allocated in the following manner:Proposal: 2%Data Description: 2%Output: 3%5-10 page write-up: 13%Empirical ProjectKristopher Cramer and Keyur JoshiTemple University IntroductionEvery Sunday, football fans watch their favorite football teams duel on the gridiron tocomplete one objective: win. The objective for every sport is to win, and there are specific traitsthat point to a winning team. The most obvious way winning is defined is by how many points ateam scores. A team’s winning percentage proves which team has more wins. However, topredict if a team will be successful is a more difficult task. The goal of this study is to determinehow significant third down conversion percentage is to achieving a higher winning percentage.Our hypothesis is that the more efficient a team is on third downs, the more likely the team willhave a higher winning percentage. The results of this study could be important for coaches toknow so they can focus their practice time on third down situations. This paper also givesfootball fans another way to look at how successful their team will be through efficiency andappreciate their coaches and players that much more. Previous to this paper, there has beenlimited research done on this topic. From what we found, there has only been one study on thirddown conversion. The theoretical model in our paper denotes winning percentage as thedependent variable, and we assume that all teams try to maximize win and efficiency. In order totest our hypothesis in our empirical model, we chose eight variables and ran them in a regression.After running tThe regression, the results showed a strong correlation between a team’s thirddown conversion percentage and their respective winning percentage. In this paper, we willdiscuss a brief background of the topic and its research. We will then look at the model tounderstand the data and the theory behind the research. Based on that data and theory, our resultsare presented and explained based on the numbers.2 Literature ReviewThis study, as stated earlier, is trying towill determine if third down conversion iscorrelated with winning. What this means is if a team that can convert on third down moresuccessfully than the other teams in the league will translate into a higher winning percentage, allelse equal. There has been one study that we found which worked with third down conversionpercentage. However, this study lacked a certain aspect which was resolved in our study. Thestudy is from the Journal of Quantitative Analysis of Sports. This study shows that third downconversion is indicative of efficiency of the offense. The study was conducted by three scholars;Ryan Cafarelli, Christopher Rigdon, and Steven Rigdon. The research was based on severaldifferent data points. They found that third down conversion rate was not useful in knowing ifthe team’s offense was efficient. The data they used was offensive rank, defensive rank, andyards to first down. They used models to show that an average team defense can stop certainNFL teams and the longer the distance to the first down the less chance to convert to a first down(Cafarelli, Rigdon, and Rigdon 2012). They did the same format for an average offense toconvert on an NFL defense, and the results were similar. The longer the distance is, the harder itis to convert. They feel that the conversion rate is a meaningless measure of an efficient offense(Cafarelli, Rigdon, and Rigdon 2012). The flaw with this study is that it does not take intoaccount several different data points which that affect the success. Also, their dependent variable,of offensive efficiency, does not translate directly to wins. This study uses offensive efficiency asthe end result, but offensive efficiency is just another measure used to see if it can translate towins.The notion of third down conversion rate’s being misleading or meaningless is alsobelieved by Brian Burke, a writer for The Washington pPost, and the creator of the website3 Advanced NFL Stats. He wrote an article for the Post, Third down conversion rate can misleadcoaches and fans. In this article, he acknowledges that third down conversion is stronglycorrelated with overall success.; hHowever, he believes that a team is better off converting onfirst or second down (Burke, 2012). He suggests that a team should try to avoid third downswhenever possible (Burke, 2012). He believes this to be true because third downs are isolatedopportunities for a ten-yard conversion rather than trying to set up for a “manageable thirddown” (which is third down and 1 yard to go) (Burke, 2012). He uses the Redskins as anexample, because at the time he wrote, the article the Redskins were at the bottom of the leagueon third downs, however their overall series conversion rate was at the current league average of68%. This number indicates the Redskins were converting on first and second down. Burke’sarticle is one of the reasons why this study’s regression included the variable first downs gainednot on third down (Burke, 2012). This study falls short of the main point to understand that teamswill not be truly successful if they cannot make the tough third down conversions. Those teamswho do are considered elite. Our research shows that there is a strong correlation between thirddown and winning percentage.ModelTheoretical ModelIn this study, success is defined as a higher winning percentage in the regular season. Inorder to maximize winning percentage, a team must be efficient, especially on third downs. Thisidea is much like firms’ in the business world wanting to maximize worker efficiency. Thetheoretical model assumes that 32 NFL teams maximize wins and holding other variablesconstant to determine if a team’s third down conversion percentage is correlated with how4 successful a team is. Due to this, it is expected that when the regression is run, the results shouldyield a correlation between third down conversion percentage and winning percentage.EmpiricalThe basis for this study was to extrapolate data which we can hold constant for all teamsto see if the third down conversion rate correlated to wins. This data that was found was later putthrough a regression with the computer program Stata. The data that we used for this was thetotal defense yards, strength of schedule, return yards on kickoffs, offensive yards, first downconverted not on third down, turnover differential, and long passes. The data for total defense,strength of schedule, returns yards on kickoffs, and offensive yards wasere extracted fromESPN.com. Statistics gathered from NFL.com consisted of turnover differential and the 20 pluspassing plays. The main statistics of third down conversion rate wasere downloaded fromFootball Outsiders. All three of these websites are considered to be credible. ESPN.com is apremier website for all sports -related stats. NFL.com is affiliated with the NFL and thus iscredible. The website for Football Outsiders is a credible source as it is affiliated withESPN.com. The statistics on Football Outsiders is known for more advanced forms of statistics,which go beyond the raw numbers.The reasons we included the variables were based on two reasons, the outcome of thestatistical analysis and intuitive thinking. The third down conversion and winning percentagewere the obvious choice as were the variables that were important to see if our assumptions weretrue. The other variables, such as team offense and defense along with strength of schedule, putinto perspective the team’s chances of making that third down conversion. The long pass tookinto account those deep plays that a team needed to complete. This was important because mostteams that take these deep passes of more than 20 yards are those that are trailing and need to5 catch up quickly. Now, this is not perfectly true as some teams have their offense set around bigplays but this can account for most basic reasoning.The data that needed to be calculated was the first down converted, not on third down. Tobegin, the total first downs in the season needed to be found. Taken with the third downconversion rate, the first down converted not on third down was calculated. The formula wastotal first downs minus quantity total first downs times third down converted. This gave the firstdown converted on all other downs except third down, which controlled how exactly how manythird downs were completed for a first down.In tThe initial stages of this paper, it had sixteen different variables. They included pointsper game, percentage third downs converted against defense, points per game allowed bydefense, return yards allowed, return touchdowns scored, return touchdown allowed, penaltyyards per game and field goals made per game. Some of the data did not relate to the study orwould not help show if the data was relevant. This included all those statistics on with points(PPG, PPG Allowed, and Field Goals) These statistics were taken out, as they are already knownto be correlated with winning percentage and would take away the possible effects of third downconversion on winning percentage. Also, it is obvious that those teams that scored more wouldimprove their win percentage. Therefore, we did not include them in our study. Some of the otherdata such as penalties had no correlation with or was not statistically significant and decreasedthe adjusted R-squared when we ran the regression. The first regression was originally ninevariables, but was reduced to eight when we ran the final regression. Finally, some of the dataseemed to be repeated. The total defense that we used can be said to include some of the effectsof third down completed against defense statistics. For that reason, the decision was to include6 the variable that encompassed more information than just a part of the defense. Based on theseimplications, some variables were taken out to reflect a more accurate picture.There are several strengths to this our data that was used. As the results will show, it ishighly correlated. It also shows the recent trend as it shows data for the past three regularseasons. 2011 statistics might be skewed due to thea lockout, as the offseason did not allow formuch practice time.There are several shortcomings to this study. Since only three seasons of data were used,the sample size was under 100 (sample size was 96). The other issue is with the strength ofschedule variable and data for strength of schedule for the previous year. For example, weneeded to know the strength of schedule for 2009 we used 2010 since 2010 was based on theperformance of the 2009 team. This however, did not account for team turnover, such as differentplayers or change of coaches. The other possible shortcoming in this study is a possible variablethat was not taken into account. There is a chance that a key variable was overlooked or deemedunimportant. These shortcomings do not make the results any less significant, but means theresults can be further improved. A further summary of the raw data is provided in the Appendix.ResultsTable 2WinningCoef.Std. Err.T-ScoreP>t[95% conf.Inteval]PercentageThirdconvtotaldefenseschedretydkoydsfirstnoton3tovdiflongpass_cons0.843814-0.00094-0.446380.0059130.0012240.0020160.009303-0.00269-0.077730.2991920.0003970.4710210.0048870.0007010.0009540.0012830.0013790.3483052.82-2.38-0.951.211.752.117.25-1.95-0.220.249138-0.00173-1.38259-0.0038-0.000170.0001190.006754.-0054331-0.770021.43849-0.00015480.4898260.01562610.00261720.00261720.01185240.00004660.6145656Table 37 SourceSSdfMSNumber of obs =ModelResidual2.631387910.9991816768870.3289230.01148596F ( 8,87) = 28.64Prob > F = 0.0000R – Squared = .Total3.63056958950.0382177248Adj R-squared = .6995Root MSE = .10717The results of the Ordinary Least Squares (OLS) regression showed that third downconversion percentage was found to be statistically significant at the t score of 2.82 p < .05. Inaddition, the correlation coefficient for third down conversions was found to be .843814.Theadjusted R-squared of this study regression was .6995. This number indicates that the results ofthis study are pretty accurate when predicting future outcomes on the basis of other relatedinformation as well as how well a the regression line fits the data. Since the highest value foradjusted R-squared possible is 1, .6995 indicates that the relationship between winningpercentage and third down conversion is fairly grouped around a best fit line. This result matchesthe study’s hypothesis that the higher the team’s third down conversion percentage, the morelikely the team is to win a game. These results make sense because the more efficient a team ison third down, the more first downs the team has. When they have more first downs, they areable to run more plays and establish longer drives. Being more efficient gives a team moreopportunities to score more points.The results of the regression also showed that a second variable, strength of schedule wasfound to be not statistically significant at the p <.05 level, although there was a negativecorrelation at .44. This result makes sense because the better the opposing team the harder it is8 to win a game, however the strength of the opposing team does not mean that much for it tomake a meaningful difference in a team’s winning percentage.ConclusionsBased on oOur findings, we would suggest that football teams should focus on their thirddown conversion percentage because it correlates with a higher winning percentage. Headcoaches and coordinators should stress to their players that efficiency on third down is veryimportant and a crucial part of the game. Teams should also try to draft and sign players who arebetter at gaining yards after catch or hard runners to push for the extra yard.Based on the results, third down conversion percentage is correlated with winningpercentage. When comparing our results to previous research, iIt appears our results differ fromBurke’s beliefs and the results of Ryan Cafarelli, Christopher Rigdon, and Steven Rigdon. WhileBurke believed there is a strong correlation between third downs and winning percentage, hebelieved that teams should be focused on first and second down (Burke, 2012). Because hebelieved this, we accounted for that variable in our regression and the result was a coefficient of .0020159 and a t score of 2.11. If he claims were to be true, the correlation coefficient should begreater, thus being more indicative of winning percentage.To say the least, oOur study is not perfect and there are ways to improve it. Possibleimprovements to our study could beare checking the variables over more than just three seasons.Our study only encompasses three seasons, which came out to 96 games. Also, it is very possiblewe missed an important variable. Our regression only included 8 variables based on the statisticswe thought were of importance to this study, which also kept our adjusted R square fromdecreasing. The inclusion of more variables should definitely be included. While this study is not9 totally conclusive and not perfect, it still shows a strong correlation between winning percentageand third down conversion percentage.There were some problems with presenting the regression results and one or two problems withinterpreting them, but, overall, I like what you did. The writing could use some attention.9210 ReferencesBurke, Brian. “Third Down Conversion Rate Can Mislead Coaches and Fans.” The WashingtonPost. The Washington Post, 10 Oct. 2012. Web. 06 Nov. 2012.<http://www.washingtonpost.com/blogs/football-insider/wp/2012/10/10/third-downconversion-rate-can-mislead-coaches-and-fans/>.Cafarelli, Ryan, Christopher J. Rigdon, and Steven E. Rigdon. “Models for Third DownConversion in the National Football League.” Journal of Quantitative Analysis in Sports8.3 (2012): 1-24. Print.11 AppendixTable 1: Summary StatisticwpctMeanStand.ErrorMedianModeStand.DeviationSampleVarianace0.5000.0200.5000.5000.1960.038ThirdDownConvertedTotalOffensiveYards0.384339.0000.0064.1590.3790.3330.0600.004336.650367.20040.7481660.371PPGTotalDefense21.8640.49122.10025.4004.81523.180340.3573.205339.350324.90031.399985.912%ThirdDownsConvertedAgainstDefensePPGAllowedbyDefenseStrength ofSchedule0.38322.0330.5000.0040.3650.0030.3830.39721.30020.8000.5000.4920.0413.5750.0250.00212.7820.001ReturnYardsGainedReturnsYardsAllowed23.3830.24623.30023.2002.4155.83223.5460.24923.45024.4002.4435.967ReturnTDsScored0.5210.0750.0000.0000.7400.547ReturnTDsAllowed0.521FirstDownsConvertedotherthanonThirdDowns186.3540.0742.1240.000186.7760.000#N/A0.72520.8120.526433.137PenaltyYards PerGame52.8310.97652.75043.1009.56191.411PassingPlays20+YardsGained47.9691.11647.00044.00010.936119.588TurnoverRatio-0.0211.0000.0001.0009.80196.063FGMadePerGame1.6390.0361.6001.4000.3570.128**Bold: data used in regression.12
Empirical ProjectYou will complete an empirical project. This project must apply regression analysis to a question involving the role of women in the economy.The 20% will be allocated in the following manner:Proposal: 2%Data Description: 2%Output: 3%5-10 page write-up: 13%Empirical ProjectKristopher Cramer and Keyur JoshiTemple University IntroductionEvery Sunday, football fans watch their favorite football teams duel on the gridiron tocomplete one objective: win. The objective for every sport is to win, and there are specific traitsthat point to a winning team. The most obvious way winning is defined is by how many points ateam scores. A team’s winning percentage proves which team has more wins. However, topredict if a team will be successful is a more difficult task. The goal of this study is to determinehow significant third down conversion percentage is to achieving a higher winning percentage.Our hypothesis is that the more efficient a team is on third downs, the more likely the team willhave a higher winning percentage. The results of this study could be important for coaches toknow so they can focus their practice time on third down situations. This paper also givesfootball fans another way to look at how successful their team will be through efficiency andappreciate their coaches and players that much more. Previous to this paper, there has beenlimited research done on this topic. From what we found, there has only been one study on thirddown conversion. The theoretical model in our paper denotes winning percentage as thedependent variable, and we assume that all teams try to maximize win and efficiency. In order totest our hypothesis in our empirical model, we chose eight variables and ran them in a regression.After running tThe regression, the results showed a strong correlation between a team’s thirddown conversion percentage and their respective winning percentage. In this paper, we willdiscuss a brief background of the topic and its research. We will then look at the model tounderstand the data and the theory behind the research. Based on that data and theory, our resultsare presented and explained based on the numbers.2 Literature ReviewThis study, as stated earlier, is trying towill determine if third down conversion iscorrelated with winning. What this means is if a team that can convert on third down moresuccessfully than the other teams in the league will translate into a higher winning percentage, allelse equal. There has been one study that we found which worked with third down conversionpercentage. However, this study lacked a certain aspect which was resolved in our study. Thestudy is from the Journal of Quantitative Analysis of Sports. This study shows that third downconversion is indicative of efficiency of the offense. The study was conducted by three scholars;Ryan Cafarelli, Christopher Rigdon, and Steven Rigdon. The research was based on severaldifferent data points. They found that third down conversion rate was not useful in knowing ifthe team’s offense was efficient. The data they used was offensive rank, defensive rank, andyards to first down. They used models to show that an average team defense can stop certainNFL teams and the longer the distance to the first down the less chance to convert to a first down(Cafarelli, Rigdon, and Rigdon 2012). They did the same format for an average offense toconvert on an NFL defense, and the results were similar. The longer the distance is, the harder itis to convert. They feel that the conversion rate is a meaningless measure of an efficient offense(Cafarelli, Rigdon, and Rigdon 2012). The flaw with this study is that it does not take intoaccount several different data points which that affect the success. Also, their dependent variable,of offensive efficiency, does not translate directly to wins. This study uses offensive efficiency asthe end result, but offensive efficiency is just another measure used to see if it can translate towins.The notion of third down conversion rate’s being misleading or meaningless is alsobelieved by Brian Burke, a writer for The Washington pPost, and the creator of the website3 Advanced NFL Stats. He wrote an article for the Post, Third down conversion rate can misleadcoaches and fans. In this article, he acknowledges that third down conversion is stronglycorrelated with overall success.; hHowever, he believes that a team is better off converting onfirst or second down (Burke, 2012). He suggests that a team should try to avoid third downswhenever possible (Burke, 2012). He believes this to be true because third downs are isolatedopportunities for a ten-yard conversion rather than trying to set up for a “manageable thirddown” (which is third down and 1 yard to go) (Burke, 2012). He uses the Redskins as anexample, because at the time he wrote, the article the Redskins were at the bottom of the leagueon third downs, however their overall series conversion rate was at the current league average of68%. This number indicates the Redskins were converting on first and second down. Burke’sarticle is one of the reasons why this study’s regression included the variable first downs gainednot on third down (Burke, 2012). This study falls short of the main point to understand that teamswill not be truly successful if they cannot make the tough third down conversions. Those teamswho do are considered elite. Our research shows that there is a strong correlation between thirddown and winning percentage.ModelTheoretical ModelIn this study, success is defined as a higher winning percentage in the regular season. Inorder to maximize winning percentage, a team must be efficient, especially on third downs. Thisidea is much like firms’ in the business world wanting to maximize worker efficiency. Thetheoretical model assumes that 32 NFL teams maximize wins and holding other variablesconstant to determine if a team’s third down conversion percentage is correlated with how4 successful a team is. Due to this, it is expected that when the regression is run, the results shouldyield a correlation between third down conversion percentage and winning percentage.EmpiricalThe basis for this study was to extrapolate data which we can hold constant for all teamsto see if the third down conversion rate correlated to wins. This data that was found was later putthrough a regression with the computer program Stata. The data that we used for this was thetotal defense yards, strength of schedule, return yards on kickoffs, offensive yards, first downconverted not on third down, turnover differential, and long passes. The data for total defense,strength of schedule, returns yards on kickoffs, and offensive yards wasere extracted fromESPN.com. Statistics gathered from NFL.com consisted of turnover differential and the 20 pluspassing plays. The main statistics of third down conversion rate wasere downloaded fromFootball Outsiders. All three of these websites are considered to be credible. ESPN.com is apremier website for all sports -related stats. NFL.com is affiliated with the NFL and thus iscredible. The website for Football Outsiders is a credible source as it is affiliated withESPN.com. The statistics on Football Outsiders is known for more advanced forms of statistics,which go beyond the raw numbers.The reasons we included the variables were based on two reasons, the outcome of thestatistical analysis and intuitive thinking. The third down conversion and winning percentagewere the obvious choice as were the variables that were important to see if our assumptions weretrue. The other variables, such as team offense and defense along with strength of schedule, putinto perspective the team’s chances of making that third down conversion. The long pass tookinto account those deep plays that a team needed to complete. This was important because mostteams that take these deep passes of more than 20 yards are those that are trailing and need to5 catch up quickly. Now, this is not perfectly true as some teams have their offense set around bigplays but this can account for most basic reasoning.The data that needed to be calculated was the first down converted, not on third down. Tobegin, the total first downs in the season needed to be found. Taken with the third downconversion rate, the first down converted not on third down was calculated. The formula wastotal first downs minus quantity total first downs times third down converted. This gave the firstdown converted on all other downs except third down, which controlled how exactly how manythird downs were completed for a first down.In tThe initial stages of this paper, it had sixteen different variables. They included pointsper game, percentage third downs converted against defense, points per game allowed bydefense, return yards allowed, return touchdowns scored, return touchdown allowed, penaltyyards per game and field goals made per game. Some of the data did not relate to the study orwould not help show if the data was relevant. This included all those statistics on with points(PPG, PPG Allowed, and Field Goals) These statistics were taken out, as they are already knownto be correlated with winning percentage and would take away the possible effects of third downconversion on winning percentage. Also, it is obvious that those teams that scored more wouldimprove their win percentage. Therefore, we did not include them in our study. Some of the otherdata such as penalties had no correlation with or was not statistically significant and decreasedthe adjusted R-squared when we ran the regression. The first regression was originally ninevariables, but was reduced to eight when we ran the final regression. Finally, some of the dataseemed to be repeated. The total defense that we used can be said to include some of the effectsof third down completed against defense statistics. For that reason, the decision was to include6 the variable that encompassed more information than just a part of the defense. Based on theseimplications, some variables were taken out to reflect a more accurate picture.There are several strengths to this our data that was used. As the results will show, it ishighly correlated. It also shows the recent trend as it shows data for the past three regularseasons. 2011 statistics might be skewed due to thea lockout, as the offseason did not allow formuch practice time.There are several shortcomings to this study. Since only three seasons of data were used,the sample size was under 100 (sample size was 96). The other issue is with the strength ofschedule variable and data for strength of schedule for the previous year. For example, weneeded to know the strength of schedule for 2009 we used 2010 since 2010 was based on theperformance of the 2009 team. This however, did not account for team turnover, such as differentplayers or change of coaches. The other possible shortcoming in this study is a possible variablethat was not taken into account. There is a chance that a key variable was overlooked or deemedunimportant. These shortcomings do not make the results any less significant, but means theresults can be further improved. A further summary of the raw data is provided in the Appendix.ResultsTable 2WinningCoef.Std. Err.T-ScoreP>t[95% conf.Inteval]PercentageThirdconvtotaldefenseschedretydkoydsfirstnoton3tovdiflongpass_cons0.843814-0.00094-0.446380.0059130.0012240.0020160.009303-0.00269-0.077730.2991920.0003970.4710210.0048870.0007010.0009540.0012830.0013790.3483052.82-2.38-0.951.211.752.117.25-1.95-0.220.249138-0.00173-1.38259-0.0038-0.000170.0001190.006754.-0054331-0.770021.43849-0.00015480.4898260.01562610.00261720.00261720.01185240.00004660.6145656Table 37 SourceSSdfMSNumber of obs =ModelResidual2.631387910.9991816768870.3289230.01148596F ( 8,87) = 28.64Prob > F = 0.0000R – Squared = .Total3.63056958950.0382177248Adj R-squared = .6995Root MSE = .10717The results of the Ordinary Least Squares (OLS) regression showed that third downconversion percentage was found to be statistically significant at the t score of 2.82 p < .05. Inaddition, the correlation coefficient for third down conversions was found to be .843814.Theadjusted R-squared of this study regression was .6995. This number indicates that the results ofthis study are pretty accurate when predicting future outcomes on the basis of other relatedinformation as well as how well a the regression line fits the data. Since the highest value foradjusted R-squared possible is 1, .6995 indicates that the relationship between winningpercentage and third down conversion is fairly grouped around a best fit line. This result matchesthe study’s hypothesis that the higher the team’s third down conversion percentage, the morelikely the team is to win a game. These results make sense because the more efficient a team ison third down, the more first downs the team has. When they have more first downs, they areable to run more plays and establish longer drives. Being more efficient gives a team moreopportunities to score more points.The results of the regression also showed that a second variable, strength of schedule wasfound to be not statistically significant at the p <.05 level, although there was a negativecorrelation at .44. This result makes sense because the better the opposing team the harder it is8 to win a game, however the strength of the opposing team does not mean that much for it tomake a meaningful difference in a team’s winning percentage.ConclusionsBased on oOur findings, we would suggest that football teams should focus on their thirddown conversion percentage because it correlates with a higher winning percentage. Headcoaches and coordinators should stress to their players that efficiency on third down is veryimportant and a crucial part of the game. Teams should also try to draft and sign players who arebetter at gaining yards after catch or hard runners to push for the extra yard.Based on the results, third down conversion percentage is correlated with winningpercentage. When comparing our results to previous research, iIt appears our results differ fromBurke’s beliefs and the results of Ryan Cafarelli, Christopher Rigdon, and Steven Rigdon. WhileBurke believed there is a strong correlation between third downs and winning percentage, hebelieved that teams should be focused on first and second down (Burke, 2012). Because hebelieved this, we accounted for that variable in our regression and the result was a coefficient of .0020159 and a t score of 2.11. If he claims were to be true, the correlation coefficient should begreater, thus being more indicative of winning percentage.To say the least, oOur study is not perfect and there are ways to improve it. Possibleimprovements to our study could beare checking the variables over more than just three seasons.Our study only encompasses three seasons, which came out to 96 games. Also, it is very possiblewe missed an important variable. Our regression only included 8 variables based on the statisticswe thought were of importance to this study, which also kept our adjusted R square fromdecreasing. The inclusion of more variables should definitely be included. While this study is not9 totally conclusive and not perfect, it still shows a strong correlation between winning percentageand third down conversion percentage.There were some problems with presenting the regression results and one or two problems withinterpreting them, but, overall, I like what you did. The writing could use some attention.9210 ReferencesBurke, Brian. “Third Down Conversion Rate Can Mislead Coaches and Fans.” The WashingtonPost. The Washington Post, 10 Oct. 2012. Web. 06 Nov. 2012.<http://www.washingtonpost.com/blogs/football-insider/wp/2012/10/10/third-downconversion-rate-can-mislead-coaches-and-fans/>.Cafarelli, Ryan, Christopher J. Rigdon, and Steven E. Rigdon. “Models for Third DownConversion in the National Football League.” Journal of Quantitative Analysis in Sports8.3 (2012): 1-24. Print.11 AppendixTable 1: Summary StatisticwpctMeanStand.ErrorMedianModeStand.DeviationSampleVarianace0.5000.0200.5000.5000.1960.038ThirdDownConvertedTotalOffensiveYards0.384339.0000.0064.1590.3790.3330.0600.004336.650367.20040.7481660.371PPGTotalDefense21.8640.49122.10025.4004.81523.180340.3573.205339.350324.90031.399985.912%ThirdDownsConvertedAgainstDefensePPGAllowedbyDefenseStrength ofSchedule0.38322.0330.5000.0040.3650.0030.3830.39721.30020.8000.5000.4920.0413.5750.0250.00212.7820.001ReturnYardsGainedReturnsYardsAllowed23.3830.24623.30023.2002.4155.83223.5460.24923.45024.4002.4435.967ReturnTDsScored0.5210.0750.0000.0000.7400.547ReturnTDsAllowed0.521FirstDownsConvertedotherthanonThirdDowns186.3540.0742.1240.000186.7760.000#N/A0.72520.8120.526433.137PenaltyYards PerGame52.8310.97652.75043.1009.56191.411PassingPlays20+YardsGained47.9691.11647.00044.00010.936119.588TurnoverRatio-0.0211.0000.0001.0009.80196.063FGMadePerGame1.6390.0361.6001.4000.3570.128**Bold: data used in regression.12
