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Abstract
In American football, an efficient quarterback is key in scoring and winning a game.T his study sought to test whether a higher quarterback efficiency value could possibly determine the chance of a probable hall of fame selection based on a TSER scale or a possible team winning record during the regular season This study was conducted based on ten African American Quarterbacks in the NFL based on a touchdown-to-sack efficiency equation. T. The ten quarterbacks selected for research were from a variety of decades from the late 1970s to the early 2010s and a sixteen game season was used as well. For each, their efficiency trend and mean, were calculated to determine a final efficiency value for their career. The touchdown-to-sack-efficiency equation was used to display the trends in how many total touchdowns were scored by the quarterbacks compared to how many times they were sacked. The higher values based on the data, were approximately around 8 to 16.2, Daunte Culpepper having the highest value. The overall data in this research was varied since the quarterback played for different teams and played with different styles of offense. This study could also be used for future determination in deciding a fixed salary for the players based on performance or can be a derivative in determining quarterback performance.

Keywords: TSER, African American Quarterbacks, Performance, NFL
Introduction 
Statistical analysis is an important aspect when it comes to sports ((Stimel, 2009)). Numbers or statistics can sometimes determine  how many yards were gained 
or lost, or how many points were scored ((Gober, 2009)). In American football, team efficiency is critical in scoring and winning a game, especially for an offense (Berri, 2012). If your offense cannot score on a consistent basis, you cannot win. On a football team, a good offense and an efficient quarterback is pivotal, especially if there is an African American quarterback at the helm ((Ingraham, 2005)). In the case of African American quarterbacks, some analysts are skeptical in determining black quarterback success in the NFL, because they were projecting whether that this race of quarterback would draw more fans to the stadiums or not. That led to some successful African American quarterbacks in college to change positions in the NFL or were deliberately drafted in later rounds or played Canadian Football ((Buffington, 2005)).
For example, In April of 1999, three African American quarterbacks were chosen in the first round of the NFL’s annual draft. Up to that point, only four African American quarterbacks had been first round draft picks in the draft’s entire history ((Buffington, 2005)). This experiment will hopefully change the standpoint of black NFL quarterbacks potential success to the NFL by comparing current African American NFL quarterbacks.
This study was conducted based on ten NFL African- American quarterbacks based on a created TSER (touchdown-to-sack efficiency rating) equation. In this study, based on ten African- American NFL quarterbacks, study tested, whether a certain TSER Value (10.0 or higher) based on the TSER Value Scale, can determine if they can earn a possible Hall of Fame selection. This information hopefully will display the varied efficiencies of the quarterbacks and can determine their efficiency success rating based on the TSER Value Scale. This also showed African American quarterbacks should not be overlooked in the NFL Draft ((Simmons, 2009)).
Methods
This study was conducted by using ten African American NFL quarterbacks from different decades, ranging from the early 1970s to the late 2010s. The determination of the quarterbacks was based on overall career  statistics with respect to number of times sacked  and approximately 100 touchdowns scored. 
The quarterbacks who were selected were: Kordell Stewart (KS), Daunte Culpepper (DC), David Garrard (DG), Steve McNair (SM), Donovan McNabb (DM), Aaron Brooks (AB), Doug Williams (DW), Warren Moon (WM), Randall Cunningham (RC), and Jeff Blake (JB).   African -American Quarterbacks were also used because there was a limited number of them in the NFL who started and there were very few successful ones with a significant amount of statistical data with respect to number of times sacked and touchdowns scored. These statistical data available were varied based on the decade they played in and the team’s style of offense. 
The data came from Pro-Football-reference and Database Football. Also, for further reference, The Official NFL Fact and Record Book was also used (NFL editors, 2009, 2008, & 2007).  The yearly TSER values of the quarterbacks were compiled in order to be compared and their career TSER value was calculated to determine their overall efficiency success. 
The equation for all the data sets to determine the TSER value was T²/S + NP= TSER. The T² value was used in the numerator to represent the number of total touchdowns by the quarterback and the S + NP in the denominator represented how many times quarterback were sacked plus the sixteen game season. With these values, standard deviation and other central tendency data values were calculated.
The years in which the quarterbacks played less than 7 games were not totaled into the career TSER value, but they were still calculated to show any trends.  The data sets were numbered 1-17, representing the number of years played and only one Warren Moon, played 17 years. All the quarterbacks were set to 17 years, even if they did not play that long and because it stay constant throughout the study. The players did not play that corresponding year received a N/A or not applicable symbol and that data was calculated in their TSER value. Meta-Chart was also used to develop a box and whisker plot and a scatterplot. Also, a scale range called the TSER Value scale  was created to determine their efficiency success according to their TSER Value. . This a randomization of numbers in the scale. This scale can be further illustrated in the results  in table 1.
Results 
In this study, The quarterbacks’ values fell between 5.00 and 18.99 on the TSER Value Scale, which means that their efficiency success correlated to either an average or good career. The scale determines their efficiency success under certain categories which coincides with the values.  

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Figure 2  displays the values from figure 1 in a histogram.

Figure 3 represents the quarterbacks’ career TSER Values. The average is 11.06 which shows most of the quarterbacks were average or had a good career. Quartile 1 or 25% of the data fell under or at 8.63. Quartile 3 or 75% of the data fell under 12.4.

Figure 5  Illustrates the TSER equation that was used to determine TSER values. The T^2 is the total touchdowns squared. The S represents sacks plus NP which is number of games played. Only the seasons in which quarterbacks played a minimum of 8 games, were calculated which determined their overall career efficiency value.
Discussion/Conclusion
The lowest value recorded in the data was David Garrard, with a career TSER value of 8.28 and the highest was by Daunte Culpepper with a value of 16.2. In Data set #1, the quarterbacks’ TSER values, fell between 0.00-5.40, because it was the their rookie seasons and they lacked the experience. After their first year, their TSER values showed significant increase due to experience at the position and playing more games. Donovan McNabb, Doug Williams, Aaron Brooks, and Daunte Culpepper had the highest TSER values for data set #2.  Their values increased to 11.9, 17.4, 11, and 32, respectively. Warren Moon and Donovan McNabb were the most consistent longevity wise. Warren Moon was the only quarterback to reach a TSER value of twenty or above three times (data set # 5, 7, and 12). On the other hand, not all the quarterbacks stayed consistent throughout their career, some fluctuated significantly. 
David Garrard had only two TSER values above ten twice, but he only played seven significant years, due to injury. In seven significant years, Kordell Stewart had only one TSER value above twenty, and his values declined after the third year, due to increase lack of confidence. Also, after Daunte Culpepper’s second year, his TSER Value dropped 23.8 TSER points, due to a crucial knee injury and holding onto to the ball too long. . There was about a +/- of 3 touchdowns scored, that could have affected the values of the quarterbacks. Randall Cunningham had the highest seasonal value of 35.0 in data set #13, due to a change in teams and offensive line play. Cunningham’s values were mainly dictated by his offensive linemen because TSER values would have been consistently higher if he played with better support. In Cunningham’s second season, he had the lowest TSER value of 1.94, due to getting sacked seventy-two times that year. As far as Jeff Blake, he had similar issues comparable to Randall Cunnigham. Even though Blake was a superb runner, which boosted his TSER values, his inconsistency in his TSER values was due to poor team performance and lack of a strong receiving corp. Doug Williams and had similar results like Randall Cunningham: lack of team performance. Steve McNair’s values were consistent to a certain degree, but injury skewed his TSER points.
The TSER values overall supported the stated hypothesis. Comparing touchdowns to sacks determined the overall performance. The values are not just representative of quarterback performance, but also team success. The ability to make good decisions and the ability to be a dual-threat (the ability to pass and run effectively) could increase the values of the quarterbacks. Also, great pass protection and great team performance affected the values as well by observing the team’s offensive ranks per season and their overall record. Avoiding injury is another pivotal factor that affected performance. These values were indirectly proportional. 
If a quarterback was sacked more than he scored, then his value was lower Although, if a quarterback scored more than he was sacked, then his value was higher. Finally, this study may  help to change opinions on how analysts view black quarterbacks because the TSER index could be used in college to predetermine their success. The TSER index could be used for future determination in deciding a fixed salary, based on performance. The index can also be used as a derivative in order to determine a quarterback performance rating, which then could be adjusted to compare to other performance algorithms.The probability of team success-how well a team could perform that season- could be calculated by using this index. The TSER value scale and the index could also be used in college football and by NFL draft analysts to determine the most efficient quarterbacks. Finally, the TSER values could be used as a validation check of their actual performance, by comparing their stats from that season and concluding on their performance level.
Acknowledgements
I will like to thank my father, for being a great mentor and helping with this arduous project of mine. 
Literature Cited

Berri, D. J., & Simmons, R. (2009). Race and the evaluation of  signal callers in the National Football League. Journal of Sports Economics, 10(1), 23-43.
Bigler, M., & Jeffries, J. L. (2008). “An Amazing Specimen”: NFL Draft Experts’ Evaluations of Black Quarterbacks. Journal of African American Studies, 12(2), 120-141.
Buffington, D. (2005). Contesting race on Sundays: Making meaning out of the rise in the number of Black quarterbacks. Sociology of Sport Journal, 21(1), 19-37.
Ingraham, A.T. (2005). A Methodology for Evaluating Production in Football: An Armchair Quarterback’s Rating System. Available at SSRN 742725.
NFL Editors (2007) NFL Record and Fact Book 2007 (official NFL Record & Fact Book). New York, NY: Time Home Entertainment.
NFL Editors (2008) NFL Record and Fact Book 2008 (official NFL Record & Fact Book). New York, NY: Time Home Entertainment.
NFL Editors (2009) NFL Record and Fact Book 2009 (official NFL Record & Fact Book). New York, NY: Time Home Entertainment.
Stimel, D. (2009). A statistical analysis of NFL quarterback rating variables. Journal of Quantitative Analysis in Sports, 5(2).

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