Millar,+P


 * DATA MANAGEMENT CULMINATING TASK**

Is there a relationship between NBA player’s salaries and how efficient they are for their teams during the course of their contracts?
 * QUESTION**

When choosing this topic I thought to myself that it would make the most sense to choose something that I am interested in. I have been a fan of basketball and the NBA for years now and I thought this would be a great topic because it is a topic that one can easily access information too, and it is a topic that I would enjoy looking up information for and I would find it interesting.
 * HOW I CHOSE MY CULMINATING TASK TOPIC**



I believe that yes, there is a strong correlation between how much an NBA player is paid and their productivity towards their team during the duration of their contracts.
 * HYPOTHESIS:**

· The more productive and valuable a player is to his team, the larger his contract · Some players are more helpful to their teams in other areas other than scoring (Rebounding, Defense, Playmaking abilities etc.) and receive a large contract because of how valuable they can be to their team in these areas

Because NBA players are all diverse and have strengths and differences in different areas, I will look into their overall player efficiency ratings to determine how productive a player is to their team. The NBA efficiency statistic is a combination of all the recorded statistics in an NBA game both positive and negative. The formula for the player efficiency rating is: [(Points + Rebounds + Steals+ Assists + Blocks) – (Field Goals Att. – Field Goals Made + (Free Throws Att. - Free Throws Made) + Turnovers] = PER

NBA seasons that I will be looking at to prove the correlation are as followed:

· 2008-2009 NBA season · 2009-2010 NBA season

To prove my statement I will take the top 20 earning players over the past two NBA seasons and their graph them to see if their player efficiency ratings show that they are deserving of their contracts. I will repeat this and graph the player efficiency ratings over the past two NBA seasons to see if there is a trend in the data.

Top 20 earning players of the 2008-2009 NBA season and their player efficiency ratings: Miami Heat || 15.4 || Detroit Pistons || 15.8 || Toronto Raptors || 16.0 || Top 20 earning players of the 2009-2010 NBA season and their player efficiency ratings: New York Knicks || 12.2 || * Player is in the final year of their contract * Player traded during the course of season * Player was waived/ released during the course of the season
 * DATA**
 * || **Player** || **Salary** || **Team** || **PER** ||
 * 1 || Kevin Garnett * || $24,751,934 || Boston Celtics || 21.2 ||
 * 2 || Jason Kidd * || $21,372,000 || Dallas Mavericks || 16.9 ||
 * 3 || Jermaine O’Neal || $21,372,000 || Toronto Raptors-
 * 4 || Kobe Bryant* || $21,262,500 || Los Angeles Lakers || 24.4 ||
 * 5 || Shaquille O’Neal* || $21,000,000 || Phoenix Suns || 22.3 ||
 * 6 || Allen Iverson * || $20,840,625 || Denver Nuggets-
 * 7 || Stephon Marbury * * || $20,840,625 || New York Knicks || N/A ||
 * 8 || Tim Duncan* || $20,598,704 || San Antonio Spurs || 24.4 ||
 * 9 || Tracy McGrady || $20,370,437 || Houston Rockets || 16.9 ||
 * 10 || Ray Allen || $18,388,430 || Boston Celtics || 17.3 ||
 * 11 || Dirk Nowitzki* || $18,077,904 || Dallas Mavericks || 23.1 ||
 * 12 || Paul Pierce || $18,077,904 || Boston Celtics || 17.7 ||
 * 13 || Shawn Marion * || $17,810,000 || Miami Heat-
 * 14 || Rashard Lewis || $16,447,871 || Orlando Magic || 16.8 ||
 * 15 || Michael Redd || $15,780,000 || Milwaukee Bucks || 17.9 ||
 * 16 || Yao Ming* || $15,106,000 || Houston Rockets || 22.7 ||
 * 17 || Pau Gasol* || $15,106,000 || Los Angeles Lakers || 22.2 ||
 * 18 || Andrei Kirilenko || $15,070,550 || Utah Jazz || 16.8 ||
 * 19 || Amare Stoudemire || $15,070,550 || Phoenix Suns || 20.3 ||
 * 20 || Mike Bibby * || $14,983,603 || Atlanta Hawks || 16.3 ||
 * || **Player** || **Salary** || **Team** || **PER** ||
 * 1 || Tracy McGrady * * || $23,239,562 || Houston Rockets-
 * 2 || Kobe Bryant* || $23,034,375 || Los Angeles Lakers || 21.9 ||
 * 3 || Jermaine O’Neal * || $23,016,000 || Miami Heat || 17.9 ||
 * 4 || Tim Duncan* || $22,183,220 || San Antonio Spurs || 24.7 ||
 * 5 || Shaquille O’Neal * || $20,000,000 || Cleveland Cavaliers || 17.9 ||
 * 6 || Dirk Nowitzki* || $19,795,714 || Dallas Mavericks || 22.9 ||
 * 7 || Paul Pierce || $19,795,712 || Boston Celtics || 18.2 ||
 * 8 || Ray Allen || $18,876,860 || Boston Celtics || 15.2 ||
 * 9 || Rashard Lewis || $18,876,000 || Orlando Magic || 14.0 ||
 * 10 || Michael Redd || $17,040,000 || Milwaukee Bucks || 12.1 ||
 * 11 || Pau Gasol* || $16,452,000 || Los Angeles Lakers || 22.9 ||
 * 12 || Andrei Kirilenko || $16,452,000 || Utah Jazz || 18.2 ||
 * 13 || Kevin Garnett || $16,400,000 || Boston Celtics || 19.4 ||
 * 14 || Yao Ming || $16,378,325 || Houston Rockets || N/A ||
 * 15 || Amare Stoudemire* * || $16,378,325 || Phoenix Suns || 22.6 ||
 * 16 || Gilbert Arenas || $16,192,080 || Washington Wizards || 18.7 ||
 * 17 || Carmelo Anthony* || $15,779,912 || Denver Nuggets || 22.2 ||
 * 18 || Chris Bosh* * || $15,779,912 || Toronto Raptors || 25.0 ||
 * 19 || Dwayne Wade* * || $15,779,912 || Miami Heat || 28.0 ||
 * 20 || LeBron James* * || $15,779,912 || Cleveland Cavaliers || 31.1 ||
 * *Player is in the Top 20 PER for that season

Upon looking at these results you may notice that the highest payed players do not have the highest efficiency ratings of the other players. Also you may notice that only some of the top 20 PER players are included in the top 20 players with the highest salaries. This means that there are several other more productive players in the league that are playing on a much smaller contracts. Some factors however, that may affect a players efficiency rating throughout the season may include, the player is in the final year of their contract, a player was traded during the course of the season, and that a player was waived during the course of the season. I thought that this is important information to list because when a player is in their final contract year, that means that they are in some cases going to be less productive then they were at the time of recieving their contracts. For example, Jermaine O'Neal and Tracy McGrady, were given their current contracts years ago when they were much more productive then they are today. This was due to their increasing age, and several injuries that have affected their play throughout the years. However, this is not the case for younger players such as LeBron James, Dwayne Wade and Chris Bosh who have not reached their full potential as players yet. The three are also the highest out of the 20 on the list for their PER ratings in 2009-2010.
 * ANALYSIS**

I do not have both Stephon Marbury or Yao Ming's PER rating listed on the tables because they both did not play a game for their teams during the season. Stephon Marbury was released by his team during the season and Yao Ming was out with an injury.



2008-2009 NBA Season
 * Player || Salary || PER || Salary (x-μ) || Salary (x-μ)2 || PER (x-μ) || PER (x-μ)2 ||
 * Kevin Garnett || $24,751,934 || 21.2 || $6,135,552.15 || $37,645,000,185,369.60 || 2.98 || 8.8804 ||
 * Jason Kidd || $21,372,000 || 16.9 || $2,755,618.15 || $7,593,431,388,609.41 || -1.32 || 1.7424 ||
 * Jermaine O’Neal || $21,372,000 || 15.4 || $2,755,618.15 || $7,593,431,388,609.41 || -2.82 || 7.9524 ||
 * Kobe Bryant || $21,262,500 || 24.4 || $2,646,118.15 || $7,001,941,263,759.42 || 6.18 || 38.1924 ||
 * Shaquille O’Neal || $21,000,000 || 22.3 || $2,383,618.15 || $5,681,635,485,009.42 || 4.08 || 16.6464 ||
 * Allen Iverson || $20,840,625 || 15.8 || $2,224,243.15 || $4,947,257,590,321.92 || -2.42 || 5.8564 ||
 * Stephon Marbury || $20,840,625 || N/A || $2,224,243.15 || $4,947,257,590,321.92 || N/A || N/A ||
 * Tim Duncan || $20,598,704 || 24.4 || $1,982,322.15 || $3,929,601,106,380.62 || 6.18 || 38.1924 ||
 * Tracy McGrady || $20,370,437 || 16.9 || $1,754,055.15 || $3,076,709,469,241.52 || -1.32 || 1.7424 ||
 * Ray Allen || $18,388,430 || 17.3 || -$227,951.85 || $51,962,045,918.42 || -0.92 || 0.8464 ||
 * Dirk Nowitzki || $18,077,904 || 23.1 || -$538,477.85 || $289,958,394,940.62 || 4.88 || 23.8144 ||
 * Paul Pierce || $18,077,904 || 17.7 || -$538,477.85 || $289,958,394,940.62 || -0.52 || 0.2704 ||
 * Shawn Marion || $17,810,000 || 16.0 || -$806,381.85 || $650,251,688,009.43 || -2.22 || 4.9284 ||
 * Rashard Lewis || $16,447,871 || 16.8 || -$2,168,510.85 || $4,702,439,306,567.73 || -1.42 || 2.0164 ||
 * Michael Redd || $15,780,000 || 17.9 || -$2,836,381.85 || $8,045,061,999,009.43 || -0.32 || 0.1024 ||
 * Yao Ming || $15,106,000 || 22.7 || -$3,510,381.85 || $12,322,780,732,809.40 || 4.48 || 20.0704 ||
 * Pau Gasol || $15,106,000 || 22.2 || -$3,510,381.85 || $12,322,780,732,809.40 || 3.98 || 15.8404 ||
 * Andrei Kirilenko || $15,070,550 || 16.8 || -$3,545,831.85 || $12,572,923,508,474.40 || -1.42 || 2.0164 ||
 * Amare Stoudemire || $15,070,550 || 20.3 || -$3,545,831.85 || $12,572,923,508,474.40 || 2.08 || 4.3264 ||
 * Mike Bibby || $14,983,603 || 16.3 || -$3,632,778.85 || $13,197,082,173,007.30 || -1.92 || 3.6864 ||
 * MEAN || $18,616,381.85 || 18.22 || SUM || $159,434,387,952,585.00 || SUM || 197.1236 ||
 * MEDIAN || $18,233,167 || 17.7 || /20 || $7,971,719,397,629.23 || /20 || 9.85618 ||
 * MODE || $21,372,000 || 16.9 || STANDARD DEV. || 2823423.347 || STANDARD DEV. || 3.139455367 ||
 * MAXIMUM || $24,751,934 || 24.4 || VARIANCE || 7.97172E+12 || VARIANCE || 9.85618 ||
 * MINIMUM || $14,983,603 || 15.4 ||  ||   ||   ||   ||

2009-2010 NBA Season
 * Player || Salary || PER || Salary (x-μ) || Salary (x-μ)2 || PER (x-μ) || PER (x-μ)2 ||
 * Tracy McGrady || $23,239,562 || 12.2 || $4,878,070.95 || $23,795,576,193,233.90 || -7.1 || 49.773025 ||
 * Kobe Bryant || $23,034,375 || 21.9 || $4,672,883.95 || $21,835,844,410,167.60 || 2.6 || 6.996025 ||
 * Jermaine O’Neal || $23,016,000 || 17.9 || $4,654,508.95 || $529,736,256,000,000 || -1.4 || 1.836025 ||
 * Tim Duncan || $22,183,220 || 24.7 || $3,821,728.95 || $492,095,249,568,400 || 5.4 || 29.648025 ||
 * Shaquille O’Neal || $20,000,000 || 17.9 || $1,638,508.95 || $400,000,000,000,000 || -1.4 || 1.836025 ||
 * Dirk Nowitzki || $19,795,714 || 22.9 || $1,434,222.95 || $391,870,292,769,796.00 || 3.6 || 13.286025 ||
 * Paul Pierce || $19,795,712 || 18.2 || $1,434,220.95 || $391,870,213,586,944.00 || -1.1 || 1.113025 ||
 * Ray Allen || $18,876,860 || 15.2 || $515,368.95 || $356,335,843,459,600.00 || -4.1 || 16.443025 ||
 * Rashard Lewis || $18,876,000 || 14.0 || $514,508.95 || $356,303,376,000,000.00 || -5.3 || 27.615025 ||
 * Michael Redd || $17,040,000 || 12.1 || -$1,321,491.05 || $290,361,600,000,000.00 || -7.2 || 51.194025 ||
 * Pau Gasol || $16,452,000 || 22.9 || -$1,909,491.05 || $270,668,304,000,000.00 || 3.6 || 13.286025 ||
 * Andrei Kirilenko || $16,452,000 || 18.2 || -$1,909,491.05 || $270,668,304,000,000.00 || -1.1 || 1.113025 ||
 * Kevin Garnett || $16,400,000 || 19.4 || -$1,961,491.05 || $268,960,000,000,000.00 || 0.1 || 0.021024999 ||
 * Yao Ming || $16,378,325 || N/A || -$1,983,166.05 || $268,249,529,805,625.00 || N/A || N/A ||
 * Amare Stoudemire || $16,378,325 || 22.6 || -$1,983,166.05 || $268,249,529,805,625.00 || 3.3 || 11.189025 ||
 * Gilbert Arenas || $16,192,080 || 18.7 || -$2,169,411.05 || $262,183,454,726,400.00 || -0.6 || 0.308025 ||
 * Carmelo Anthony || $15,779,912 || 22.2 || -$2,581,579.05 || $249,005,622,727,744.00 || 2.9 || 8.673025 ||
 * Chris Bosh || $15,779,912 || 25.0 || -$2,581,579.05 || $249,005,622,727,744.00 || 5.7 || 33.005025 ||
 * Dwayne Wade || $15,779,912 || 28.0 || -$2,581,579.05 || $249,005,622,727,744.00 || 8.7 || 76.475025 ||
 * LeBron James || $15,779,912 || 31.1 || -$2,581,579.05 || $249,005,622,727,744.00 || 11.8 || 140.304025 ||
 * MEAN || $18,361,491.05 || 19.3 || SUM || $5,835,410,289,043,530.00 || SUM || 434 .34145 ||
 * MEDIAN || $16,746,000 || 19.4 || /20 || $291,770,514,452,177.00 || /20 || 21.7170725 ||
 * MODE || $15,779,912 || 17.9 || STANDARD DEV. || 17081291.36 || STANDARD DEV. || 4.660157991 ||
 * MAXIMUM || $23,239,562 || 31.1 || VARIANCE || 2.91771E+14 || VARIANCE || 21.7170725 ||
 * MINIMUM || $15,779,912 || 12.1 ||  ||   ||   ||   ||

Throughout my research, I only used the past two NBA seasons, so I cannot really say that because of what had occured in these specific seasons happened other past NBA seasons. Also, one might say that some people would be underepresented because I used an arguably small sampling size of 20 players. Some ways I could have eliminated these biases are that I could have looked at players seasons in other past seasons to see if there is still a relationship, or I could have taken more than 20 players with the highest salaries and PER ratings.
 * BIAS**

Upon looking at my research, I can say that I was wrong when determining my hypothesis. And I can say that its not always true that the most skilled and productive players recieve the best contract. Here are some reasons why some of these players may be undeserving of their contracts:
 * CONCLUSION**

- Players could have been substantially better and more productive when they recieved their contract - Team could have offered a player that is not very skilled a larger contract by poorly judging his potential - Team could have offered a player a contract just for the sake of them to stay with the team - Team could have willingly taken on a larger contract to use in another trade or as cap relief once that players contract is up - Team could have willingly taken on a larger contract in a trade - Player could have been significantly injured during the course of the contract - Player could have been unhappy with the current situation the team is in and therefore not playing to his full potential

1.) "2005-06 NBA Leaders." //Basketball Reference//. N.p., 2006. Web. 17 Nov. 2010. 2.) "2006-07 NBA Leaders." //Basketball Reference//. N.p., 2007. Web. 17 Nov. 2010. 3.) "2007-08 NBA Leaders." //Basketball Reference//. N.p., 2008. Web. 17 Nov. 2010. 4.) "2008-09 NBA Leaders." //Basketball Reference//. N.p., 2009. Web. 17 Nov. 2010. 5.) "2009-10 NBA Leaders." //Basketball Reference//. N.p., 2010. Web. 17 Nov. 2010. 6.) "NBA Salaries." //HoopsVibe//. N.p., 2007. Web. 17 Nov. 2010. 7.) "NBA Salaries." //Inside Hoops//. N.p., 2010. Web. 17 Nov. 2010. 8.) "Top 20 NBA Salaries 2009-10." //Sporcle//. N.p., 2010. Web. 17 Nov. 2010.
 * BIBLIOGRAPHY**