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# Investigate the correlation between the field goals attempted (FGA) and field goals made (FGM) of 50 different basketball players in NBA.

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Introduction

Philip Ng                                                                                                        25/03/2003

Statistics 2 Coursework

Aim

In my coursework, I am going to investigate the correlation between the field goals attempted (FGA) and field goals made (FGM) of 50 different basketball players in NBA.

It is worth to do because it will prove if the players attempt more field goals, whether he will get more points or not. Furthermore, the accuracy of shooting is dependent on many factors, such as the performance of players, home and away match, the shooting distance, the player’s position. To consider these factors, the percentage of field goals should be different from each NBA players. Also, it is useful to discuss whether a player will get more points if he makes more shootings in the games. Because it is necessary for the coach to know whether a reliable player will keep his accuracy on shooting even if his field goals attempted is large, and to find out whether it is easier to get points inside rather than outside in the basketball court. This is the important factor to win the match.

Data Collecting

The data is collected from NBA 2003 league. There are totally 476 players in NBA, and 29 teams, 65 international players from 34 countries.

As I only need 50 sampling, so I choose my 50 sampling randomly from different teams. In my sampling, it contains Centre, Power Forward, Small Forward, Shooting Guard, and Point Guard. Field goals attempted (FGA)

Middle

763

355

Chris Webber ( Sacramento Kings)

1,069

496

Antawn Jamison ( Golden State Warriors)

1,110

515

Donyell Marshall ( Chicago Bulls)

788

365

Amare Stoudemire ( Phoenix Suns)

650

301

Karl Malone ( Utah Jazz)

1,026

475

Kenyon Martin ( New Jersey Nets)

859

397

Mike Bibby ( Sacramento Kings)

520

240

Predrag Stojakovic ( Sacramento Kings)

804

371

Steve Nash ( Dallas Mavericks)

859

396

554

255

Lorenzen Wright ( Memphis Grizzlies)

571

262

Kerry Kittles ( New Jersey Nets)

534

245

Tony Parker ( San Antonio Spurs)

802

367

1,454

665

Drew Gooden ( Orlando Magic)

712

324

Richard Hamilton ( Detroit Pistons)

990

450

634

288

Kobe Bryant ( Los Angeles Lakers)

1,520

689

Corliss Williamson ( Detroit Pistons)

638

289

Scottie Pippen ( Portland Trail Blazers)

582

262

Juwan Howard ( Denver Nuggets)

992

446

Gary Payton ( Milwaukee Bucks)

1,197

537

Desmond Mason ( Milwaukee Bucks)

794

355

Gilbert Arenas ( Golden State Warriors)

895

398

Modelling procedures

In the case of the data in my sample, there are two variables, FGA and FGM. This is an example of bivariate data, where each item in the population requires the values of two variables. The best way I can do to present these data is to plot a scatter diagram. However, I have to decide which variable is independent and which is dependent. The independent one is going to be x-axis, and the dependent one is going to be y-axis. Anyway, it is very obvious in my sample that FGA must be independent, because the player has to attempt the field goal for the field goal made in the game. So FGA is my x-axis, and FGM is my y-axis.

Conclusion

As a result, my data are in good quality.

However, there ae some possible sources of error, which may have affected my data.

From the scatter diagram, it shows that there are outliers in my sample, we regard these as outlier because these two sample are far awasy from the group of data. These outlier may make the correlation becomes more positive. The correlation may get closer to +1.

And from my data source, they are collected from NBA league. However, I think that I can improve the data, by collecting the sample which is not only from NBA league, but also in the other countries, like Britain or China. Because NBA, the league in Britain or China are at different level, it is clear that NBA players are much better than the players in China. So ensure that FGM(field goals made) is based on FGA(field goals attempted), without considering the ability of players, the best way to do is to collect the data from more different leagues. Also, to take even more sample to ensure that the sample is really large enough to represent its parent population. Finally, the data should be collected from the professional players only, this is also the restriction. Because only the professional players can keep his accuracy from time to time. We should not collect the data from the junior basketball match, like inter-house basketball in the school, but the large league like NBA or universities league.

This student written piece of work is one of many that can be found in our AS and A Level Probability & Statistics section.

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