1. The Boston Celtic’s current star, Paul Pierce versus the Boston Celtic’s legend Larry Bird. Which player is the greatest pure scorer in Celtics history? By: Tom Schlesinger-Guidelli Introduction: On April 20, 2003 the Boston Celtics played the Indiana Pacers in the first round of the 2003 NBA Playoffs. In this first game at Conseco Fieldhouse in Indianapolis Celtics star Paul Pierce, number 34, scored 40 points to lead the Celtics to a 103-100 victory. The next day Boston Globe sports columnist discussed Pierces' amazing game. In this article Bob Ryan, who has covered the Celtics for the last 24 years, said “Ready for some heresy? Paul Pierce may be the greatest pure scorer the Celtics have ever had.” This is as one can imagine a statement that created much outrage in Celtic country. A team that has one 16 championships in its history and yet its best pure scorer has yet to win a championship? Larry Bird, number 33, many would argue is the greatest scorer the Celtics have ever had. He led the Celtics to three championships in his 13 years with the team. He put up amazing numbers and as Ryan admits later in the article Bird was the best all-around player in Celtic’s history. “This isn’t about who the best Celtics player was, or is. Bill Russell was the greatest winner in the history of American professional sport. No one ever had a more plentiful and direct correlation between his presence and victory than Russell, who won in college, won in the Olympics, and won 11 times in 13 years as a professional. But he was not the best all-around player in Celtics history. Bird was.” Ryan continues and discusses the fact that Bird may be the best all- around player, but he was not the best pure scorer the Celtics have ever had. That’s Pierce whose 40 points against the Pacers, he was 21 for 21 from the line makes him as Ryan claims, “an LPS, a Licensed Professional Scorer, and the Celtics never have had a better one.” The question then becomes is Ryan’s claim true from the perspective of statistics. Yr-Pierce GMs-Pierce Min-Pierce Pts-Pierce Pts/Min-Pierce 1998- 1999 4816327910.484681 1999- 2000 73258314270.552458 2000- 2001 82312020710.663782 2001- 2002 82330221440.649303 2002- 2003 79309620480.661499 Yr-Bird GMs-Bird Min-Bird Pts-Bird Pts/Min-Bird 1980 8229551745 0.590525 1981 8232391741 0.537512 1982 7729231761 0.602463 1983 7929821867 0.626090 1984 7930281908 0.630119 The above graph has an additional point that I created to emphasize the differences in slopes. This point was for Bird, 1632 minutes and 1967 points. This was determined using the best-fit line that the five original points made. Using the equation, Pts-Bird = 2157.47 - 0.116703 Min- Bird. I then took Pierces lowest number of minutes played (1632) and entered them into the equation for Bird’s points. The two slopes here are very interesting because as Pierce plays more minutes, his points go up. In contrast, Bird had a negative slope implying that his minutes going up does not correlate to more points being scored. Clearly this seems logically backwards, but Bird’s numbers say that he was not necessarily going to score more points with more minutes. On the right we have a side-by-side box plot which demonstrates Pierces’ higher median than Bird, at the top of his potential, but shows (through the whiskers) that Bird, had seasons in which he was much more efficient with his minutes and point scoring than Pierce. On the left, we have a normal probability plot of points per minute for Bird and points per minute for Pierce. As we can see there is not a straight line created by either set of points, the red being Pierce and the black being Bird. Both curves are more S-shaped and this would lead us to believe that using the 2-sample t test which is based around the mean is a bad idea because the distribution of the data is not normal. This instead points us in the direction of the Mann-Whitney test. Both tests are below and as we can see, neither test is significant at the.05 or even the.1 level with p-values of.904 and.5309 respectively. Based off of these tests we cannot conclusively determine that Pierce is a better scorer than Bird. We cannot reject the null hypothesis that they are equal. At the same time, we only have five data points for each person and must thus be wary of any statistical inference we try to make about which one is a better scorer. Mann-Whitney Test and CI: Pts/Min-Pierce, Pts/Min-Bird Pts/Min-Pierce N = 5 Median = 0.6493 Pts/Min-Bird N = 5 Median = 0.6025 Point estimate for ETA1-ETA2 is 0.0314 96.3 Percent CI for ETA1-ETA2 is (-0.1178,0.1119) W = 31.0 Test of ETA1 = ETA2 Vs ETA1 not = ETA2 is significant at 0.5309 Cannot reject at alpha = 0.05 Two-Sample T-Test and CI: Pts/Min-Pierce, Pts/Min-Bird N Mean StDev SE Mean Pts/Min-Pierce 5 0.6023 0.0803 0.036 Pts/Min-Bird 5 0.5973 0.0373 0.017 Difference = mu Pts/Min-Pierce - mu Pts/Min-Bird Estimate for difference: 0.0050 95% CI for difference: (-0.0968, 0.1068) T-Test of difference = 0 (vs not =): T-Value = 0.13 P-Value = 0.904 DF = 5 Descriptive Statistics: Pts-Pierce, Pts-Bird Variable N Mean Median TrMean StDev SE Mean Pts-Pierce 5 1696 2048 1696 582 260 Pts-Bird 5 1804.4 1761.0 1804.4 77.6 34.7 Variable Minimum Maximum Q1 Q3 Pts-Pierce 791 2144 1109 2108 Pts-Bird 1741.0 1908.0 1743.0 1887.5 Descriptive Statistics: Min-Pierce, Min-Bird Variable N Mean Median TrMean StDev SE Mean Min-Pierce 5 2747 3096 2747 678 303 Min-Bird 5 3025.4 2982.0 3025.4 125.5 56.1 Variable Minimum Maximum Q1 Q3 Min-Pierce 1632 3302 2108 3211 Min-Bird 2923.0 3239.0 2939.0 3133.5 Descriptive Statistics: Pts/Min-Pierce, Pts/Min-Bird Variable N Mean Median TrMean StDev SE Mean Minimum Maximum Q1 Q3 Pts/Min-Pierce 5 0.6023 0.6493 0.6023 0.0803 0.0359 0.4847 0.6638 0.5186 0.6626 Pts/Min-Bird 13 0.6261 0.6182 0.6238 0.0744 0.0206 0.5112 0.7673 0.5684 0.6851 Confidence Intervals: When we look at both the two-sample t test and the Mann-Whitney test, we are given confidence intervals for both mean and median respectively. For the two-sample t test, which uses the two mean, we can see that we get a 95% CI of: (-0.0968, 0.1068). Since this confidence Interval includes zero we cannot conclude that there is a significant difference between the scoring of Pierce and the scoring of Bird. At the same time, the Mann-Whitney test give us a similar result for a 96.% Confidence Interval we get: (-0.1178,0.1119). Again, zero lies within the Confidence Interval and thus neither test conclusively proves Pierce or Bird to be a better scorer than the other. Conclusion: In terms of the Basic Statistics, Larry Bird has a higher mean for games played per season, minutes per season and points per season as well as for points per minutes per season, but in all of these areas, Paul Pierce has a higher median. This is a clear demonstration of how much the mean can be affected with only five data points for each person. Particularly when one of the points is so drastically different from the rest as Pierces’ first season clearly is with only 48 games played and thus only 1,632 minutes and 791 points. In Pierces most recent three seasons, 2000-2003, he has a higher points per minutes as well as minutes per season and points per season than Bird had for the final three seasons used here. This may give us a similar notion to Bob Ryan because Pierce is clearly becoming a much better player than he used to be. This progression is clearly demonstrated in the Descriptive Statistics of Pts/Min because I chose to use all thirteen seasons for Bird in order to give a better idea of his career. Similarly, if you remove Pierces’ first season, his means are significantly above Bird in all categories. What does all of this mean? Ultimately it does not clearly or with any sort of statistical evidence prove Pierce to be a better scorer than Bird nor does it prove the opposite. What Pierces’ statistics show is a trend towards betterment. A trend that Bird demonstrated, but as his numbers show, he was great from the first moment he stepped onto the Boston Garden Parquet floor, he was more consistent with his ability than Pierces’ first two years have been in comparison with his last three. Bob Ryan brings up a great point though in that Pierce, may in time prove himself to be a better scorer than Bird particularly considering the amazing last three years he has had. In 2000-2001 Pierce became the first Celtic since Larry Bird did it in 1988 to break the 2000 point mark. This was Pierces’ third season, it took Bird till his sixth season to do this and Bird only did it four times, Pierce has already done it three times and has many more years to play. In conclusion, we cannot determine to a statistically significant level which player is a better scorer, but we can say they are both great scorers!!! Reference List: Larry Bird’s Base Career Statistics. http://www.rawbw.com/~deano/ar ticles/magicbird/birdbase.htm http://www.rawbw.com/~deano/ar ticles/magicbird/birdbase.htm NBA.com: Paul Pierce Player Information. Copyright 2003. http://www.nba.com/playerfile/pa ul_pierce/index.html?nav=page http://www.nba.com/playerfile/pa ul_pierce/index.html?nav=page Ryan, Bob, “Pierce: Pure Brilliance.” Boston Globe.4/21/03