Tyler Brody '21
Introduction
Believe it or not, there was a time when the center was the marquee position in basketball. Many maintained no team could win an NBA championship without a dominant interior scorer, and legendary big men like George Mikan, Bill Russell, and Kareem Abdul Jabbar carried their teams to multiple titles through back to the basket dominance. In today’s game, however, you would be hard-pressed to find an offense run through the post, and, since Shaq, we have not seen a dominant five bulldoze his team’s path to a championship. In fact, the role of the big man in today’s game is almost unrecognizable from that of the past, as many centers have transitioned from jump-hooks in the key to pick-and-pop threes. This paper examines how the introduction of the three-point shot initially diminished the offensive value of centers and how big men adapted their style of play to become more effective in the three-point era.
Part 1: Analyzing Offensive Win Shares Across Eras
To assess how the introduction of the three-pointer impacted the offensive value of an NBA center, I investigated the difference between centers’ average offensive win shares before and after the first season with a three-point line (1979-1980). Basketball Reference’s offensive win shares statistic estimates the ratio between each player’s marginal points produced and their team’s marginal points per win (details here). This metric serves well as an indicator of a given player’s overall offensive value because it approximates how they contributed to their team’s success through their points produced. By investigating the difference in centers’ average offensive win shares before and after the three-point shot was introduced, I could quantify how this change impacted the offensive value of big men to their teams.
The dataset I worked with contained all NBA players listed as a C or a C/F on Basketball Reference from the 1951-52 to 2018-19 NBA seasons. I filtered the players under consideration to exclude centers that played less than 11.5 minutes per game and less than 40 games in each respective year because players who did not participate in a significant portion of the season will have lower win share metrics by construction, which may not accurately reflect their value. Also, including bench players in the analysis could mask the potential trend of interest because their average offensive win shares are likely low and consistent before and after the 1979-80 season. After removing these data points, I conducted a two-tailed Welch’s t-test with an alpha of 0.05 on the average offensive win shares of centers before and after the 1979-80 season to assess the hypothesis of no difference in means. I used the Welch’s t-test because the two groups do not contain the same number of seasons and therefore have different sample sizes.
As the figure above illustrates, the average offensive win shares of NBA centers declined after the 1979-80 season, and the p value for the Welch’s t-test of 0.036 indicates a statistically significant difference in means at the 95% significance level. This result demonstrates that the offensive value of centers to their teams lessened following the introduction of the three-point shot, a result that makes sense given how the game has changed. As offenses became more perimeter-oriented, the importance of a proficient interior playmaker diminished. Three-point shooting turned into a critical asset, and traditional back-to-the basket post-ups became a relatively inefficient way to score. The drop off of just 0.2 offensive win shares might appear slim, however the decrease in centers’ offensive value is even more pronounced when considering the league’s most elite big men. To analyze just the top centers, I filtered the dataset to only include players above the 80th percentile in offensive win shares. I then performed the same statistical test as above and discovered a difference of 1.5 offensive win shares between the means of the two groups with a p value of 1.13 * 10-12. This larger discrepancy among the top centers demonstrates that the addition of the three-point line had a more severe impact on dominant centers’ offensive value.
Part 2: Evolution of NBA Centers During the Three Point Era
While centers’ offensive value declined on the whole after the 1979-80, analyzing the trending yearly averages reveals that their mean offensive win shares have recovered to pre-three-point era levels in recent seasons. This resurgence suggests that big men have regained their value by adapting their style of play. To assess this hypothesis, I compared the basic per game offensive statistics of an average center in the 1979-80 season to an average center in the most recent completed NBA season. Below, I report the contrast between the offensive metrics for these two seasons, and I conducted two-tailed Welch’s t-tests with an alpha of 0.05 to evaluate which differences were statistically significant.
Table 1: Comparing the per game basic offensive metrics of average centers in the 1979-80 and 2018-19 NBA seasons
| 2PA | 2P% | 2P | 3PA | 3P% | 3P | FT | FT% | AST | ORB | |
| 1979-80 | 8.66 | 0.49 | 4.34 | 0.05 | 0.11 | 0.005 | 2.22 | 0.707 | 2.00 | 2.24 |
| 2018-19 | 6.68 | 0.57 | 3.83 | 1.24 | 0.26 | 0.42 | 1.98 | 0.714 | 1.72 | 2.09 |
| Δ | -1.98 | 0.08 | -0.51 | 1.19 | 0.15 | 0.414 | -0.24 | 0.007 | -0.28 | -0.15 |
| p-value | 0.003 | 1.6e-16 | 0.145 | 2.0e-8 | 7.4e-7 | 6.8e-8 | 0.295 | 0.634 | 0.133 | 0.346 |
The analysis above reveals statistically significant changes in 2PA, 2P%, 3PA, 3P%, and 3P. The average center in the 2018-19 season attempts two fewer two-point field goals per game and shoots 8% better from this range compared to the average center in the 1979-80 season. While virtually no centers attempted threes in the 1979-80 season, they now shoot one per game and make them at a 26% clip on average. Both of these trends align with the league’s offensive shift from the paint to the perimeter, illustrating that big men have also adapted to the new era. As teams began shooting more threes, it follows that centers received fewer two-point shot opportunities. With less emphasis on feeding the post, it is likely that centers needed to create their own inside shot less often, which may somewhat explain their improvement in two-point efficiency. Big men also improved as threats from deep in line with the rest of the league, and this change has occurred primarily in recent years and at a remarkable pace. Since 2010, centers’ average three point attempts per game have skyrocketed from 0.27 to 1.24, and their mean three-point percentage also exploded from 13.9% to 25.5%. The figure below shows this sudden improvement from beyond the arc.
The two main areas that centers improved were two-point field goal efficiency and three-point shooting, however it is not apparent which of these two factors was more responsible for their offensive win share recovery. To determine which improvement was more significant, I regressed offensive win shares against 2P, 2P%, 3P, 3P%, FT, FT%, ORB, and AST. I excluded 2PA and 3PA attempts from the regression analysis because they have high correlation with 2P and 3P and they do not capture additional information about centers’ offensive productivity outside of the variables chosen. Although the primary focus of the regression was on the coefficients for 2P%, 3P%, and 3P, I included the other variables to get more interpretable regression coefficients and avoid omitted variable bias since points produced relies on more than just shooting percentage and three pointers made. In other words, I wanted to compare the effects of 2P%, 3P%, and 3P with “all else equal” to better understand these metrics’ true impact on offensive win shares. The adjusted r-squared value for the regression model was 0.731, and the coefficients are displayed in the figure below.
Table 2: Regression coefficients from OLS regression model. (Note: coefficients for percentage variables should be interpreted in terms of percentage points i.e. a 1% increase in 2P% leads to a 0.156 increase in mean OWS)
The regression coefficients alone do not reveal which area of improvement was most significant because the size of the changes in 2P%, 3P%, and 3P since 1979 also matters. So, I used the coefficients along with my knowledge of how each metric changed throughout the three-point era to estimate which changes impacted offensive win shares the most. Specifically, I multiplied the change in each metric between average centers from the 1979-80 season and those of the 2018-19 season by their corresponding regression coefficients. These products yield estimates for each metric’s contribution to the change in centers’ mean offensive win shares during the three-point era. These estimates are only useful in assessing the relative magnitude of each metric’s impact on offensive win shares. This is because the regression model only explains around 75% of the variation in offensive win shares and therefore the coefficients are inexact measures of each variable’s causal impact. But, the results are still useful in assessing which variable had the largest impact on the recovery of centers’ offensive value. The figure below represents each variable in the regression’s estimated impact on the change in centers’ mean offensive win shares between the 1979-80 and 2018-19 seasons.
This analysis reveals that centers’ 8% improvement in two-point shooting percentage had a significantly larger impact on the resurgence of their mean offensive win shares than any of the other variables, including their enhanced three-point shooting capabilities.
Conclusion
Essentially, the offensive value of NBA centers diminished after the three-point shot was introduced. However, in recent seasons their offensive win shares have recovered to pre-1979 levels, and this resurgence is primarily due to big men’s improvement in two-point shooting percentage. I hypothesized that this improved two-point efficiency resulted from less need for centers to create their own shots in the paint. However, this is only a theory based on my intuition for how the game has changed, and perhaps future research could try to explain why big men’s two-point percentage has improved. Also, this paper only analyzed value via offensive win shares, however there are many additional avenues to explore how centers evolved to adapt to the three-point era. Future studies can also take defensive metrics into account to study how the game’s transition to the perimeter impacted centers’ defensive roles. Or, it could be useful to take a broader perspective on centers’ contributions by analyzing the average win percentage of teams with and without “elite” centers before and after the three-point shot was introduced. Whatever the direction may be, there is still much to explore regarding how big men have evolved to a changing game.