I've always assumed that defenders--centers, in particular--that focus more on blocking shots sacrifice opportunities for defensive rebounds as an attempted block puts the defender out of position to box-out opponents and secure defensive rebounds. To measure this assumption, I pulled blocks (Blk), defensive rebounds (DRB), and defensive rebounding percentage (% of DRBs a player grabs while on the floor) for centers from NBA stats (games as of February 28). I focused on centers that played at least 50 minutes and appeared in at least 5 games during the 2013-14 season (which resulted in a population of 103 centers).
I standardized blocks and DRBs both per minute played. DRB% was already standardized. Below are two charts. In the top one, I plotted Blks/ minute (vertical axis) against DRBs/minute (horizontal axis). In the bottom chart, I plotted Blks/ minute (vertical axis) against DRB%. For both I included a linear regression line (blue line) with a 95% confidence region (grey area). The line and grey area give some indication of the relationship between blocks and defensive rebounding. The anomalies in the upper right hand corner of each chart are Javale McGee in the top chart--indicating that he is exceptional as a defensive rebounder and shot blocker--and Cole Aldrich in the bottom chart--indicating that he is an exceptional shot blocker and grabs a disproportionate % of his team's DRBs. Both players present anecdotal evidence that shot blocking and defensive rebounding are unrelated.
If players with more blocks were poorer defensive rebounders then the blue line and grey area would start at the top left of the plot and slope down toward the bottom right of the plot. But that doesn't happen. In both plots the blue line is effectively horizontal, which indicates that there is no relationship between blocks and DRB or DRB%. In other words, blocks have no effect on a player's defensive rebounding.
There are some limitations to this approach to measuring the relationship between defensive rebounding and shot blocking. First, it would be better to have a measure of attempted shot blocks rather than just shot blocks. Unfortunately, the NBA does not collect this statistic (they do collect the number of shots a player has had blocked), and even if they did, it would be difficult to capture what qualifies as an "attempted shot block" as most field goal attempts are contested and, thus, could potentially be blocked. (In other words, does an attempted shot block only occur when a defender leaves his feet? Should the defender also have to have a hand raised in contesting the shot?)
Second, this approach only measures the relationship between shot blocking and two measures of defensive rebounding separately. It ignores intervening factors in the relationship, such as the DRB and shot blocking ability of teammates or a team's defensive scheme. (If there were a scheme where Kevin Love is only supposed to grab defensive rebounds and his teammates should focus on contesting shots--as often appears to be the case with the Timberwolves--then shot blocking could be indirectly related to DRB. As evidence of this Love is second to last in blocks per minute but second to best in DRB%.)
I standardized blocks and DRBs both per minute played. DRB% was already standardized. Below are two charts. In the top one, I plotted Blks/ minute (vertical axis) against DRBs/minute (horizontal axis). In the bottom chart, I plotted Blks/ minute (vertical axis) against DRB%. For both I included a linear regression line (blue line) with a 95% confidence region (grey area). The line and grey area give some indication of the relationship between blocks and defensive rebounding. The anomalies in the upper right hand corner of each chart are Javale McGee in the top chart--indicating that he is exceptional as a defensive rebounder and shot blocker--and Cole Aldrich in the bottom chart--indicating that he is an exceptional shot blocker and grabs a disproportionate % of his team's DRBs. Both players present anecdotal evidence that shot blocking and defensive rebounding are unrelated.
If players with more blocks were poorer defensive rebounders then the blue line and grey area would start at the top left of the plot and slope down toward the bottom right of the plot. But that doesn't happen. In both plots the blue line is effectively horizontal, which indicates that there is no relationship between blocks and DRB or DRB%. In other words, blocks have no effect on a player's defensive rebounding.
There are some limitations to this approach to measuring the relationship between defensive rebounding and shot blocking. First, it would be better to have a measure of attempted shot blocks rather than just shot blocks. Unfortunately, the NBA does not collect this statistic (they do collect the number of shots a player has had blocked), and even if they did, it would be difficult to capture what qualifies as an "attempted shot block" as most field goal attempts are contested and, thus, could potentially be blocked. (In other words, does an attempted shot block only occur when a defender leaves his feet? Should the defender also have to have a hand raised in contesting the shot?)
Second, this approach only measures the relationship between shot blocking and two measures of defensive rebounding separately. It ignores intervening factors in the relationship, such as the DRB and shot blocking ability of teammates or a team's defensive scheme. (If there were a scheme where Kevin Love is only supposed to grab defensive rebounds and his teammates should focus on contesting shots--as often appears to be the case with the Timberwolves--then shot blocking could be indirectly related to DRB. As evidence of this Love is second to last in blocks per minute but second to best in DRB%.)
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