Thanks for the confidence intervals. Now we’re on to something.

Because they don’t overlap, we can see that the slopes for off & def rebounds are different and this is probably the only piece of info we’d get out of the analysis with some (95%) confidence.

So in other words we’ve just proved that offensive rebounds are far more important for a team than deffensive rebounds, cause we’d get the deffensive ones anyway. That’s actually a nice fact.

Cheers

As I’ve mentioned a few times, goodness of fit (something R-squared measures) is not important here. I’m not trying to fit a model correctly in order to predict lineups’ rebounding rates. If so, I would include more variables and like you said, try different regressions besides linear.

The slope for offensive rebounds has a standard error of 0.06902. Therefore, a 95% confidence interval of the slope would be (0.6326, 0.8597). The slope for defensive rebounds has a standard error of 0.05130. It has a 95% confidence interval of (0.2487, 0.4175). As you can see, we can say with pretty high confidence that the slopes are different.

Again, goodness of fit is not an issue here. I’m not trying to fit a model.

What BigT is trying to say, is that because of the Rsq so low, the slopes cannot be trusted. Ie the error on them is so big that if you are getting a slope of .7, it is as likely for the real slope to be .2 or .99

The data here is not linear, so you cannot use linear regression to come up with answers.

Remember that misuse of statistical tools was a major factor leading to the current bank crisis.

I think you should read the article more carefully. Nobody here is trying to predict actual rebound rates based on projected rebound rates. That would be foolish to do based on, as you mentioned, the low R^2′s. The importance is the slope, because that is what shows the diminishing returns. And yes, the slopes are statistically significant, at extremely low levels (such as .000000000000001).

As the article says,

“Of course, like with every graph so far, the R^2 is still very low. This means that we can’t really predict how many steals a lineup will get simply by adding the Steal Rates of all of its players.”

Before throwing math and statistics at a topic to give it more cred, I would advise on learning about the very methods you derive your conclusions from.

That is true, but this study doesn’t include team offensive rebounds.

High individual assist counts tend to come from a high occurance of the “I pass, you shoot” meeting of mentalities. When every player is pass-inclined, this occurance breaks down. Also, high assists require a certain amount of ball domination that is less likely on a team with good overall ball-movement. I.E., ball-dominating passers get assists because their teammates don’t take them.

Sink-hole players. Some teams record very few assists because their big time scorers work best in isolation. Adding a high-assist player to this team won’t change this. Dwayne Wade doesn’t become a spot up shooter just because he’s on Steve Nash’s team. I.E. ball-dominating scorers are taking assists away from their teammates.

Pace. More possessions mean more assists, but they also require shorter possessions, which require fewer passes and faster shots. This usually means fast breaks, and loads the assists onto one player. Thus, if 5 pass-happy players play together, either most of them have to sacrafice assists to one player in the name of fast pace, or they all have to sacrafice possessions in the name of ball movement.