After posting my adjusted defensive impact metrics yesterday, I said this on Twitter:

One surprising thing I learned from this–interior defenders affect opposing shot location. Wing defenders don't.

— Austin Clemens (@AustinClemens2) May 22, 2014

I was referencing the bars at the bottom of each player’s chart. Before I continue, let me explain how to read these. Here is Al Horford:

This means that when Horford is on the court as a defender, the probability that any given shot will be a close shot (which I define as <8 feet from the basket) is increased by 2%. The probability that any given shot will be a midrange shot is increased by 4%, and the probability that any given shot will be a 3 is decreased by 6%. These should sum to 0, although occasionally they may not due to rounding. Now take another look at the adjusted defensive impact charts and compare, for example, Roy Hibbert to Paul George or, as @gswhoops mentions, Andrew Bogut to Andre Iguodala. The results show pretty consistently that big men tend to alter where an offense takes its shots. Wing defenders don’t. @WhrOffnsHppns asked if this might be a consequence of the method and as I sat at my work computer, with no access to my code, I realized that I couldn’t even really remember what the method was. I implemented this weeks ago and then just kinda forgot about it. So below the cut I outline the method in detail and look at some descriptives to buttress the big man findings. The short version though is that I do not think these results are just an artifact of the method and I want to double down on what I think is a true finding: “Interior defenders affect opposing shot location. Wing defenders don’t.”

**The Method**

^{1}^{2}The dependent variables are indicators for every player in the NBA who features in more than 1,000 shots in my dataset. Actually every player gets two indicators: one for if they are on the defensive end of the shot, and one for if they are on the offensive end of the shot. This means there are something like 600 independent variables, two each for 300-ish players. Mathematically:

Close shot indicator = Defensive_P1 + Defensive_P2 + … + Offensive_P1 + Offensive_P2 + …

Like I said there are three regression, one for close shots, one for midrange shots, and one for 3-point shots. OLS was largely chosen for convenience. I could have used logistic regression or even a multinomial logistic regression (in which case I could have had just one regression for all three locations). I actually ran the multinomial logit last night and it does not significantly change the story: big men still have big coefficients, wing defenders have small coefficients.

Is this result an artifact of the method? I’m not sure how. While OLS isn’t theoretically perfect, I doubt that logit or multinomial logit would change the story. It’s not clear to me what else I could control for. The comparison group is all players with <1,000 possessions,^{3} which doesn’t strike me as unreasonable.

That said, the magnitude of some of the results is surprising. Hibbert, for example, is shown as having a +11% effect on midrange shots. I don’t include errors on the chart (maybe in a future version) but that result is significant. The 95% confidence interval is 6.4-14.4%. With a surprising result like this, it’s useful to look at some descriptives and see if the estimate has face validity.

**Some Simple Descriptive Support**

So here’s something much simpler: a few tables the tell the same story. League-wide, 32% of shots come from the midrange (again, >8 ft) according to my data. What about when Paul George or Roy Hibbert is on the floor?

% midrange shots taken by offense | |

Roy Hibbert Defending | 39% |

Paul George Defending | 38% |

Both produce midrange %s much higher than league average. These guys play together a lot though (57% of defensive shots taken according to my data), so we can’t really tell which one of them is causing this effect. Next let’s look at situations where one is on the floor, and one isn’t.

% midrange shots taken by offense | |

Hibbert defending, George sits | 40% |

George defending, Hibbert sits | 34% |

George defending, Hibbert and Mahinmi sit | 29% |

When George sits, Hibbert’s number barely budges. The Pacers are still forcing a huge number of shots into the midrange. When Hibbert sits and George plays, however, midrange shots drop considerably. When both of the Pacers’ centers sit, opposing midrange shot volume plummets. That makes sense–these are small lineups that make it easy to punish the Pacers near the basket. But this provides some simple descriptive evidence for my point: big men have a big impact on where opponents take their shots, wing defenders not so much.

Here’s another one of the league’s dynamic defensive duos: Andre Iguodala and Andrew Bogut. Both these guys are excellent defenders, but we can see the same pattern regarding midrange shot volume.

% midrange shots taken by offense | |

Andre Iguodala Defending | 38% |

Andrew Bogut Defending | 41% |

Iguodala defending, Bogut sits | 34% |

Bogut defending, Iguodala sits | 42% |

- I’m trying something new–click the arrow to hide all the methods crap and skip to the layman’s explanation. ↑
- I keep meaning to write a data caveats post but for now I’ll just note that my data set is not completely perfect. It is scraped and there are some errors, including a few games that were not scraped because the nba.com data for them was corrupted or unavailable. I think it was only 3 or 4 games though. Generally these data errors shouldn’t affect the results. ↑
- There’s actually a small, weird bug in my data to do with this, the threshold is more like 1,100 for some players. It only affects these 3 regressions so I’ve been too lazy to change it. I doubt it has a big effect on the regressions. ↑

Good stuff. I don’t think it is against the grain to say that bigs have a larger impact defensively, outside of steals which correlate to back court players.

One other possible avenue to look at is unassisted close shots, where I suspect wings may have a bigger impact (possibly) stopping dribble penetration as opposed to cuts to the rim and feeds to the bigs.

Right, I’m not exactly shocked but I do think the magnitude is interesting. You would think that a really good wing defender like Tony Allen could at least force some shots away from the 3-point line. Good thought on the assists, unfortunately I am not set up for that. I just had another thought which is that wing defenders have a much larger area to patrol and consequently have less influence over the possession than a big who is mostly going to be standing a few feet from the hoop. If Tony Allen is on the court but the other wing defenders aren’t that great, there’s really nothing he can do about a whiffed assignment that leads to a corner 3 or something if it isn’t his man.