Most Finishers Finish the Same

I’m coming out of the stats cave for a quick second to look at a post on TrueHoop today.  Henry got some numbers from Hoopdata about which players convert well at the rim.  It turns out that Kevin Durant has the top field goal percentage of anyone who played at least 20 games and had at least three attempts at the rim per game.  That puts him ahead of guys like Dwight Howard, Andrew Bynum, and Blake Griffin.  But is Durant really the best?

I took the numbers from Henry’s post and put them in a logistic regression.  You want to use a logistic regression because any given shot can be made or missed; it’s like a coin flip with an either/or outcome (binomial, to use the stats name).  I was able to get this post up because it’s very easy in R; here’s the extent of my code:

summary(glm(makes/attempts~player,weight=attempts,family=binomial,data=rim))

That’s it, two lines.  The first one reads in a text file with Henry’s data; all I did was add a column in Excel that created each player’s shot attempts from the makes and percentage provided and saved it as a text file.  The second one runs the regression.  You’re predicting field goal percentage (makes/attempts) by who the player is, with that data weighted by how many shots each player took.  We know more about Dwight, who took 545 shots, than we do about Shaq, who only took 170.  Then you can look at the p values in the output to get a sense of who’s different from Al Horford, the default ‘intercept’ since he comes first alphabetically.

It turns out that Kevin Durant (#1)  isn’t significantly better than Horford (#4) despite shooting 3 percent better; it isn’t even close at p=.4.  So no one above Horford is better than him.  How far down the list do you have to go to find someone significantly worse?  It turns out that Blake Griffin, at number 33, is the first player to be worse even at a trend (p=.067).  The first significantly worse player is #41, Dwayne Wade, who shot 66.6% to Horford’s 74.2%, or nearly 6 percent worse.  The differences aren’t strictly about the order by percentage; as I mentioned, the number of attempts is also important.  Since we don’t have as much info about guys near Wade but with fewer attempts, like Luol Deng or Dorell Wright, they only come out at trends to be worse than Horford.

I think people might be surprised to see that you can have that much information and not have significant differences.  That’s because of the either/or outcome of shots.  Think of it like flipping a coin: say you flipped one coin 500 times and it came up heads 260 times and then you flipped another coin 500 times and it came up heads 245 times.  Would you think that the first coin was ‘better’ at coming up heads, or that it was an unfair coin?  It’s probably just noise; 15 flips out of 500 isn’t a big deal.  But if I said one coin came up heads 52% of the time and the other 49% after 500 flips, maybe that sounds like a big deal to you.  Similarly, Durant took 281 shots at the rim and made 217, which sounds impressive when you say 77.2%, but it really isn’t too different from Kris Humphries making 196 out of 292 (67.1%).

Instead of a list detailing who, in order, is best at finishing at the rim, you’d probably be better served grouping them into tiers.  The top 30 or 40 guys are top-tier finishers, but not very different from each other, and so on.  The bottom of each tier wouldn’t be that different from the top of the next, of course, but if you insist on having a ranking.

To add a little actual basketball to the conversation, Henry says he’d like to add in free throw info, so you would know who’s getting extra value by drawing fouls and getting to the line.  I agree that would be helpful.  I think it would also be helpful to know how those shots came at the rim.  I didn’t see a lot of the Thunder last year, but I imagine that Dwight had a much higher degree of difficulty on his at-rim shots (presumably with people hanging all over him) than Durant (presumably soaring in on break-aways or after beating his man).  In some sense that would make Dwight ‘better’ at finishing even if he shot a lower percentage because many other players probably would have shot worse if they had taken Dwight’s attempts.  Then again, I just finished saying that the top finishers all finish about equally well, so I could be wrong.

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