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Creating A Very Simple Shooting Index
IntroWanting to expand on some of the ideas in this post, this post, and even this most recent post, I thought a lot about the process of creating a one-number summary of a player's shooting ability.
Shockingly, I still find people arguing about the shooting capabilities of particular players with these stats (in order of decreasing awfulness):
-eFG% and TS
I almost feel like it's too obvious to go over why this makes so sense, but then again, I still see people cite these stats. At a basic level, all of these stats include shots at the rim, which I'm not interested in with a shooting statistic. Even if that wasn't the case, they also just mash everything up, so you can't actually glean if a player is a good midrange shooter, a good three point shooter, or both. And at a more advanced level, they don't look at context: was this player shooting off the dribble? Were they tightly defended? Do they sit in the corner waiting for a pass?
What I wanted was a program that would automatically perform my general process when I check how good of a shooter a player is: check midrange splits, look at 3 point percentage, how often they shoot in the corner, look at assist rate, and, if I really need to be thorough, look at average defender distance. Generally, these things give a good idea of a shooter's capabilities.
Througout this post, it's important to keep in mind what this IS and what this is NOT. This is not a statistically perfect method of determining the best shooters. This says nothing about the value that these players provide. All this post is is an exploration of an idea, the thought process that goes into thinking about creating a one-number statistic, and a quick and dirty way to double check if a player is actually a good shooter or not (for the next time you get into a spat with someone on the nba subreddit.)
If you're not interested in the thought process behind the index, just skip to the results section to see the tables and plots! :)
The DataI could go into all sorts of ideal scenarios, considerations, and hyper-specific concerns of what I would want from a shooting statistic, but all of that is pointless unless I can get data that actually reflects those ideas. What I mean is, if I want to adjust for defender distance, it doesn't matter unless I can actually find data that includes defender distance.
The data that I got a hold of takes every shot attempt from 2013, and has the following information:
Zone: either <10 feet, >=10 feet (2 point attempt), or 3 point attempt
Defender distance: wide open (6+ feet of space), open (4-6 feet), tight (2-4 feet), or very tight (0-2 feet)
Shot clock: 24-20, 19-15, etc.
Number of dribbles before attempt: 0, 1, 2, etc
Touch time: <2 seconds, 2-4 seconds, 4-6, 6+
The good: we have defender distance, which is probably the most important metric to keep track of. We have a way to exclude shots around the rim, and we have a discriminant between midrange and 3 point attempts.
The bad: I was hoping to get finer resolution on the zones; splitting up between "short" midrange and "long" midrange can be helpful, as well as splitting up the 3 point zone between corner and above the break shots. Ideally I would just have a raw distance from the basket, but oh well. We also don't have assist rates, which I was hoping to use as a proxy for catch and shoot, but that's okay (more on this later.)
MethodologyI decided to go with a simple logistic regression for this project. The goal here is NOT to create the perfect shooting index. With the lacking data I have and the limited statistics knowledge I possess, there is no way I could come up with anything more comprehensive or statistically powerful as what was done, here, here, or even here
On the other side of things, there still needs to be some sort of methodology. I can't just wave my hands and vaguely account for defender distance by saying it should probably be, like, 2%+ per every 2 feet of space the player gets and wiggle that number until it sorta looks right.
So let's think about the predictor variables we have.
Defender distance seems like it should obviously have the most weight to it, so there's no additional pre-processing we need to do with that predictor. As a very simple check, let's look at what our regression predicts a player's 3P% should be based on defender distance alone just to make sure we're not making any immediately obvious mistakes:
|Defender Distance||Predicted 3P%|
I vaguely recall Ben Taylor tweeting about wide open 3 point attempts last year, and stating that league average (when wide open) was 40%, so this seems very reasonable and believable.
Now, I could just run the regression on all the predictors listed earlier, but I'd like to comb the data a bit before I do that. Shot clock time doesn't actually seem like a real predictor of anything; what I mean is that taking a shot at 18 seconds probably shouldn't have much of a difference between taking an identical shot at 12 seconds. If anything, shot clock seems like it's probably just correlated to defender distance. What I attempted to do was split up shot clock into 2 groups: <4 seconds and >4 seconds. I figured that taking a shot at almost any time is not going to have an effect, but less than 4 seconds might cause the player to rush the shot. The issue is that when you do this, it becomes heavily correlated with defender distance, making it pretty redundant. Thus, I opted to just scrap shot clock as a predictor.
For dribble time and touch time, I figured that they were in and of themselves correlated, so I combined them into a single predictor. I also figured that the most relevant information was when touch time and dribbles were very low vs very high. I mentioned earlier that I wanted assist rate as a predictor, because I think it is a good proxy for shot difficulty. Well instead, I decided could just classify "touch time < 2 seconds" & "dribbles < 2" as a catch and shoot, and everything else as a pull up attempt to get a rough estimate for catch and shoot vs pull up players. Generally, the idea is that if you have a touch time > 2 seconds before taking a shot, you're probably isolating the possession. And isolation shots are usually more difficult than catch and shoot. An unintended consequence of the change of this grouping was that it made our defender distance predictor less correlated with our new catch & shoot predictor. Great!
So, living up to our title, we have a very simple predictor of FG%; all we use is defender distance in 4 bins, and a catch & shoot or pull-up category.
Let's run the regression and look at the midrange and 3 point categories and see if it passes the "sniff test", so to speak:
|Player||Expected Midrange %|
So far so good; Ibaka and Horford are good names to see at the top of the list, as they generally take spot up, wide open mid range shots. Seeing Durant, Gay, and Crawford at the bottom of the list also seems reasonable. Other names near the bottom of the list: Irving, Carmelo, Wiggins, Booker. Now let's take a look at three point shooting:
|Player||Expected 3P %|
Again, this looks very reasonable. Seeing Harden at the very bottom of the list is a good sign, as well as Lillard.
Now all that's left is to determine the actual "score", which, again, we're going to keep very simple. The score is just going to be FG% - expected FG% for each zone, and then averaged.
For example, if player A is 45% from midrange and 35% from 3, but has expected values of 38% from midrange and 36% from three, their score is
((45-38) + (35-36) / 2) = 3
ResultsAfter running the regressions, here is what the top 7 and bottom 7 look like (of players who have at least 1000 midrange and 3 point attempts in the last 7 seasons):
|Player||C&S Percentage||Shooting Score|
The reason I like to list C&S percentage alongside these results is that people have different ideas of what a "good shooter" entails. The ability to create a shot by moving off ball and shooting after curling off of a screen is a different kind of difficult than being able to create a shot with the ball in your hands like Harden does. So, to some people, it might be pertinent to only compare shooting scores with players who have a similar play style (and C&S can sometimes be a good proxy for that.)
To see this list as a visualization, you can click here.
For an additional visualization, here is the graph of midrange scores vs three point scores, so you can see the players that are particularly good at one over the other.Only a handful of players are labeled to keep it from being crowded. If you're curious about a name that didn't show up, it's probably an issue of the midrange cutoff; I set both 3P and midrange attempts to > 1000 to avoid clutter in the graphs. If you're curious about any particular players that you can't find, let me know and I'll grab the values for you!
For the most part, this shooting score is not that much different than a naive score (just averaging midrange and 3P percentages), which is good; we shouldn't expect a gigantic shuffling of players. But we do see a small handful of drastic changes in expected places: in a naive ranking, James Harden is ranked 48th, Lillard 21st, Ibaka is 17th, and Kevin Love is ranked 49th. In this model, however, Harden goes to 18th (+30), Lillard goes to 15th (+6), Love goes to 60th (-11) Ibaka goes to 43rd (-26).
DiscussionThe names that we expected to see are there:
Curry and Durant top off the list, and our friend Chris Paul lands very high, which I'm happy to see. Harden gets a big boost due to his difficult shot selection, and Lillard does as well. Lillard might not be as high as I'd like him to be, but that's an issue with the data; Lillard takes the deepest threes in the league, but I didn't have access to that with this data set.
Names that stuck out:
McCollum finally gets his due here as an absolutely elite mid range shooter. He doesn't get enough praise for how nuts he is in that area.
Jamal crawford is rated surprisingly high despite his pedestrian percentages; he apparently has one of the most difficult shot selections in the league.
Aaron Gordon didn't show up on the plots and tables I shared because of a midrange attempt cutoff, but he's secretly one of the worst shooters in the league. I knew he was bad, but he has some of the easiest attempts in the league and simply can't find a way to convert.
Anthony Davis also shows up near the bottom of the list. He's credited as a below average midrange shooter, and an awful three point shooter. I'm sure if I used only the last couple of years, his name would jump up the list a bit, but it still surprised me.
Jokic is a below average three point shooter, but (if you lower the attempt requirement a bit,) shows up as the third best midrange shooter, behind CP3 and Durant. Very impressive and unexpected (to me.)
Arron Afflalo. Surprisingly good all-around shooter. Just kinda forgot about that guy to be honest.
A consideration to make here is about volume. Usually, volume is a proxy for shot difficulty, so a low volume would assumed to not have much of an effect here. However, there might be something to be said here for how you're defended. If a player takes very few mid range shots, the defender might not expect it, even though they'd be listed as "tightly guarding" the player shooting. Conversely, a player like Harden might be even better than the list would indicate because the defender goes into the matchup knowing almost exactly what he's going to do (step back three), and Harden is still able to convert at a high clip. Maybe this has almost no effect, but I thought it might be something worth mentioning.
Another consideration is that "creating space" is sometimes in and of itself more difficult than a tightly guarded shot. Again using Harden as an example, him doing a stepback might create enough space for the shot to be listed as "open", meaning the regression would expect a higher probability of making the shot. But this act of creating space might be seen as more difficult than shooting a tightly contested shot in the first place. It all comes down to the definition of "shooting". Regardless, we don't have access to information that specific anyway.
I'm pretty happy with how this turned out; again, this is not a perfect or even particularly good statistic; I mostly just wanted a program I could run to generate a list I could glance at when someone says Player A is a good/bad shooter to see if it warrants a closer investigation. I also made it because, to be honest, I was surprised that a very simple shooting index didn't really exist anywhere. I'm certain many people have done it before at a basic level, but all of the good ones are proprietary or using data that is no longer publicly available.
One note is that I could have included FT% as part of "shooting". I didn't add it because I was feeling lazy, to be honest. I don't think it would change much, but I would be interested in seeing the outlier, e.g., players with a high shooting index but low FT% and vice versa.
If there's interest, I can PM a google sheets file with the full list of players with their C&S percentages, expected FG% from each zone, and overall shooting score. I would link it here, but I'm not sure if it's against the rules so I'll refrain.