Prior to writing for Liberty Ballers and accumulating the enormous riches associated with part-time blogging, I conducted a reasonable amount of work in the field of spatial analysis. So, once I figured out how to create shot charts (maps of where shots occur in the half court), I decided to take a look at how Joel and Ben have changed (or not) since last season with regards to their spatial distribution of shot attempts and makes.
Before we get going on the results and pretty(ish) pictures, we need to first go over what density means from a spatial standpoint. Most commonly, we see spatial density in terms of population per square mile. For example, Philadelphia has about 11,400 people per square mile, but we understand that not each mile has exactly 11,400 individuals, and the data represents a sort of average or smoothing of the population over a specified area. That general idea is a simpler version of the underlying methods here, but the idea of smoothing the count of individual events across an area is what you need to consider.
This general process involves determining the density of shots (attempts and makes handled separately) at 1x1 grid cells across the entire two-point range of play. This exercise is done for 2017-18 and 2018-19 separately. Then, the calculated density (adjusted for total number of events) for 2018-19 shot attempts is divided by the calculated density for 2017-18 shot attempts. The result of the division can be called the relative density — the larger the number, the greater the 2018-19 density compared to 2017-18, whereas the smaller the number, the lesser the 2018-19 density compared to 2017-18. However, unlike many scales where the midpoint is zero, because two numbers are being divided, the midpoint of this scale (where the two densities are the same) is set at 1.
First, we look at the relative density of shots attempted in Figure 1.
This makes sense to me based on the greater emphasis on bully ball, according to both Embiid’s own words and those of Brett Brown. What is interesting to me is the lack of symmetry in the changes. Is that just a random effect or something that is a factor of the structure and spacing of the offense?
Again, what we like to see is that Joel is making more shots around low left block and around the key. Even better, these areas overlap with areas from Figure 1 where Joel is shooting more often. Figure 3 makes that point with a little more clarity.
Areas on the court that are green are where Joel is both attempting and making shots at a higher density in 2018-19 than 2017-18. Areas in red are where he is attempting at a higher density this season, but making at a lower density than the prior season. Locations in blue are all other permutations.
While Joel’s charts were both easy to interpret and meshed with talking points regarding his play, I am not entirely sure what to make of Ben’s. Figure 4 presents his shot attempts comparing this season to last.
It appears that Ben has taken shots at a bit higher density along the baseline right corner, and then at a lower density pretty much everywhere else. Given that he takes so few shots that are not within 10 feet of the hoop, my bet is that the right corner is an end of shot clock heave that ends up distorting the values due to its relatively disproportionate importance. Figure 5 seems to indicate that he is certainly not making as many shots in the mid-range, except the left baseline.
I personally would have liked to see an increase in both mid-range attempts and makes at the rim. However, only makes at the rim appear to be the case — Simmons seems to be dunking more than last year from the ever-so-reliable eye test. Figure 6 shows the areas on the court where Ben has both increased attempt and make densities in 2018-19 (in green), and areas where he increased attempts, but not makes.
- There appears to be more than lip service to the idea of Joel playing bully ball down low.
- Ben is shooting better than last year in terms of makes and attempts both at the rim and rim adjacent, but has not made a serious change at all in regard to the mid-range.
- This data only runs prior to the Butler trade.