*One of our core values here at The Nylon Calculus is accessibility, not just of our content but of the guiding ideas of basketball analytics. What We Know is a series that aims to do just that. We want to press pause, take a deep breath, and recap the ground that has been sprinted over in the past few seasons. This is not about formulas or specific statistics, this is about the big ideas that statistical analysis has brought to the table.*

The idea that shot selection matters to a player’s or team’s offensive performance is far from revolutionary. It’s been preached by coaches at every level for as long as there has been organized basketball, and chances are you’ve even felt its power during your own pick-up career. Every player has certain places they are more comfortable shooting from and, in the aggregate, shots are easier to make the closer you are to the basket. But while this understanding has been ingrained in the basketball mind for years, it has never been a bigger focus than it is in today’s NBA. What the analytics movement has brought to the table over the past few years is a fuller understanding of just how powerful shot selection is and how much advantage can be gained by the implementation of small changes.

At this point we don’t have great publicly available statistics on the proximity of defenders to a shooter, or the quality of defensive pressure applied to a shooter (at least not for all shots), so this discussion of shot selection is about where shots are taken from, not whether they are open or contested. With a little help from Austin Clemens, we can see in the graph below how distance from the hoop affects the likelihood of a shot being made.

This graph is based on every shot taken by every player during the 2013-2014 season. The red line — showing the average FG% by distance — drops dramatically until you get to about three feet, and from there everything has about a 40% chance of being made. On average, a team that takes more of their shots within three feet of the basket will make a higher percentage of them and thus, have a more effective offense. But there is one rule in the NBA which adds a layer of complexity — the three-point line.

The blue line on the graph above shows the effective field goal percentage (eFG%) by distance. Since eFG% accounts for the extra point scored on a three-point basket, what we’re seeing is the *average value* of shots by distance, not just how likely they are to be made. Both lines are the same until we get to the three-point line, where the extra point on those made shots causes the eFG% to bump back up. Looking at this graph you can see why so much analytic discussion has revolved around three-pointers and long two-pointers. On average, the more shots a player or team takes between three and 21 feet from the basket, the less value they are getting for their shots. Moving just a few feet back, behind the three-point line, doesn’t dramatically reduce the likelihood of a shot going in and the bonus of that extra point on a made shot makes it much more valuable.

However, there is still a disconnect in how we view FG% on two-pointers and three-pointers. I would argue that our mental scales are not calibrated. In general anyone who shoots 45% or better from the field is considered a respectable shooter. I would put public perception of that benchmark for three-point shooters at around 35%. However, those numbers don’t even begin to match up. The table below shows two-point FG%s and the equivalent three-point percentage — essentially at what percentage a hundred two-point baskets and a hundred three-point baskets would need to be made to provide the same value.

You can see that the line for respectability on each scale doesn’t necessarily match up. However, on this issue it’s really important to draw a distinction between a large and small sample. If you are talking about a group of players across an entire season, three-pointers made at a 33.3% clip and and two-point shots made at a 50% clip should provide roughly the same value. But there may be specific instances in specific games where the two-pointer is is far more valuable. In a single instance where a team needs a basket, a 50% chance of being made is much better than 33%.

We also know that, in looking at averages, we are smoothing together the abilities of many different sorts of players. For example, Dwight Howard is probably much better around the rim than the average NBA player, but doesn’t have three-point range and would not see the same eFG% bump at the three-point line as a typical outside shooter would. But a much better example of how this typical trend of efficiency in shot selection can vary for an individual player is Dirk Nowitzki.

This graph contains all of Nowitzki’s shots from last season. You can see he is much more effective around the basket than the average player, but where he really sets himself apart is with his mid-range shooting. Remember that on the graph for all shots, from all players, everything from three feet out to the three-point line had an average FG% of about 40%. Although there are peaks and valleys in Nowitzki’s performance from this range he is mostly well-above that mark. In fact, his FG% at 19 feet is almost exactly the same as the all shots, all players, three-point eFG% peak of about 23 feet. So while in the aggregate, shots at the rim or behind the three-point line are statistically preferable, there are certain players who buck that trend from certain spots.

Keeping in mind that things can differ depending on the players involved and the specific game situation, the graph at the very beginning of this article is really what shows the understanding of shot selection that is reshaping the league. The average NBA team took 6,806 shots from the field last season. On each individual shot the difference in average value between different locations is tiny fractions of a point. But if a team is willing to change their patterns (like the Houston Rockets who have made a point of avoiding mid-range shots like the plague), moving hundreds of shots to players and locations that provide a slightly higher average value, those fractions of points add up quickly and huge benefits are there to be exploited. Research that I did last season showed that about 19% of a team’s offensive efficiency can be explained by their shot selection.

This balancing act between a single shot and the thousands of shots a team takes throughout a season can be difficult to see. On an individual possession, the understanding of shot selection hasn’t really changed in the last 50 years — who’s shooting and how open they are still define most of what makes a good or bad shot. But when we put all those shots together we can see that commitment to a process, and a certain team or player-specific definition of what makes a good shot can change everything.

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