Part 1: How Powerful is the Benefit of “Spacing”?


The league is changing. As the season closed, League three-point records were broken again. At the height of Larry Bird’s reign in 1986, teams averaged a mere 77 three-pointers for the entire season. Dallas led everyone with 144, which has been surpassed by an astounding 25 individual players in 2014. The smallball philosophy of the Nash-era Suns, utilizing big men with outside range, has bled into other teams, and the two-time champion Miami Heat downsized and urged Bosh to shoot three’s to supercharge their offense and give LeBron and Wade more space to operate. But how important is this trend? And, beyond the simple fact of increased efficiency from using this type of shot, is the effect of spacing real?

There’s no denying the trend of elite offenses relying on outside shots. In fact, both more recent finalists were three-point reliant, as the Spurs were ranked 9th in three-pointers per field goal attempt and the Heat 5th. Looking at the past 14 years, what has the strongest relationship to SRS (basketball-reference’s team rating for strength): turnovers, steals, free-throws per field goal attempt, assists per field goal, or three-point attempts per field goal? It’s three-pointers, and this doesn’t even include accuracy. Simply put, taking a lot of three-pointers is an indication of being a good team.

But what needs to be untangled first is the efficiency of three-pointers from just the spacing. If spacing exists, then we should see the positive benefits from taking more threes even after adjusting for the expected efficiency of those shots.

One technique we can use is breaking down lineup data. This is essentially what RAPM does: we can explain the scoring margin of five-man lineups. First we calculate the expected offensive efficiency of a lineup based on the offensive rating and usage rate of each player from basketball-reference; then we compare it to the actual offensive efficiency of those lineups.  The usage rate weighs certain players higher, so for example, Kobe’s offensive rating has more of an effect on the expected lineup offensive efficiency. The disparity between the actual and expected outcomes can inform us of factors that drive successful offenses beyond simple individual efficiency ratings – in this case that factor is “spacing”, measured as three-pointers attempted per 100 possessions.

Using a regression on five years of lineup data from seasons 2007 – 2008 through 2011 – 2012, it is reinforced that units shooting more three-pointers are significantly better offensively. Adjusting for homecourt advantage and the expected offensive efficiency of the lineup, for each one unit increase in the average 3PA per 100 offensive possessions, the offensive efficiency increased by 0.77 points per 100 possessions. With a t-value over 9 and nearly 53,000 observations, that is highly statistically significant. And recall this is already corrected for shooting efficiency via the offensive rating inputs; the results suggest the benefit of spacing are meaningful and indicative of something powerful. Replacing one non-shooter with a three-point bomber, by the numbers, can lead to a couple more games won based on spacing alone.

One facet missing here, however, is that spacing is usually measured by how many shooters are on the court, not their average three-point rate. One quick metric for this is using the harmonic mean* of the three-point rate of each player, serving to penalize lineups for having non-shooters. Using this method to calculate each lineup’s three point shooting rate, the results of the regression were even more significant, as the model explained more of the variation. For each one unit increase in the harmonic mean of the three point shooting rates, the expected offensive efficiency increased by 1.51 points per 100 possessions.

Breaking the lineups down even more, the results were plotted by how many “shooters” and “non-shooters” there were. “Non-shooters” are defined as any player taking less than one three-point attempt per 100 team offensive possessions – Chris Anderson for example in Miami – while “shooters” are defined as having rates above 5 attempts per 100 team offensive possessions. This way the marginal impact of adding players who rarely shoot threes or shoot a lot of them can be explored. And remember, this is already adjusted for the individual offensive ratings of the lineups.  The first graph reflects the impact of adding more “shooters”.

spacing shooters-2

Since there were so few lineups with 5 shooters, those possessions were pooled together with 4 shooter lineups. It is fairly arbitrary to slice lineups by players with five 3PA’s per 100 offensive possessions, but the pattern is still clear. Likewise, the graph reflecting the impact of adding “non-shooters” shows the same conclusion, as shown below.

spacing nonshooters-2

Numbers are just numbers, and despite Daryl Morey’s best efforts, you cannot field a team comprised solely of numbers. So what’s actually going on here from a pure basketball point of view? Due to rule changes over the years and defensive sophistication, help defense is very quick and aggressive now. As a star player driving to the basket, that guy will likely be picked up by another defender en route. If there are enough defenders able to sag off their men, the paint is virtually off limits. This was Miami’s problem when first attempting to integrate LeBron and Wade. How does a team fix this? The answer is to surround driving players with outside shooters. A defender at the three-point line has a longer distance to cover to help on LeBron James, and due to the power of the three-pointer, the opponent simply can not abandon the shooter for fear of giving up an open look. The floor is spread, and LeBron has more “space” to operate. Spacing is real, and its effects are significant.

Bringing this back to gotbuckets realm, if you check the yearly leaders in RAPM, three-point shooters do very well. Another pattern is that few big men make a large positive impact on offense. The exceptions from 2014 (everyone above +2.5 and 1000 minutes) are listed in the table below. Also listed is how much they’re being underrated by PER from their total RAPM (using a linear regression of PER on RAPM.) It’s a small group of players, but besides no-stats all-star Nick Collison, they all have one thing in common: significant range. Dirk, Love, and Frye are three-point shooters, while Aldridge and Amir Johnson have range that nearly extends to outside the arc. With the exception of the high-scoring, high-rebounding Love, they’re also being underrated heavily by PER. Two players who barely missed the cutoff are even more illuminating; Matt Bonner and Ryan Anderson finished just below an RAPM of +2.5 on offense and 1000 minutes, respectively.

Table 1: Big men over +2.5 on offensive RAPM for 2014

Player Offensive RAPM PER estimate error
Dirk Nowitzki 4.54 3.04
Nick Collison 3.75 7.06
LaMarcus Aldridge 3.29 4.11
Kevin Love 2.94 -0.07
Channing Frye 2.61 3.36
Amir Johnson 2.55 4.97

This suggests spacing is more valuable for big men than many people think. And if so, just how valuable is it? It’s a question that’s affecting championship contenders right now, as the Spurs continue experimenting with lineups, the Thunder insist on starting Perkins, and the Heat encourage Bosh to hoist more three’s.

Part 2 will investigate how the value of spacing changes specifically for big men.



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