# Nylon Calculus: Color-mixing and lineup synergies

My basketball buddy, Joe, came to the gym wearing pink shoes this weekend. He didn’t know they were pink — at least, not until after the third person teased him about his avante garde new kicks. Joe is color blind, you see. He thought his new sneakers were white. And we all had a good laugh because it seemed not to be a big deal to Joe, but I’m sure it sucks to be color blind. Lots of people are. So, I just want to start with a sincere apology to Joe and everybody else who shares his burden — you’re probably not going to enjoy this post very much.

That’s because we’re about to embark on a technicolor adventure. We’ll dissect every hue in the spectrum of modern NBA skills — from the dazzling ruby red of Ben Simmons to the electric green of J.J. Redick to the sumptuous cobalt blue of Steven Adams. We’ll examine all the pigments that teams are using to paint the modern NBA landscape to find out which colors complement each other and which colors clash.

## The three primary colors

The NBA is increasingly dominated by players who excel at one of three skills: ball handling, 3-point shooting, or rim protection. Guys who can do more than one of these things become stars and guys who can’t do any of these things become marginalized.

These defining attributes can be quantified using three stats provided by the NBA: individual time of possession, 3-point attempts, and field goal attempts defended within six feet of the basket. We’ll use this information to sort players into groups and, later, into colors. To categorize both starters and bench players on equal footing, we’ll look at all of these stats on a per-36 minute basis.

Let’s start by sketching out the rough outline of the 2017-18 NBA landscape using some arbitrary cutoff values: any player who possessed the ball for 5+ minutes per 36 is labeled a “Ball Handler” (shown in pink, below), a “Rim Protector” is any player who defended 5+ FGA inside six feet per 36 (in blue), and I’m calling any other player who attempted 5+ three-pointers per 36 a “3-point Shooter” (in green). A fourth group comprising all of the leftover guys — those players without a modern skill set — are displayed in brown.

Now, to evaluate which type of player is having the biggest positive impact on his team we’ll take a look at the offensive component of Jacob Goldstein’s Player Impact Plus Minus statistic, sorting by skill group.

Each block represents one NBA player and each row is a group of players within the same tier of O-PIPM. The top section of the chart shows the 85 ball handlers who played at least 100 minutes in 2017-18; 39 had a beneficial impact on their offense (46 percent). That’s a bigger positive fraction than was found for any of the other groups. Houston Rocket, Chris Paul, is highlighted near the top of the pile with an O-PIPM of plus-4.47. Overall, the average ball handler O-PIPM was plus-0.15 points per 100 possessions; all the other groups had a negative average.

By far, the least productive type of player was the “other guy”. There were 123 of these misfits, but only 13 of them (11 percent) managed to post a positive O-PIPM. Jeff Green, for example, was stuck at minus-0.71 points per 100 possessions and he was actually BETTER than average for his group (which was minus-1.23, on average).

Offense is only half the story, though; so let’s look at the defensive side of Jacob Goldstein’s PIPM stats, too.

There is some predictable balancing here, as the rim protectors earn some credit for their defensive contributions (average of plus-0.58 D-PIPM) and the ball handlers lose some of their shine because of their defensive limitations (average of minus-0.41 D-PIPM). But, in the aggregate, the brown group at the bottom definitely lagged way behind the rest. Sadly for these guys, the lack of impact on the court is translating to a lack of dollars in the bank.

## The color of money

A few weeks ago, Andrew Johnson surveyed this summer’s free agent market and concluded that big men were getting underpaid. And it’s true — solid rotation bigs like Nerlens Noel and Greg Monroe have been forced to sign minimum contracts during the free agency period; others, like Lucas Nogueira, are still looking to ink a deal. But, a subset of big men who offer rim protection, like Clint Capela and DeAndre Jordan, continue to be in demand and got paid.

In contrast, there were at least 20 free agents from the “other guy” group who signed a contract this summer (excluding those who cashed-in their player options). Only one of them (Rudy Gay) will earn eight figures next season and more than half of them will play for minimum contracts.

Even more so than big men, it is this group of anachronistic players represented by the brown blocks who is getting squeezed out of the current market.

## All the colors of the rainbow

Well, this is where I was planning on wrapping up this post. I’ve made a tidy point and it was very nearly “on to the next one”. But, there was something a little unsatisfying about lumping quality players like Jimmy Butler and Jrue Holiday in with the “other guys” group. I didn’t feel right about condemning them to basketball irrelevance, just because they dribbled a total of four-point-something minutes per 36 instead of five-flat or because they shot four-point-something 3-point attempts. In fact, Jimmy and Jrue were stuck in my craw and that’s right where they stayed until I coughed up another approach.

What if, instead of charting three primary colors with bright-line delineations between groups, we were to consider the full spectrum of possibilities? We could include all possible combinations of the three stats of interest and make a chart to span the entire rainbow of NBA skills.

To functionalize this concept, I changed each of the three per-36 stats into percentile ranks among the 456 individuals who played at least 100 minutes in 2017-18. Then I used the RGB color model to convert the percentile ranks of each player into a characteristic color. For example, Ben “Shoot-a-3-you-coward” Simmons was in the 96th percentile for time of possession, the ninth percentile for 3PTA, and the 23rd percentile for FGA defended inside six feet, which translated to Red=245, Green=24, and Blue=59, creating a bright red (and a color pretty similar to the official 76er red, actually; RGB: 237,23,76). For comparison, J.J. Redick was in the 34th percentile for possession, the 94th percentile for 3PTA, and the third percentile for FGA defended near the rim, producing a Slimer-esque incandescent green (RGB: 87, 239, 7). In contrast, Steven Adams’ ranks in the fourth, fifth, and 77th percentiles turned him a sapphire blue (RGB: 9, 14, 196).

After assigning each person a unique color, I used k-means clustering (kmeans in R) to arrange the players into 20 groups, by color.

You can see that the one-dimensional players highlighted above are found, here, inside clusters of red (Simmons), green (Redick), and blue (Adams); whereas, multidimensional guys like James Harden (yellow) and Nikola Jokic (purple) straddle two contributing colors. The luminosity of each dot is an indication of the player’s underlying percentile ranks in the stats. Players who appear brighter — like Harden — dominated at least one stat category. Players who appear dull – like Tony Allen (25th, 21st, 38th) — had low percentiles in all three stats.

## Lineup fit: Mixing and matching colors

Next, I organized the players into 127 five-man units that played together for at least 100 minutes each during the 2017-18 season. To group lineups into similar-looking five-color combos, I once again used k-means clustering (k=10 this time). Then, I tabulated the median net rating for each grouping of clustered lineups. These were the best lineup structures:

Among the top group of ten similar-looking lineups, the common theme is a bright blue line running along the right side (a rim-protecting center) and a lot of yellowish-green in the middle (multidimensional perimeter players). This lineup combo was generally pretty effective, producing a median net rating of plus-9.9 per 100 possessions.

Each of the ten lineup combinations in the middle group contained a player that does NOT fit any of the modern archetypes (e.g., Andrew Wiggins, E’twuan Moore, etc. in gray); however, these units remained mostly positive, anyways (median net rating of plus-9.1). In each instance, a pairing with a skilled big man (Cousins, Anthony Davis, Karl-Anthony Towns, Giannis Antetokounmpo, etc. in light purple) seems to have been crucially important.

The next block of twelve lineups shows an idiosyncratic orange-yellow-green-blue-purple rainbow that reflects a conventional PG-SG-SF-PF-C positional approach. These if-it-ain’t-broke lineups achieved a very respectable median net rating of plus-8.8.

The next three lineup groupings had lower, but still positive, net ratings:

The top grouping of 15 lineup combinations once again harbored one of the “other guys” (e.g., Corey Brewer, Evan Turner, Andre Iguodala, etc. in dark green/red); however, the long-distance shooting of the lead guards (e.g., Stephen Curry, Kyrie Irving, Damian Lillard, etc. in yellow) opened up space for thesee teammates to score and kept these lineups in the black.

The middle grouping of 17 five-man units feature a lot of yellow, green, and teal blocks indicating that there were lots of 3-point shooters playing together. This strategy worked well for the Rockets, who have six different positive combos in this set.

The bottom grouping of nine lineups was unique as it featured more blue and purple blocks than any other. These big-heavy lineups would have had no chance to succeed with a non-shooting lead guard, so it makes sense that there are no red blocks to be found in this grouping.

The next three sets of lineups were all slightly off color and, as a result, they posted negative net ratings.

The top block of lineups seems to have had too many one-dimensional players as there is a preponderance of red, green, and blue squares with too few yellow, teal, and purple ones.

The middle group of lineups seems to have leaned too heavily on that stripe of orange cells along the left side – asking the likes of Russell Westbrook and Kemba Walker to shoulder too much of the creative burden without the support of a secondary creator (i.e., too few yellow or purple squares).

The bottom grouping provides an interesting contrast to some of the effective lineups above. Once again, there are a lot of “other guys” (e.g., Andrew Wiggins, Courtney Lee, Evan Turner, etc., in dark red/green); but, here, there was insufficient teammate support to cover up their shortcomings. There are a lot of non-shooting lead guards (in red) and not enough 3-point shooters (in green) or skilled bigs (in purple) to keep things from getting mucked up.

The final grouping of lineups is just, intuitively, very unattractive. These are combinations that generally feature no more than one 3-point shooter. The most egregious of the bunch was New York’s combination of Emmanuel Mudiay, Tim Hardaway Jr., Enes Kanter, Courtney Lee, and Michael Beasley who Knickerbocked their way to a minus-18.8 net rating during the 119 painful minutes they shared on the court, together.

In the end, I’m glad I took a second look at these players who don’t fit the modern archetypes. Because, yes, at first glance, they struggle to provide a beneficial impact on an elite level. And, yes, they are getting squeezed into smaller deals by the cutthroat business of the NBA. But, I see their true colors shining through. In the right circumstances, these guys can still be part of successful lineups and they can still contribute to a winning effort.