Nylon Calculus: How do we know if an NBA lineup will work?

We built an app that searches for NBA lineups with specific combinations of player archetypes so you can imagine how well new lineups might fit together.

As NBA teams continue to be eliminated from championship contention, for many front offices, it’s self-evaluation season. Why did we lose? What was our team missing in the end? And, leading up to the draft and free agency, teams will be asking: what players can we add and how will those new pieces fit into our existing roster?

The Philadelphia 76ers, for example, had a disappointing finish to their postseason – as they were swiftly ushered out of the bubble by the Boston Celtics in a first-round, four-game sweep. It has been suggested that the Sixers two young stars — Ben Simmons and Joel Embiid — are not a perfect pairing, which has led to persistent rumblings about possible trades involving one or the other. The concerns are probably overblown, as Philadelphia’s starting lineup of Simmons, Embiid, Josh Richardson, Tobias Harris, and Al Horford was actually pretty darn good this year, with a net rating of +8.4 points per 100 possessions throughout the regular season. But it’s fair to wonder if the Sixers are making the most of all their young talent, especially given the immense price tag of that starting lineup (which is owed $129.5 million next year).

Setting aside the tougher questions of its effectiveness and value for a moment, I think we can all agree that the Philadelphia starting lineup is definitely pretty WEIRD. They start three guys who were, at one point in time, each considered to be a power forward. They have a ton of size, plenty of playmaking, but an obvious lack of elite perimeter shooting. So what should the Sixers brass do this offseason? Should they break up Simmons and Embiid? Should they bring in a shooter to help space the floor? How would that new lineup look and how can we be sure the new players would fit together any better than the current ones?

I built the Similar Lineup Finder app to help us answer questions just like these.

The app is based on the idea that the three most important jobs that an NBA player can do for his team are to create offense, space the floor, and protect the rim — and that you can figure out a lot about what type of player somebody is by looking at how often they do each of those three things. If we start with that premise, we can sort out all the players in the league using a trio of per-100 stats: (1) the number of times per 100 possessions that a player directly contributed to his team’s offense with a shot, pass, or turnover (ie. Ben Taylor’s usage stat “Offensive Load”); (2) the number of 3-pointers attempted per 100 possessions; and (3) the number of field-goal attempts contested within 6 feet of the basket per 100 possessions. I re-scaled these three rates to reflect the players’ percentile ranks and regressed low-minute players towards the league average to define the three skill dimensions that will help us evaluate the differences and similarities between lineups so that we can learn more about which combination of players might work well together and which ones probably won’t.

For the app, I used the RGB color model to visualize the differences between types of players, with red symbolizing offensive creation, green indicating floor spacing, and blue showing rim protection. With that in mind, here’s a look at the tapestry of player types that make up the NBA this season.

I’ve labeled a few of the players who logged the most minutes this season so you can get a sense for how the colors work. Guys in the red, green, and blue circles are (more-or-less) one-dimensional players who can only create (eg. Russell Westbrook), shoot (eg. Tim Hardaway Jr.), or protect the rim (eg. Rudy Gobert). Guys in the orange, yellow, teal, pink, and purple circles do a combination of useful things to varying degrees and players in the dark neutral tones don’t do much of any of these three most important NBA jobs.

We can examine how the current cohort of NBA players spans these three dimensions of skill, starting with a look at offensive creation and floor spacing.

A lot of the league’s biggest stars occupy the right side of the chart reflecting their roles as the engines driving their teams’ offenses — with a gradient of circles ranging from the trey-happy Trae Young at the top in sunshine yellow to the 3-point-averse Simmons in brick (pun!) red at the bottom. There are bands of electric greens (eg. Duncan Robinson) and blues (eg. Gobert) at the top and bottom of the left side of the chart, with more muted hues falling in between the two.

Next, let’s slice our cloud of player bubbles in another direction and consider the relationship between offensive creation and rim protection.

This viewpoint separates the players into four quadrants: the reds, yellows, and oranges in the bottom right corner are high-usage perimeter players, the greens and browns in the bottom left corner are low-usage perimeter players, the blues are low-usage bigs, and the pinks and purples are high-usage bigs. In all of these charts, it’s fun to find the players who are the sole occupant of a big void, like Robert Covington is here. He played a unique role in Houston as evidenced by all that white space around his teal circle.

Finally, we can look at our player pool from the third perspective by charting floor spacing and rim protection.

Here again, we see the perimeter players on the bottom of the panel and the bigs on the top, but now the shooters are on the right side and the non-shooters are on the left. This gives us a clear look at the icy blues of Kristaps Porzingis and his fellow 3-point shooting, rim-protecting unicorns.

Finally, just for good measure, we can squish these three scatter plots together to visualize the players’ positions across all three skill dimensions, at the same time.

The Similar Lineup Finder starts with five user-supplied players and tries to find the 50 most similar lineups that played at least 20 offensive possessions together during the 2019-20 regular season. Lineup similarity is defined by the Euclidean distance between pairs of individual players across the three skill dimensions: offensive creation, floor spacing, and rim protection. As a reminder, the system is based on how OFTEN each player does these things not how WELL he does them (although, obviously, those two things tend to be pretty tightly correlated in the highly optimized NBA environment).

Now that we know a little bit more about what the app is trying to do, let’s go back to the question of how to make the most out of that Sixers starting lineup. We can plug Richardson, Harris, Horford, and Embiid into the app and then play around with trying to find an ideal fifth starter to round out the group.

Would a dose of bright green medicine in the form of 3-point specialist Duncan Robinson be the tonic for what ails the Sixers? How about bringing back erstwhile teammate J.J. Redick to free up some space inside for the other guys to operate again? Of course, they still have some capable shooters left on the team. What about subbing out Simmons for Furkan Korkmaz, Mike Scott, or Glen Robinson? Shake Milton was asked to inject some perimeter shooting into the beefy starting lineup at the end of the season — could that be a longer-term solution for Philly?
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If we swap in Shake for Simmons alongside the other four Sixers and feed that new starting lineup to the app it will look for the 50 most similar 5-man units from the 2019-20 season, by doing something like what is being visualized below.

In this case, the app identifies several of the Nuggets lineups as being similar to the proposed Sixers unit, including the Jamal Murray-Gary Harris- Will Barton-Paul Millsap-Nikola Jokic combination that was the most common one in Denver this year. The app’s goal is to minimize the combined distances between each inter-lineup pairing — ie. between Shake and Jamal, Josh and Gary, Tobias and Will, Al and Paul, and Joel and Nikola — across the three-dimensional space. The app compares the proposed lineup to each of 2,347 lineups that played at least 20 offensive possessions this season and tries every permutation of pairs for each potential lineup comparison. You can compare the returned lineups yourself and check how well the colors match on the second tab of the app. Here’s how the comps look for the Sixers lineup we proposed.

Once the app has the 50 lineups that it considers to be the most similar to the proposed lineup, it looks up the offensive, defensive, and net ratings for each comp and then calculates the weighted average across them all. This gives some hint as to how well the new lineup might perform over a sustained period of time.

For example, here are the ratings for the 50 lineups most closely aligned with our hypothetical Sixers starters.

The results of our tinkering are not very promising as we’ve achieved a pretty modest average net rating of just +2.9 points per 100 possessions among our 50 comparable lineups. We can actually do much better if we keep Simmons and drop Horford for more shooting (which, incidentally, was what Brett Brown decided to do in the seeding games prior to Simmons’ knee injury). But, I’ll leave it to you to find the perfect combo for the Sixers as well as the best landing spots for Simmons (or Horford…or Embiid…or anybody else you want to see moved).

So that’s how the app works. You can go play with it. Have fun!

…

OK. It’s just us now.

I wanted to say that I have some misgivings about this new app. For starters, I’m a little concerned by the fact that you can input two nearly identical proposed lineups and end up with very different weighted average net ratings for the resulting comps. The app is built to emphasize transparency perhaps at the cost of a lack of generalizability. It would be nice to add some modeling to smooth things out a bit, as I’ve tried to do in the past with a previous look at optimizing lineup fit.

Furthermore, the app returns exactly 50 lineups that are most similar to the proposed lineup regardless of how good the matches are (ie. there is no minimum similarity score cutoff). If you propose a lineup with 5 centers, the app will have no problem finding the 50 closest matches for you, but the results might not really tell you much about the feasibility of playing big ball. I leave it to the user to check the similarity scores and RGB color schemes to decide how much he/she really trusts the comps. A good rule of thumb seems to be that a similarity score of 80 or so is indicative of a truly close comparison. If you find yourself looking at “similar” lineups with scores of 65 or less, then the differences between the proposed lineup and its comps are actually pretty vast.

Finally, focusing on lineups with 20 or more possessions (for the sake of faster loading times) imparts some bias towards higher performing lineups. Lineups that work well tend to get more opportunities to play together. Lineups that are disastrous might not get a second chance to see the court. When things are running smoothly, teams play their best lineups. When there are injuries, foul trouble, or blowouts, teams may be forced to experiment with unusual (ie. less effective) combinations. As a result, the weighted average net ratings across the lineups included in the app is slightly higher than zero (+0.3 points per 100 possession).

Still, I think the app has some pretty neat potential. Because of the extreme randomness associated with evaluating a five-man lineup combo across a limited number of possessions, it’s a really powerful approach to look collectively at how well several similar lineups have performed. In the app, you can also choose to include similar lineups from within your own team or you can exclude the selected players from the search results.

Personally, I think it’s a lot of fun to imagine new lineup possibilities. Consider how somebody from the bench might slot in next to your team’s starters. Think about how a player acquired via trade or free agency could fit into your current roster. Map a potential draft pick or G-League player onto his closest NBA comp and then project how he might help your team. The possibilities are endless. Go try the Similar Lineup Finder now and experiment for yourself.