Nylon Calculus: Visualizing lineup balance and understanding team fit

In the NBA’s news cycle of trades and free agency and the draft, one buzzword tends to dominate the discussion – “fit.” Is Player X a right fit for Team A? How will Player Y fit into the starting lineup? Understanding how a player’s strengths and weaknesses fill in the puzzle that is a 5-man lineup is a critical component to evaluating their effectiveness on a specific team.

For example, when Kevin Durant went to Golden State in free agency, it was widely presumed that the Warriors would roll because Durant’s skillset was a perfect fit for that team, as an actually elite version of Harrison Barnes. When the Atlanta Hawks replaced Al Horford with Dwight Howard, they had to weigh the tradeoffs within the context of the other players they had. Horford was a great playmaker and could stretch the floor, but Howard brought more physicality and rebounding.

One way to model and understand this concept of fit is something that I have termed “lineup balance.” Balance is composed of three components: synchronousness, complementariness, and skill. Synchronousness captures if multiple players’ skillsets overlap. A perfectly synchronous pair of players will have exactly overlapping statistical profiles. Synchronousness can be valuable if looking to create a lineup with multiple talented defenders and rebounders or an all-out spacing lineup with 3-point marksmen. Complementariness, on the other hand, captures if multiple players’ have skillset that cover each other’s weaknesses. A perfectly complementary pair of players will have statistical profiles that exactly fill in each other’s gaps.

Read More: Comparing draft prospects by unassisted field goal attempts

To create a balanced lineup, you need multiple players that can do certain skills very well (synchronousness), but you also need those players to be able to cover for the deficiencies in each other’s games (complementariness). The final piece of the puzzle then is skill level. It’s great to have a lineup that has a well-rounded set of skills, but if all their skill levels are below average, being simply nominally balanced won’t do much good for anyone.

The two-man lineup examples below illustrate these concepts that comprise good balance. In these radar charts, 17 statistical features (using current data in the 2016-2017 season) were selected to create a statistical profile that was a mix of both playing style and effectiveness. All stats were then standardized as percentiles among players who’ve played at least 100 minutes this season so far.

One of the reasons that a Nikola Jokic-Jusuf Nurkic pairing tanked for the Denver Nuggets was that they had overlapping skill sets that still left some pretty glaring deficiencies, namely a lack of spacing and the tendency to foul. Neither player was above the 25th percentile in 3-point attempts or personal fouls committed. And while they turned the ball over at a higher clip than average, they didn’t really force steals to get those balls back. As Jokic is clearly the superior player, Nurkic clogging up interior space was holding Jokic, and consequently the Nuggets, back.

Read More: Nikola Jokic is the best passing big man in the NBA

On the flip side, a Kyrie Irving-Tristan Thompson pairing is illustrative of how two complementary players can fit together. While Irving provides the ball-handling and scoring prowess, Thompson brings the interior physicality and ability to protect the basket and handle the grunt work. Whereas Irving-Thompson are a good pair, Chris Paul and DeAndre Jordan together are utterly dominant. This is a duo that bring synchronous skills (scoring efficiency, defense at all levels, and an ability to get to the free throw line), complements each other well (while Paul can space the floor well and handle the ball, Jordan can dominate the boards and doesn’t need the ball in his hands), and does all of those things at an extremely high level. That’s what a well-balanced pairing looks like, and it’s why people have questioned whether having the trio of Paul, Jordan, and Griffin on the court together offers only marginal advantages over staggering them in pairs.

Of course, basketball isn’t played two-on-two. The next step is visualizing how a five-man lineup fits together. The key caveat here is keeping in perspective the importance of lineup balance. Balance is also dictated by game and stylistic context. Depending on a certain game situation, sometimes you want to put out an all-shooting lineup, or a slogging defense-only lineup, and in those cases, balance is less important.

With that said, in order to do this, I’ve chosen one “primary” lineup (a somewhat subjective decision made by weighing total minutes played as a unit, effectiveness, and team record) from each team in the league and displayed each player’s statistical profiles juxtaposed together in stacked radar charts for each of those lineups. Since each player can contribute up to the 100th percentile in any one area, the outermost rim is 500 percentile “points” – the theoretical extreme if all five players were 100th percentile in a statistical feature (and the center is 0, with each ring in between at the 100 percentile multiples). If each player were exactly middle of the pack (50th percentile) in a certain category, they would sum up to 250 percentile points, a decent baseline for what constitutes “average” skill level.

Overall, it’s an effective way to see the statistical strengths and weaknesses in a lineup, where tradeoffs where made, and how individual players contribute to the overall identity of a lineup. We can use a tool such as this to clearly grasp the nebulous concept of “fit” and better analyze player movement in team context. So without further ado, here are the lineup balance charts for each team in the NBA so far this season.

We can also take this further. Keeping in mind that a perfectly balanced lineup would fill out the entire area of the radar chart completely, an approximate way to quantify the lineup balance can be derived from dividing the geometric area of the lineup’s total radar charts from the theoretical maximum area (a more exact method for future work would involve independently quantifying synchronousness, complementariness, and skill and aggregating those measures). This returns a percentage score for how “balanced” a lineup is. Those scores are displayed in the below table and plotted against their raw plus-minus ratings thus far (raw plus-minus was used rather than net rating, since due to small sample size caveats with regards to minutes played for many lineups at this point in the season, I didn’t want to project an outsized image of their efficacy).

The distribution of balance scores for each team’s selected lineup demonstrates an underlying principle of the real world. No lineup is perfect. Even those that we think are near perfect, like the Golden State Warriors, have clear weaknesses and top out at 39 percent balance. It’s all about tradeoffs. No lineup with all high usage players, for instance, could survive without combusting. Additionally, while having a high balance score is not a singular predictor of effectiveness one way or the other (from this limited analysis of 30 data points), the only team with a below average balance score to register an above average raw plus-minus rating was the Marc Gasol-led Memphis Grizzlies. Through a spate of injuries and expanded roles for young players still finding their way, Gasol has absolutely carried the Grizzlies way above reasonable expectations (this concludes my Marc-for-MVP plug).

Here are a few other notes on the lineup balance charts from each team:

• The Nets are an example of a team that’s reasonably well rounded, that has synchronousness and complementariness in their lineup, but a limited skill level and thus a limited ceiling.
• Look at that gaping hole for Chicago where 3-pointers and spacing are supposed to be.
• If we needed another measure for understanding how good Charlotte is on defense, look no further than the fact that their primary lineup has three players above the 80th percentile in Defensive Box Plus-Minus, and collectively they don’t commit fouls nor do they slip up in the defensive rebounding department to give up second chances.
• The Suns, Mavericks, and Heat are the three worst-balanced lineups in the league, with each of them struggling to cross the cumulative 300 percentile points mark on most statistical features. There is no balance without skill.
• Golden State’s “megadeath” lineup may mercilessly hunt assists and have the highest balance score, but they also have a glaring lack of rebounding ability (especially on the offensive glass), unsurprising given the tradeoffs of small ball.
• Indiana may be a mess right now, but Paul George and Myles Turner provide a really solid foundation to try and build around.
• One more Grizzlies note — none of those players aside from Gasol are going to jump off the screen, but collectively it might be one of the best defensive lineups in the league. (even with Troy Daniels). Long live Grit-and-Grind.
• The Timberwolves’ lineup that was supposed to be full of promise and potential has instead been horrid defensively and sloppy with the ball, a disastrous combination.
• HELLO JOEL EMBIID.
• HELLO GEORGE HILL.

All research and data courtesy of NBA.com/stats and Basketball-Reference.