# Nylon Calculus: Visualizing lineup rotations for the Golden State Warriors

Increasingly, advanced basketball statistics evaluate a player’s value based on how his team performs while he is on the court. There’s an ever-growing collection of plus-minus stats — Adjusted Plus-Minus, Real Plus-Minus, Box Plus-Minus (and its derivative, value over replacement player or VORP) — as well as on-off comparisons like with-or-without you and two-way WOWY.

These stats are built on statistical methods that try to account for the context of who a player shares the floor with. However, it’s useful to actually understand the context in which the player finds himself, not just have it mathematically embedded in a model. Which of his teammates is he playing with and who is on the court when he goes to the bench? As such, a graphic representation of a team’s lineup rotations would be a useful tool to complement modern basketball statistics.

Here, I create a few visualizations of the lineup rotations employed by the Golden State Warriors as a proof-of-concept and describe a few observations that can be gleaned from this variety of graph.

## An example from a single game

Let’s start by looking at Golden State’s lineup rotation during a single game, their Nov. 28 matchup with the Atlanta Hawks in Oakland last month.

Lineup rotation for the Golden State Warriors vs. the Atlanta Hawks (11-28-16)

This particular game was tightly contested — with seven ties and seven lead changes — ultimately ending in a five-point victory for the Warriors. As such, the rotation decisions represent something like the default choices for the Golden State coaching staff this season; for example, trotting out Stephen Curry, Draymond Green, Klay Thompson, Zaza Pachulia, and Kevin Durant as starters, and featuring Curry, Green, Thompson, Durant, and Andre Iguodala as the finishing unit.

Eleven Warriors entered the game; five as starters (shown in pink above) and six as reserves (shown in green above). Green played the most minutes of any Warrior (39:10) and Pat McCaw the fewest (3:48). Kevin Durant was the most frequent visitor to the scorer’s table, heading to and from the bench on four different occasions.

## A new rotation pattern

Now that we have a template for visualizing the Warriors’ lineup rotations for a single game, we can look at the average rotations for the entire season. For each second of every game in the season thus far (thru Dec. 16), I assigned a player a ‘1’ if he was on the court and a ‘0’ if he was off and took an average across all games. In this way, the plot below shows the probability that a player would be in the game at any given moment.

Average lineup rotations for the Golden State Warriors; 2016-17 regular season

We can take a lot of information from the plot above. The solid pink in the upper lefthand corner indicates that Curry, Green, Thompson, and Durant have each started every game this year; not so, however, for the slightly-lighter-pinked Zaza Pachulia. We can see that nominal reserves, JaVale McGee, Kevon Looney, and even Anderson Varejao have all taken turns starting in place of the injured Pachulia. Notwithstanding these sporadic starts, Looney, Varejao, and James Michael McAdoo are mostly appearing exclusively in “garbage time,” during the fourth quarters of non-competitive contests.

Likewise, rookie Damian Jones — who has been bouncing back and forth between Golden State and its Santa Cruz D-League affiliate — hasn’t played much. The rest of the Warriors reserves have settled into a mostly consistent substitution pattern. The one exception is, perhaps, the battle for backup shooting guard being waged by McCaw and Ian Clark. The two have cannibalized each others minutes in the rotation, with either one or the other featured in reserve units or, less often, the two playing together.

You can see the effect of garbage time on the starters’ rotation pattern as well, as the pink bars for Curry, Green, Thompson, and Durant all look a little washed out at the end of the fourth quarter. Perhaps the most intriguing observation from the plot above is the substitution pattern for the starters during the first three-and-a-half periods. You can see the rotation is much different than it was last year.

Average lineup rotations for the Golden State Warriors; 2015-16 regular season

During the 2015-16 regular season, both Curry and Green generally played most — if not all — of the first quarter, before taking a trip to the bench for several minutes at the start of the second quarter. The erstwhile starting small forward, Harrison Barnes, was subbed out about halfway through the first quarter so that he could return at the start of the second quarter. This pattern repeated in the second half at the start of the fourth quarter. The result was that Barnes was left to prop-up five-man units comprised of mostly bench players for at least ten minutes each game, sometimes with the support of Thompson.

In contrast, this season, assistant coach Mike Brown has reorganized the Warriors’ rotation scheme so that the starters’ appearances and departures are staggered throughout the game. Durant and Thompson are both typically removed from and returned to the court before the end of the first quarter. They hit the bench again during the second quarter for a quick breather. Green and Curry, too, are being subbed earlier in the first quarter than they were last year. Brown’s clever adjustment ensures that the Warriors have no fewer than two All-NBA stars on the court at any given time. Moreover, the new-and-improved rotation sets up the Warriors to routinely finish the first half with the Slim Reaper’s death unit of Curry, Green, Thompson, Durant, and Iguodala.

## Disappearing depth

While this summer’s addition of Durant was mostly lauded as a coup for the Warriors, there were some lingering questions about the perceived cost of the transaction: did Golden State sacrifice its depth for star power? Indeed, in addition to Barnes, this summer, the Warriors were forced to part ways with Andrew Bogut, Leandro Barbosa, Marresse Speights, Festus Ezeli, and Brandon Rush, all important members of the championship team in 2015. How would these losses impact the Warriors?

From the plots above we can see, on a very basic level, how the minutes of the departed players have been redistributed to their incoming counterparts: Barnes-to-Durant, Bogut-to-Pachulia, Barbosa-to-McCaw/Clark, Speights-to-West, Ezeli-to-McGee, and Rush-to-Looney. Unfortunately, our lineup graphics won’t offer much information about how well these replacements are performing for the Warriors, but they can give us a clue about how important depth will be for the Warriors for the remainder of the season. For example, let’s take a look at Green’s rotation pattern last year throughout the regular season (shown in pink below) and during the postseason (in purple).

Draymond Green rotations; 2015-16 regular season (pink) and postseason (purple)

Again, in the regular season, we see the same substitution pattern that was described above — Green playing most of the first and third quarters with long visits to the bench at the start of the second and fourth quarters. You can also see many instances of the Warriors blowing out their opponents, when Green played little or none of the fourth quarter. What’s interesting to note is that, when you reach the bottom of the log, during the Western Conference Finals (WCF) and the NBA Finals, Green played more of the second quarter and (when the game was in question) more of the fourth quarter as well. This trend culminated in Game 7 of the Finals, the last game of the season, when Green played a herculean 46:54, resting for just 66 seconds on the bench.

While these observations aren’t necessarily surprising, they serve as a good reminder of the difference between regular season rotations and playoff rotations. As a team nears the ultimate prize of a championship, it will tend to rely more on its key players to shoulder the burden of responsibility for wins and losses and, as a result, the bench will “get shorter”. So that, in the end, depth may be more of a luxury than a necessity for a championship contender.

Perhaps inspired by their disappointing Finals loss last season, the Warriors seem to have bought into a starpower-over-depth philosophy. Specifically, they seemed to have realized that the center position just isn’t a priority for them. To illustrate my point, let’s take a look at how the Warriors used centers over the course of the season last year (shown in orange below).

Average lineup rotations for the centers (orange) of the Golden State Warriors and for Andre Iguodala (green); 2015-16 and 2016-17 seasons

As you can see, for most of the regular season, the Warriors tended to keep at least one center (i.e., Bogut, Ezeli, Speights, or Varejao) on the court at all times. That approach softened in the postseason, as the center minutes started to erode from the ends of the second and fourth quarters. By the time the Warriors reached the Finals, they were basically not using a center for most of the second quarter and most of the competitive portions of the fourth quarter. The only exception to this trend came in the form of some garbage-time run for Varejao et al. (remembering that only Game 7 of the Finals ended with a close score).

This season, Kerr, Brown, and the Warriors coaching staff have sustained the center-eschewing rotations that they established in the 2016 Finals. Pachulia and McGee (and to a lesser extent Varejao and Jones) are only playing at the start of the first and third quarters and at the very end of non-competitive games.

On the other side of the coin, Andre Iguodala was the primary beneficiary of the minutes lost by the center position in 2015-16. You can see how his green bars spread further across the game’s timeline during the Western Conference Finals (WCF) and the NBA Finals; he even started three games during those final two series of the year.

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His 2016-17 regular season rotations have looked very much like his rotations from 2015-16 regular season and it’s reasonable to expect that he will start stealing minutes from Pachulia and McGee this postseason as well. In short, if the Warriors plan to lean heavily on the small-ball unit of Curry-Green-Thompson-Durant-Iguodala during the biggest moments of the biggest games this season, then the loss of Bogut, Ezeli, and Speights will have little bearing on the ultimate success or failure of the team.