Nylon Calculus: Stephen Curry, a case study in visualizing plus-minus

Plus-minus is a stat that measures — for a given player — the score differential between the player’s team and his opponents, during the time while he is on the court. It’s a pretty common metric these days, you can find it in all the box scores. It also forms the basis for several advanced statistics in basketball.

Despite its common use, we don’t see it visualized in context nearly as often as we see the raw numbers, so I thought I would make some charts to show exactly how it works. I’m going to use Stephen Curry, the league’s leader in plus-minus this season, as a case study.

Plus-minus for an individual game

Let’s start by looking at Curry’s outing on Dec. 5, 2015 against the Toronto Raptors. This was the quintessential 2015-16 Golden State Warriors performance: Curry and his fellow starters built a double-digit first-quarter lead, which the bench subsequently squandered in the second quarter. With Curry back in the game, the Warriors maintained a cushion throughout the third quarter; but, while he was resting again to start the fourth quarter, the reserves allowed the Raptors to take the lead. Ultimately, Curry returned and carried the Warriors to a narrow victory.

You can see the game flow in the chart above. The lighter gray sections indicate the periods of the game when Curry was on the bench. During these stretches, his pink plus-minus line is flat and it diverges from the purple score-margin line of the Warriors, as a whole. By definition, when Curry is in the game, the two lines (pink and purple) always run in parallel. The Warriors dropped eight and four points, respectively, during Curry’s two trips to the bench. As a result, Curry posted a plus-minus of +15, despite the Warriors’ relatively small margin of victory (+3).

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Here’s another oh-so-Warriors performance from last season: Dec. 8, 2015 against the Indiana Pacers. The Warriors hung 111 points on the Pacers over the course of the first three quarters and cruised to a 28-point lead entering the fourth. Coach Steve Kerr pulled the starters, but the bench immediately began barfing up points. Curry’s lineup had to re-enter the game (you may remember, this was the one where Klay Thompson sprained his ankle mopping up the bench’s mess) and the Warriors managed to eke out an eight-point win. Curry finished +18, ten points better than the team as a whole.

Here’s another example of just how dependent the Warriors were on the brilliance of Curry last season: Jan. 16, 2016, a rare loss to the Detroit Pistons. Curry was good enough: +2 during his time on the court; but the bench let him down by giving up two big runs to the Pistons when he sat to start the second and fourth quarters.

Finally, here’s an exception to the rule: a game when Curry needed the bench to bail him out! It happened Jan. 11, 2016 when the Warriors beat the Miami Heat by eight points.

This was a rare game when Curry was actually a net-negative; he finished with a plus-minus of -3. You can see, however, that the reserves actually increased the lead during both of Curry’s trips to the bench, allowing the Warriors to prevail in spite of his below-average showing.

Plus-minus for all of 2015-16

We can repeat this process for every game Curry played in the 2015-16 season and chart his plus-minus as it accumulated over the course of an average game.

You can see the extremes: a +37 night in a 50-point blowout against Memphis and a -18 night in a 32-point shellacking at the hands of Portland. On average, Curry finished the fourth quarter +12.7, nearly two points better than the Warriors’ (impressive-in-its-own-right) +10.8 average margin of victory.

Aside from the two mostly-flat sections at the start of the second and fourth quarters (when Curry was usually on the bench), you can see how the average plus-minus line ticks up steadily over the course of the game. Basically, whenever Curry was playing, the Warriors tended to be building a lead. The plot above shows the cumulative plus-minus as it grows and shrinks over the course of the game, but we can also look at the per-game point differentials for various increments of time: for one-minute blocks, for three-minute blocks, for six-minute blocks, and by quarter in 2015-16.

Curry was at his best in the seventh minute of the first quarter, when — with his help — the Warriors outscored opponents by 1.0 points per minute in an average game. Check out the three-minute blocks: excluding the four periods when Curry was mostly on the bench, he was at least +0.5 for 11 of the other 12 three-minute segments of the game. Similarly, he was at least +1.4 during each half-quarter in which he played regularly. Finally, if we look at plus-minus per game by quarter, Curry’s success in the first period stands out. What’s amazing, though, is that — despite the fact that Curry finished more than half of the Warriors’ games on the bench and despite the fact that he sat out 16 fourth quarters entirely — Curry was +2.5 in the final period. In fact, if Curry had sustained the per-minute plus-minus rate that he notched in the fourth quarter over 48 minutes he would have averaged a plus-minus of +25.8, the best such rate in the NBA.

Plus-minus for all of 2016-17

Curry has looked a little different this season while sharing the spotlight with his new co-star, Kevin Durant. In the average game, Curry’s total plus-minus is pretty much identical to what it was last year (+12.8), which is better than any of his teammates or anybody else in the league. However, the shape of his average game plus-minus curve is different this year.

The biggest change from a season ago is the way that Curry has helped the Warriors absolutely crush the third quarter this year. With Curry on the court, the Warriors are outscoring their opponents by an average of 5.5 points per game in the third. For a recent example, look no further than the Warriors 46-point beating of the Los Angeles Clippers this past Saturday (not included in the above plot). Curry and the Warriors were +22 in the third quarter on the back of his 25-point outburst during those 12 minutes.

In contrast, Curry’s fourth quarter plus-minus has been pretty flat this year. His late-game heroics have been mostly absent; consequently, his fourth-quarter plus-minus has been scaled back to +0.7. It’s worth noting that Curry has been playing even less frequently in the fourth quarter this year: finishing a meager 41 percent of the Warriors’ games on the court and skipping out completely on 14 fourth quarters to date; but, his per-minute plus-minus fourth quarter stats are also less impressive this season. If we extrapolated his fourth-quarter plus-minus rate to a full 48-minute game, he would be averaging a plus-minus of +7.7; definitely respectable, but no longer as outstanding.

Plus-minus comparison for the past two seasons

I’ve alluded to it above, but here’s a more direct comparison of Curry’s average plus-minus charts from the past two seasons. Again, the total plus-minus is very similar between this year and last. The biggest difference is the hump in the 2016-17 curve that is noticeable in the third quarter and the subsequent flattening out of that green curve in the fourth quarter.

Not coincidentally, Curry’s level of play has felt a bit reduced this season. Some of that is just an unavoidable regression to the mean after an historic season and some of it is down to his sharing the ball with Durant; but, in addition to those two things, I think it’s also been the smaller number of meaningful fourth-quarter performances that has diminished Curry’s aura of otherworldliness this time around. It’s hard to say if these patterns are meaningful yet. We’ll need to wait until May to find out if the stiffer tests of the Playoffs will expose a diminished Curry or reveal his greatness once again.