# Nylon Calculus Week 10 in Review: A new spin on assist stats

As the world turned the page on another year, we’re just one more week into the NBA season. We’re nearing the halfway point, and the All-Star Game is right around the corner. All the bizarre numbers at the beginning of the season — the Los Angeles Clippers performing like an all-time team, the Chicago Bulls shooting well from outside, the Golden State Warriors looking mortal — have regressed heavily. The state of the league is pretty stable, though there’s still the possibility of a massive second-half change; those happen occasionally.

The common thought before the season is that we were headed toward another Cavaliers-Warriors showdown in the finals, and that does still appear likely. But the NBA is fast and chaotic, and changes can quickly take hold. We now accept Giannis Antentokoumnpo is an MVP-caliber player, and that would have been unthinkable just a few months ago. Let’s prepare for the second half.

## Are there too many 3-pointers?

There’s been some discussion bubbling recently about the continuing upward trend of 3-point field goals. The league-average ratio of 3-point attempts to all field goal attempts is just shy of one-third, and the 3-point-shooting center is no longer a rare beast. This is remarkably different than what we’ve seen in the past, and the changes have actually been accelerating. We can all agree, for the most part, on why teams are doing this and why it’s beneficial, but is this entertaining? Are we going to reach a point where this isn’t aesthetically pleasing?

The equilibrium point for 3-point rate is shaped by a simple fact: a 3-pointer is not the best shot in basketball. Instead a shot at the rim is the best shot, and going to the free-throw line is (usually) better too. So if the league traded all its midrange shots (from ten feet and out) for ones behind the arc, you’d have a ratio of 0.56 3-pointers per field goal, or roughly 0.5 per true-shot attempt. I understand those are all assumptions, and that if you stop taking mid-range shots it can change the frequency of your open looks at the basket or behind the line; but this is just a rough estimate. Houston right now, for example, has a 3-point to field goal ratio of 0.46. They’re approaching the theoretical limit where you’re in danger of missing out on more valuable shot types, like free throws, if you keep pushing outside shots.

There’s no correct way to answer a question about aesthetics. I understand the concern about variety. If all we see are drives to the basket or 3-point shots, events are easier to predict and, thus, more boring. But if we’re simply replacing other types of jump shots, I don’t think think this is a major issue. There’s still a lot of action and shot types around the rim, including that awkward area from three to ten feet.

But if we’re sincerely concerned about the prevalence of the 3-pointers, then we need real solutions: move the line back about a foot and make it uniform all the way around. And yes, this would mean widening the court, which is my real dream for the NBA. We could allow more angles to attack and make shots that are worth 50 percent more a little tougher to convert. I doubt that’ll happen, so for now prepare yourself for a league where 3-point ratios approach half of all shots.

## Westbrook: Triple-double update

I feel as though we’re not freaking out about this as much as we should: Russell Westbrook is still averaging a triple-double, he’s got a bit of wiggle room, and it’s January. A decade ago, John Hollinger, preeminent NBA statistical writer who’s currently using his voodoo magic on the Grizzlies to extract wins from stone, noted that the modern-triple double season was virtually impossible. This was in the era of young LeBron James and rebounding phenom Jason Kidd, who was actually the closest to accomplishing the feat. I

would think the increase in the pace of play explains much of Westbrook’s numbers, or perhaps more missed shots from all the 3-pointers, but it’s more than that: he’s grabbing a significantly higher percentage of rebounds than Kidd. This is an anomalous individual performance, and while his teammates are conceding many easy rebounds to him, it’s still unprecedented.

## What happened to the Pistons?

The Stan Van Gundy era has not been a renaissance for Detroit. They’ve got about the same adjusted point differential as last season with a lower win percentage, and they’re only slightly better than two years ago. They’re still a lot better than they were pre-Gundy, but any other progress has been virtually nonexistent. Much can be tied to the stalled development of their prized big man, who was supposed to be Stan’s next Dwight Howard.

Andre Drummond, unfortunately, hasn’t changed much at all in the past couple years, and he’s been arguably worse than he was before Van Gundy. This version of Drummond is much more active on offense, but has traded that usage for efficiency — he’s gone from a true shooting percent of 59.3 and a usage rate of 16.9 percent in his first two seasons to a combination of 50.5 and 20.3. I understand the desire to expand his game, but crafting Drummond into a post player, a guy who can’t shoot free throws or pass well, downplays his strengths and has been largely a mistake.

Outside of their center, Detroit does have a handful of decent players, and their best player, according to most advanced stats, might surprise most fans: Kentavious Caldwell-Pope. He doesn’t stand out in any particular area, but he’s a well-rounded, good outside shooter who plays solid defense. But he’s no one’s idea of a franchise player, unless he takes a Jimmy Butler-esque leap. Reggie Jackson was supposed to be their best player, or ideally their second-best behind Drummond, but he’s had a disappointing season. Tobias Harris and Jon Leuer have been good, but, again, they’re not franchise cornerstones.

Before this season, the Pistons enjoyed a little bit of success with the combination of Reggie Jackson and Andre Drummond, torturing teams with pick-and-rolls. Jackson was injured, and he hasn’t been too effective this season. And the Drummond post-up experiment, as I’ve repeatedly stated, should be ended. He should be used like DeAndre Jordan, focusing on shots inside, screens, rebounding, and defense — that’s okay. You can have one starter like that, and it plays to his strengths. The Pistons should perform better over the course of the season, but I’m concerned about their long-term success: who will they become, and which players will remain in their core? This isn’t enough to compete with the top classes of the league.

## The three centers

We’ve had no change with the three-center conundrum in Philadelphia, but I think one fact reveals the position: Joel Embiid and Nerlens Noel have only played a little under two minutes together, per Basketball-Reference[1.]. Thus, since they have not tested this big man combination in real games, I doubt this is the combination they want going forward. That’s no surprise, but you don’t want to show your intentions and it’ll be easier for other teams to buy Noel. They’ll likely be giving up a young asset for a lot less than he’s worth. But at the very least, can we see how the team performs with Embiid and Nerlens? Experimentation is fine; it’s not like they’re fighting for playoff seeding.

## The Beard and the revenge of the 50-point game

James Harden just had a monster 50-point game, where he tied Wilt Chamberlain for the most points with a triple-double. These ridiculous games have been oddly common this season. In fact, we may be in a bit of a 50-point golden age for the modern era. We’ve have seven so far this season, and we’re not even at the halfway point[2.]. Back in 2011, there were only two such games, and only three in both 2010 and 2012, respectively. This surge hasn’t been from just one player either, like Wilt’s effect in the 60’s. All seven games this season have been from unique players.

James Harden’s 50-point game was pretty special though. He created a huge chunk of his points thanks to some high difficulty 3-pointers, often well behind the line and/or right in front of a defender. Look at the outside shots he made at the end of the second period in this playlist — those were not easy. He had a huge number of assists, and those were contingent on some excellent shooting from his teammates, many of Harden’s assists were high-quality, drive-and-create passes. And his rebounds were important for the team: as the lead shot creator and passer, it’s a more efficient and faster way to start the offense. It was hard to imagine a 50/15/15 game happening in the modern era, and now I’m wondering what else is possible.

## 538 and win projections

One of the more popular destinations for win projections for the rest of the season is FiveThirtyEight. I understand this, and they’ve been pretty decent with their coverage. Their projections are more involved than simple ones, like Basketball-Reference’s. But their pre-season projections are not performing well. Some of their wilder picks, like Minnesota for 46 wins and Chicago for 45, which completely diverged from most of the analytical world, are starting to look worse and worse. They may have had overfitting issues with their closest player/age curve algorithm, where they tried to predict future individual performance by looking at statistically similar players. So I would advise some caution when using their win projections. I’m not quite sure how their pre-season ratings affect their current ones, but it warrants mentioning.

Defense is particularly difficult to analyze and tease out the useful information. Even with more advanced stats, we’re still largely in the dark, and for some players that means we’re missing the bulk of their contributions. We understand defensive rebounds, at least to some extent, and we have a wealth of information about shot-blocking and rim protection; and then there’s the area of turnover creation, headlined by the basic steal stat. But what about the class of players who don’t excel in those obvious areas: the plus defensive guards with low steal rates?

The representative here is Avery Bradley, a known defensive menace with a good reputation but disappointing defensive stats. In fact, the issue is illustrated by the range of stats in the table below. Starting from the left, you have a box-score metric, then a mix of +/- and box-score stats, then pure +/- models. He performs better when we’re more detached from the traditional box-score world. Of course, you can also see another pattern: his defensive stats have been plummeting, and opponents are scoring at a blistering 112.8 points per 100 possession rate when he’s on the court this season (and just 98.3 when he’s off.)

 Season DBPM DRPM DRAPM (single) DRAPM (multi) 2011 0 NA -0.16 -0.04 2012 0.3 NA 2.72 2.4 2013 0.2 NA 1.01 1.13 2014 -1.4 1.22 0.65 2.07 2015 -0.9 0.73 1 1.7 2016 -0.3 -1.24 -0.5 0.2 2017 -0.3 -2.31 NA NA

*Single season RAPM and multi-season included.

Bradley played his usual pressure defense against the Cavaliers in a game last week, but to no avail. The worst moment was probably when he was knocked over by a screen, though in his defense it should have been called a foul. He played Kyrie Irving close again far from the basket, and after having problems fighting over the rare double screen, he recovers and takes out his frustration by nailing Kyrie with a hard foul in the paint. You can see the issue with his pressure defense, especially against a spread team like the Cavaliers: if the opposing guard can drive past him, he has an open lane to the rim. You had similar issues versus Russell Westbrook, and while Westbrook is a nightmare defensive assignment, you can see how he tracks too closely and gets blown by after a crossover. Russell missed that finger-roll, but he didn’t miss another one later in the game: watch how Westbrook can easily round the corner against a defender who’s guarding him tight on the perimeter.

There’s some evidence Bradley was a good defender before this year, but his +/- numbers have never been spectacular. He’s limited by the easiest way elite defensive guards can shape that end of the court: he doesn’t force turnovers. Ironically, this is the one season where he does stand out in the box-score: he’s rebounding on defense at an elite rate for his position, but his overall defensive stats are trending well below-average. Defenders of his type are hard to measure — other no-stats defensive guards include Klay Thompson and Joe Dumars — but with enough seasons you can get a sense of their impact.

## Assist value by position

All assists are not the same. We all accept this fact, but rarely do you see any statistical adjustments. We can get near universal agreement that an assist leading to a shot at the rim is better than, say, an assist leading to a mid-range jumper. And you may have heard a handful of remarks like, “Rondo stat-pads, so his assists are worth a bit less.” Or, “LeBron James has high-value assists because he’s great at nailing 3-point shooters.” Or maybe, “Big men assists are more valuable because they’re usually to guys at the rim or past the 3-point line.” But is that last one really true?

This question originated in a Nylon Calculus email chain, and it’s one I’ve definitely heard before; it seems plausible too. Answering the basic form of the question is pretty easy. I have dunk and layup assists going back to 1997, as well as a decent index of positions for every player in that time frame too[3.]. I have “tweener” positions too: you’ll see some graphs with positions of 1.5 for combo guard, 2.5 for shooting guard/small forward 3.5 for tweener forward, and 4.5 for power forward/center. You can see the results in the graph below.

The differences are virtually nil across the board. The range of the proportions here are 0.364 to 0.387 — basically, it means that over a hundred assists, the difference in the number of layup/dunk assists would be two. It doesn’t change if you look at more recent seasons either; it’s a pretty consistent pattern. There’s something resembling a legitimate correlation when you look at 3-point assists, as you can see below. But it’s nothing world-bending, especially when you consider big men shoot significantly fewer of those shots anyway.

But shouldn’t we make some adjustments? Big men shoot at the basket more frequently, so there are fewer opportunities for them to assist on those shots. We can likewise do the same with 3-point assists to see what the pattern really is.

The adjustments were a pain, and some assumptions were made, but I wasn’t going for absolute precision[4.] — I wanted to see if the myth was plausible. You can see the results below for dunk and layup assists. Since centers more frequently score at the rim, their passing targets are players who, on average, convert fewer dunks and layups. Thus, we’d expect a lower rate of assisted dunks and layups. Centers, and big men in general, may actually offer a higher value of assists from a certain perspective. That straight line we saw in the first graph was from a confluence of factors.

Looking at the next graph, we have the opposite pattern. Centers rarely shoot outside shots, at least over this 20-year period, so their targets are more likely to be 3-point shooters. Yet they have only a marginally higher proportion of those assists over, say, small forwards. Perhaps these two adjusted graphs can be explained by geometry and basic basketball mechanisms. Big men are usually closer to the basket, so it’s more likely they assist there too; and since they’re further away from the 3-point line, they assist there more infrequently. You can factor in play types too. Outside shots are often assisted by driving-and-dishing or passes around the arc.

I would caution that these are all inexact numbers. Even the official stat, the assist, is mired with subjective calls and inconsistent scorekeeping. But we’re probably reaching when we say big men assists are more valuable. They’re not more likely to serve up assists at the rim, and even after some adjustments you have to concede that they should have more 3-point assists. What’s important here instead is that assists should be evaluated player-by-player. Some centers are wondrous passers who use the high post like a pitcher’s mound, finding targets with great accuracy; some have hands of stone who pass the ball out of the paint to a contested jump shooter with 3 seconds on the shot clock.

We can’t exactly say big men serve up high value assists more often. The truth, as usual, is more complicated.

[1. Looks like Philadelphia wants to experiment with the pairing after-all. Perhaps they found that the market for Jahlil Okafor was cold. Or perhaps they read my drafts.]

[2. We’re at 8 now, thanks to Jimmy Butler on January 2nd. It tied the “record” for most unique 50 point scorers in a season.]

[3. The dunk leaders are obvious; it’s all dominated by Dwight Howard, DeAndre Jordan, Shaquille O’Neal, et al. But the layup leaderboard is more fascinating. Random trivia answer: the player with the most attempted layups in a single season is Antoine Walker in 1997 (his rookie season. In retrospect, perhaps we should perceive this volume 3PT-shooting, layup creator differently; he was born before his time.]

[4. I had to assume that once a player of a specific position was out of the game, then no other player of that position was sharing the court too. I also simplified the positions into just five types: 1 through 5. Then I estimated an expected rate of assist types. I know positions are tricky and there’s lots of lineup mixing, not to mention usage and shot distribution concerns, but this is just a rough estimate.]