Nylon Calculus Week 3 in Review: Early season surprises and historic 3-point rates

At some point when the season settles in we’re going to have to stop using the “early” disclaimers, but this is still the part of the season where Nemanja Bjelica and Aaron Gordon are in the top 3 in 3-point percentage, so let’s not write the final bylines just yet.

But there’s enough in the league to keep fans engaged, from Cleveland’s implosion to Orlando and Detroit leaping to the top of the Eastern Conference standings. We’ve also got a new generation of stars imprinting themselves onto the league, like Giannis Antetokounmpo and the rookie Ben Simmons. I’m optimistic about the rest of the season, and I’m won’t fall into the negativism of “oh the Warriors will just win it all anyway.” There’s a lot still to enjoy, and we can all still marvel at the greatness of Golden State as they demolish everyone else.

James Harden’s 56

Against one of the best defenses in the league with All-Defensive players like Rudy Gobert, Thabo Sefolosha, and Ricky Rubio, James Harden dropped 56 points with an eye-opening 13 assists. He had one of the best first quarters you’ll ever see in the NBA — 8-for-8 from the floor with a couple of free throws, totaling 22 points, and four assists. It was a whirlwind of a performance; his teammate Trevor Ariza noted that when he’s on, he’s nigh impossible to guard, even if you threw two guys at him. He had 54 points through three quarters, and sat for half of the last period — in a more competitive game, 60 points could have been pretty easy.

Also, it’s time for a mini-rant. You may have seen a lot of people laud him for scoring so many points on only 25 shots. But for players like Harden, field goals are very misleading. He scores on free throws too! It makes no sense to ignore those. It’s like saying some sharpshooter was very efficient because he scored 12 points on zero 2-point field goals. Sure, that’s true, but isn’t that misleading? Free throws should count too.

With Chris Paul still out with a knee injury, now is indeed the time for MVP-contender, 2017-James Harden to appear and drag the team forward. We were all wondering how these two would play with each other, and, well, we’re still wondering that — anyone with a usage and assist rate in Harden’s stratosphere will suffer some diminishing returns with a point guard like Chris Paul. It may derail his young MVP case for the season, which took off with a bang this weekend, but we still have to see the experiment in action.

Oh and LeBron James had 57 the other day because he’s immortal and all.

Space through time

I’m afraid too many people missed this excellent article on the history of spacing in the NBA. Too few writers today ignore the NBA pre-Michael Jordan or Larry Bird/Magic Johnson, and there’s still a lot to learn from the earlier eras. Watching the evolution of spacing is fascinating — it makes me consider that all those comparisons of who would win against whom from history are useless because so much has changed. But I’m glad we get to experience this era; I’d rather see stars zoom around with enough space to operate and improvise.

How a draft can fail

Every year, teams make mistakes when drafting NBA players — mistakes that cost millions of dollars and affect the lives of very young (usually) players who are still developing. We can all play armchair draft analyst, but once you actually have to draft for a team, reality crashes in and all the cognitive biases and human errors screw up the execution of any draft plan. For instance, here’s a first-hand account of the NBA draft process inside the organization and how psychology can warp good decisions.

We’re already seeing people do retro-grades for the 2017 draft with how players are performing. Yes, it’s a bit early to grade a player, but even with the obvious misses we should try to understand the thinking behind them. Sometimes drafts (or rookie seasons) just have odd results, like how the best Lakers rookie right now is Kyle Kuzma, the No. 27 pick. (This guy has been a revelation so far.) Some of the worst decisions come when teams overthink the process or obsess about one detail, like drafting a senior as they value “NBA-ready” but fail to realize the player isn’t even NBA-caliber or going for a raw player with the physical attributes of a star but without the actual ball skills. It’s all too easy to fall for the wrong choice in the draft, and if you want to improve you should understand how those failures occur broadly speaking.

Victor Oladipo in Indiana

The Indiana Pacers have been one of the league’s surprises this season, although they’ve cooled off lately. But there are some quick-to-the-trigger opinions out there about how Indiana has actually won the trade with Paul George. It’s too early to make that call, but we can still play the game of, “Mirage or real trend?” Oladipo’s numbers with the Pacers are indeed better, but it’s mostly just his usage rate — it’s exploded to a little over 30 percent, and he hasn’t hit 25 percent since 2015. That is not something that would have been possible in Oklahoma City, of course, with Russell Westbrook dominating the ball, and it’s a key point in why it’s hard to say Oklahoma City “lost” the trade.

Given that it was difficult for Victor to show his true value in Oklahoma, it’s then difficult for the franchise to get a better price for him in a trade. If anyone has failed, it’s other teams for not realizing Oladipo’s value — if you do think he’s quite valuable. He’s still a pull-up fiend; he’s just doing it more often now. He’s dishing out well too; you can see a Steve Nash-esque keep your dribble alive under the rim and kick it out assist here. The issue is that, besides his usage rate, his shooting efficiency is what’s changed sine Oklahoma, and I would not expect him to keep shooting 44 percent from behind the arc given the types of shots he chooses to take. His overall stats will regress a bit due to that, but maybe he is a high usage beast — it’s just something that could only happen on a team like the Pacers.

What in the Fultz?

Last week I discussed the strange case surrounding Markelle Fultz, and we can add another entry to the list. He was shooting left-handed jumpers in practice because … well I guess this team can’t do anything normal when it comes to injuries. Perhaps this is nothing and Fultz just wanted to do some shooting drills no matter what, but it’s concerning given the front office’s track record with injuries. Let’s just hold off on evaluating him until he’s fully healed, and remember that this injury staff isn’t strong.

Porzingis: The Darko we were promised?

Years ago during a generation-defining NBA draft, Darko Milicic was promised as the next European superstar big. He was 7-feet tall and preferred draining in outside shots and driving like a smaller guy, but he was still stronger than other big man shooters and tough as nails, trash-talking and dunking with authority — or at least that’s how he was advertised. That Darko was a bust, and his failure still has reverberations today.

But we finally have the Darko we were promised, and he’s taken the form of Kristaps Porzingis. His start is no mirage; he’s legitimately playing like a star, and it’s downright scary. He’s huge, he doesn’t get pushed over easily, and he still dances around on the court like a wing player, hitting 3-pointers and driving hard to the rim. Even today it’s difficult for opposing centers to cover big man shooters, but you can cheat often because they’re usually slow as molasses and don’t have dribbling skills. But not true for Porzingis. It’s frustrating to cover him effectively, and you can see his potential on the defensive end, where his size and agility are intriguing — you can see that in the clips below, or in these blocked shot videos.

https://twitter.com/World_Wide_Wob/status/926626531631394816

The slim and fast NBA

As I’ve long said, basketball is for skinny people, so I’m perplexed whenever critics pick apart a guy for being too skinny and applaud others for bulking up. The league is starting to swing around to this idea though, and we’re starting to see a lot of guys dropping a substantial amount of weight. Even if we’re just talking about muscle weight, this puts less stress on key joints and other areas, and it takes less energy to run around and jump. I expect this trend to continue.

The Big Penguin uses his legs

The Pistons have been one of the pleasant surprises of the young NBA season. We were waiting for this Stan Van Gundy team to gel, and a few of the indicators are positive for their future. One of Detroit’s most visible improvements, for example, is Andre Drummond’s free-throw percentages, and the improvement seems legitimate because his form is completely different now.

With Drummond shooting in the mid-70’s from the line since preseason, the game-plan surrounding him is fundamentally different. Gone are the hack-a-Andre fests, and his efficiency has risen substantially. He’s a great experiment in how a player’s game responds to better free-throw shooting too, and oddly enough his free-throw rate is virtually unchanged. For a player with a high foul rate this is greatly important — his true shooting percentage would fall to 52.3 percent from 59.0 percent with his pre-2018 career free throw percentage. I’m hopeful Andre Drummond has pulled a Karl Malone-esque ascendance at the line because few players need it more.

Predicting the future from 23 feet, 9 inches

Once again, NBA teams are taking more shots from outside the 3-point-line than ever before. The league-average 3-point-rate record, whether you measure it by per game or per possession or per shot, was set last season, and it appears as though it will last for exactly one season. We’ve come to expect this, but it leads me to a natural question. When will this trend stop? At some point we’ll reach an equilibrium point where it won’t make sense to give up, say, easy shots inside for 3-pointers — or at least it won’t be physically possible to take more outside shots.

To see where this trend is heading, let’s take a step back and look at this visually. First of all, I’m not looking at per game attempts because then the trend would be confounded by pace and rebounding effects. I also don’t want to ignore free throws because many of those are shooting possessions too. Think of this: if you shift more shots inside, many of those attempts will end up as free throws and, if you were just looking at field goals, they would be lost. Thus, I’m focusing on 3-point attempts per true shot attempts (FGA +.44*FTA.)

You can see that graphed below for every team and every season since the line was introduced. I’ve included a red line for league averages too. Throughout the first half of the 80’s, the line was utilized rarely, but by the second half — perhaps because the new generation had grown up with its existence and were more comfortable — it began to be used more often and the growth accelerated into the 90’s. Then we saw the shortened line boom years of 1995 to 1997 where the distance was changed to a uniform 22 feet all around (that’s currently the distance in the corners.) After that we saw steady yet noisy growth for years until this data-ball era. The last few years have been explosive growth in the shot, especially for the Houston Rockets who look like they’re playing a different game entirely.

(Houston stands out, but don’t forget about the anomalous 2004 Seattle Sonics, who shot 3-pointers like it was 2018.)

If you want to model that trend, you can use a logistic curve. This is a popular form of regression used a lot in cases like this where you’re dealing with proportions. After all, the rate here isn’t linear because it can’t keep increasing forever — you can’t go above 100 percent. This is easy to do in R or other programs. You can use the glm (generalized linear model) function with a logit link, for example, or even beta regression. But there’s a major issue here fundamentally with those approaches. I put the results from the regression below from glm.

Rate = 1 / [1 + exp(135.6-.75*Short line-.0669*Season) ]

The issue may not be apparently readily, but think about what happens to the function as the season variable keeps increasing. Mathematically, we’d be taking the limit as “season” goes to infinity, but you don’t need a math-heavy background to understand this. Basically, as the season increases, everything inside the exp parentheses become more and more negative. And when exp becomes more negative, it shrinks. Ergo, as season increases the equation simplifies to 1/[1 + 0] or simply 1. That means that in a far enough future, theoretically according to this model, every true shot attempt will be from behind the 3-point line. Does that make sense?

Instead we should use a variant of that function where the number on top (the “1”) is a coefficient too. This may be known as the “alpha” or you can just think of it as the asymptote, which is just the upper limit of the function. It’s the goal when we’re asking, At what point will this 3-point shooting trend stop increasing? The most common function for this in R is the nls function, where you can use a number of algorithms to estimate the “best fit” for any custom function. Using the results from the previous regression as the initial estimates, you get an estimate for the asymptote: 0.32. You can go back to the graph above or look at the numbers this season to see how that doesn’t make sense — we’re already at 0.30 this season, and I don’t think the growth is over.

The issues are there visually: the curve isn’t smooth, and there are many kinks. It’s tough to figure out where the inflection point is. Around 2010, the rate started to plateau, but then it accelerated. This reminds me of a famous case in history about prediction: Hubbert peak oil. Back in the 50’s, Hubbert predicted the US’s oil production would peak in the late 60’s, and he wasn’t far off: production peaked in 1970, which sent shockwaves through the US economy. However, production has increased in the past couple decades because technology has allowed greater resource extraction and from unconventional sources (e.g. shale oil.) This is akin to the revolution now. We’re not simply just launching more outside shots from our league’s snipers; we’re converting an incredible array of players, including big men, into 3-point shooters. The idea that players like Dewayne Dedmon and Brook Lopez would become outside shooters would have been laughable five years ago, but now it’s the everyday NBA. That is what the logistic curve is failing to model — and it’s tough to adjust.

My best solution was to weigh the model by recency, but that’s not perfect either. The weighing scheme is ultimately arbitrary, and I went with something fairly conservative where the weight for the 2018 was only twice as large as the weight for 1980. You can see the results below where the upper limit was 0.38, as well as the results from the model where the weighting was “season – 1979”, which meant recent seasons were several orders of magnitude more important. Yes, the growth recently doesn’t fit the conservative model, but it does mirror the trough we had around 2010. We already have teams beating that upper limit — hello, Houston — but they’re also teams who have the best shooters in the league. Not every team can have Stephen Curry or James Harden or even Ryan Anderson.

Rate = 0.379 / [1 + exp(173-.833*Short line-.0862*Season) ]

There is an additional use for the function too. Let’s say there are proponents who want to move the line back in the future. What would the effects be? If distance change is about the same as the change back in 1995, just flip the sign — yes, that’s all guess-work, but it’s a good starting point. If you do that for 2018, you’ll see an estimate that pushes the league back to roughly 2010 in terms of outside shooting. Of course, it’s all more complicated than that, as players have to adjust for a longer line, and then you have to deal with the short corners, but it’s an interesting example and, again, a starting point.

Next: Nylon Calculus -- Blake Griffin has been playing Moreyball

By the way, if you want to know what the change year-to-year is with that function, you can use a little bit of calculus. A derivative allows you to compute the rate of change with a function, and that’s what you want here. You can use the quotient or reciprocal rule here — they’re equivalent ultimately. Ignoring the shortened line variable, take the derivative of the bottom portion (denominator), divide it by the square of the denominator, and multiply it all by -0.379. (The exp() function is an easy derivative to work with, but don’t forget to bring out the coefficient of season in front of exp() when you differentiate.) The resultant formula is below. When you plug in the 2018 values you get 0.0066 — or 0.66%. We’re greatly outpacing that growth this season, and I would expect some regression eventually, even if we have to wait a couple years.

0.379*0.0862*exp(173-0.0862*Season) / [1 + exp(173-0.0862*Season)]^2

Modeling the future is a fool’s errand, but the exercise in itself is a good way to understand how unpredictable trends can be. I don’t know if we’ve already reached the upper limit on how many outside shots the we can take, or if Houston has, or if it’s even higher. Shots within five feet of the rim constitute about 34 percent of all true shot attempts right now, and when you factor in free throws that’s another 10 percent for true shots that are already being funneled into high-value areas. So maybe you can say ~55 percent is the true upper limit — I don’t know. But I imagine in the future something no one expects will change those trends and surprise everyone; because that’s the one constant of history and predictions.