For the (very) few people reading this from the future, yeah, last week was the week Donald Trump was elected president of the United States. Tensions are high and everyone is distracted by matters like who’s going to be Secretary of State and the future of NATO. We’re in a bubble culture too, as I imagine most NBA fans who follow advanced stats closely were not aligned with Trump’s universe.

But I would like to take a moment and appreciate how progressive the NBA has become and how the league has allowed its figureheads speak out on public issues, and take stances on social matters. If you haven’t yet read the transcripts, Gregg Popovich and Stan Van Gundy both had impassioned reactions to the elections. I know there’s a vocal group out there who believe we should all “stick to sports,” but when you have an outlet and people listen to you, it’s a moral imperative to speak out and defend values you feel are being attacked. And with that, let’s go back to our fantasyland of basketball and discuss the last week in basketball….

Boston’s Defense: Stuck in Molasses

The Celtics finished fourth in the league in defensive efficiency last season with one of the better point differentials overall too, so it’s a bit jarring to see them muddled in mediocrity with the NBA’s worst performing defense. You can blame some injuries, but it’s a deep team and they still have the Brad Stevens voodoo. It’s just strange to see them completely plummet in, say, forcing opponent turnovers, which isn’t a volatile stat. You can point to their opponent three-point percentage, which isn’t sustainable, but it doesn’t explain all their issues — it’s not even close.

Read More: Is LeBron James the healthiest star ever?

More tellingly, Boston and Golden State, two of the most disappointing teams of the season, are also the two worst rebounding teams on defense. Given the interconnected nature of the game, this makes sense — if you don’t grab a defensive board, you have fewer fast break opportunities and your opponents get better opportunities of their own. It’s a killer effect on both ends of the court. And Boston, the worst team in terms of defensive rebound percentage with a measly rate of 70.9 percent; was significantly better last season. This is the limiting agent when it comes to small ball because while teams can amass a lot of skill with smaller players, rebounding will always be crucial and it can kill your defense.

The glimmering hope on the horizon for the Celtics is that when both Jae Crowder and Al Horford are back they can play at an elite level. Crowder’s their best defensive player, if it isn’t Al himself, who will be a major upgrade over Tyler Zeller. The team has so far rebounded much better by a large margin when Al Horford is on the court, and Crowder, a big wing, helps too. The unheralded positive sign for the team this season is that their offense has been electric — roughly five points better per 100 possessions than last season — and if their defense performs even close to their previous standards, they can once again threaten the top of the Eastern Conference. Let’s see how they are fully loaded first before passing any more judgement, and with a few more games under their belts.

Video Killed the Box Score

One of the reasons I started doing “week in reviews” was so I could use the video feature on stats.NBA.com to breakdown players and explain different statistics and metrics. If, say, RPM doesn’t see Rajon Rondo as a good defender, then you can find video examples in the play-by-play instead of just proselytizing about advanced statistics. Unfortunately, that feature hasn’t been available this season, and I’m pessimistic it’ll be available again. You can see for yourself here — there are icons indicating there’s a video, but nothing comes up.

I think people had grown complacent about just how tremendous stats.NBA.com has been in providing a wide breadth of stats, and there’s no strong incentive to keep every feature, especially one as comprehensive and, presumably, expensive as the video box score. Not only could you access a video for almost every play, but you could, say, go to Hassan Whiteside’s page and watch every blocked shot he’s had for the season or just for one game. But we’ve been through this song and dance before with some of the more detailed SportVU data, which has yet to come back, and I fear it’s the same instance here.

I’m lamenting here because it was an invaluable tool and it’s sad when progress is stalled and advancements revert. And for any other incredible tool still on the site, we need to cherish its access and availability before it’s too late.

Would You Like Some Frye With That?

When the Cavaliers brought over Channing Frye, I thought it was a fun move but they had a bit of a front court logjam and I wasn’t sure how he would fit in. Now with Timofey Mozgov gone, there’s more of an opportunity to use him, and he had a huge game versus the Hornets, nailing six 3-pointers and coming up with a huge block on Spencer Hawes — that’s not the kind of vertical jump I’d expect from Frye. It’s a welcome sign from him because I feared he was due for a down season; his performance levels season-by-season are consistently pendulum-like, as you can see from the chart below. But virtually every pattern breaks eventually, and this might be the year. This is vital because with him at center, the team can play five-out basketball with LeBron James, which is tortuous for every mortal defense out there.

Dwight Howard’s Homecoming

The Atlanta Hawks are 7-2, and Dwight Howard is enjoying his best personal numbers since he left Orlando. One could say this is a case of conventional wisdom triumphing over loft, out-of-touch analysis, but Howard was not a highly praised player in Houston — Al Horford was, even by more traditional NBA fans — and few people expected a resurgent season from the Hawks. So what’s going on, and what did we all miss?

Right now, Dwight Howard’s BPM is higher than it’s ever been in his career, including the seasons where he was an MVP contender in Orlando. This is a good time to mention this is still early in the season, but it’s important to see where Howard has actually improved and what’s sustainable. What’s most striking is that his offensive rebound rate has skyrocketed to nearly 20 percent, which is Dennis Rodman territory. But his steal, block, and efficiency numbers are up too while his turnover rate is at its lowest point in years. It’s a wholesale improvement, and for a center with a recent history of injuries in his early 30’s this is surprising for a reason.

Slicing Howard’s numbers into smaller pieces, Howard actually isn’t posting up less often, as the play type statistics on NBA.com have his post-up frequency increasing from 30.5% to 33.9%. Per 40 minutes, his post-up rate has gone up by nearly 1.5, although his efficiency hasn’t improved much. He has been, however, more active as a roll man — from 9.3% to 13.4%, respectively — and his points per possessions have gone from 1.1 to 1.28. Structurally, his game isn’t too different now, just more effective, and one could instead point to his recent positive comments about coach Budenholzer. His effect on the Hawks is quite apparent though because they’ve gone from one of the worst rebounding teams in the league to one of the best. This is actually something supported by advanced analysis: team rebounding follows a nonlinear path in such a way that weak rebounding teams are helped the most by high rebounders. In that way, Dwight was actually a great fit.

But there’s a winning bias in perception, and it’s tough to say if Howard’s positive relationship with the staff led to his improved play or if the improved play led to the positive relationship. Most people will assume what they want to assume without having been behind the coach lines, so I’ll just end the section with this: let’s see how Howard, and the Hawks, play the rest of the season before falling to hard conclusions, because it’s the entirety of the season that matters, not a few games.

Brook Lopez: Upgraded

As the league continues to move in the data-ball direction where more teams and players take three-pointers, it’s fun to see who the new converts are. Brook Lopez is one unlikely example, he of the ground-bound, behemoth variety. But he is truly making 3-pointers a legitimate part of his game, and he’s nailing them so far, even with that one inch of vertical lift.

And here’s the important part: he’s almost entirely excised long two-pointers. People fear that a big man experimenting with a behind the arc game means they’ll stop scoring inside, but that hasn’t really happened with Brook Lopez. As a good check, his free throw rate is right near his career average, showing he’s still using his size and skills inside. We still need a considerable length of time to evaluate his three-point shooting, but he’s at 39 percent for 2-pointers beyond 16 feet and he has a nice touch at the line, so given his considerable volume so far and his long history with the jump shot, I’m fairly optimistic that Brook Lopez can be a legitimate outside shooter. That’s the kind of strange sentence we’ve grown accustomed to in this era.

PROCESSING…….

The exploits of Joel Embiid are well-known now to hardcore NBA fans, but I have to mention him because what he’s doing is wildly impressive both on the stat sheet and on video, even before taking his inexperience into account. He’s a massive center nailing 3-pointers and pulling off Hakeem Olajuwon moves with ease. You can see examples of those in the videos below, where he’s even blocking post-up master Al Jefferson. He’s the realized dream of every time a team takes a raw seven-footer in the lottery, more wish fulfillment than reality. And he’s somehow competing with Russell Westbrook for highest usage rate in the league.

We’re obviously quite early in the season, but have we seen anything like this before? I quickly wrote up a similarity measure (Factors: Age, usage, TS%, 3PA/FGA, FTA/FGA, AST%, TOV%, STL%, BLK%, DRB%, ORB%, and FT% where age and usage rate are weighed higher) and found that the two most similar seasons came from young Orlando Shaquille O’Neal, that surprisingly skinny beast of a player who found himself in the finals at age 22 and brought down entire backboards. Then it dawns on you that Embiid has a much higher usage rate and is actually a good shooter. I would expect some of his numbers to go down, mostly because some of them don’t even make sense. Yes, this is some fun with small sample theater, but a few of his noteworthy stats, like usage rate and rebounding, stabilize pretty quickly.

However, we already know enough about healthy Embiid as a player where we can imagine the kind of player he could become. Normally, 3-point shooting big men are soft defenders and generally just hangout at the arc. Functionally, you can treat them like wing players, and tactically it’s damaging to the opponent when you can just throw a small forward at them for long stretches without retribution — it’s easier to switch pick-and-rolls, you don’t have your center awkwardly guarding the 3-point line, etc. But you cannot do that with Embiid because he’s too massive and too aggressive as a scorer inside. A team can play big with many of the merits of small ball because of him. It’s an unfair advantage, and we’ll see how teams adjust to him in the future and how his game develops — this is going to be fun.

Make TS% Great Again

As a few readers here know, true-shooting percentage is a measure of efficiency, but it’s an estimate and not an exact figure. Given how widely spread the stat is, I think it’s prudent to, once again, examine the stat and give examples of “real true-shooting percentage.”

For a refresher, true-shooting percentage is PTS/(2*(.44*FTA +FGA)). It’s just a way to mimic field goal percentage while appropriately dealing with the added efficiency of three-pointers and free throws. In essence, it’s points divided by true shot attempts. That pesky 0.44 coefficient is there because not all free throws denote the same kind of opportunity, but with a careful probing of play-by-play logs we can do away with that factor.

Before we go further, we must acknowledge the philosophy behind the number. It’s all about how well a player scores per opportunity, and consequently it’s about efficient production for said opportunity. Think of it like this: if you take a shot, you’ve used up an opportunity; and if you are fouled and go to the line for two attempts, you too have used an opportunity. But sometimes players go to the line for three free throws, or they go once after a made basket, or they take technical foul shots — which don’t even use an opportunity. Thus, we can calculate “real” true-shooting percentage based on actual free throw data.

Part of the calculation, by the way, involves ignoring all technical and flagrant free throws. I expect there will be disagreements here, but they don’t make sense for a few reasons. Firstly, they don’t end a basketball action in the traditional way. Secondly, the shooters usually aren’t the ones who have created the free throws and, finally, it’s an entirely replaceable skill. If you don’t go up to the line, someone else will, and there’s probably only a slim marginal loss in the foul shot going to someone else — and the players chosen to take them aren’t always the optimal choices. Perhaps one can argue you can add an adjustment via the league average tech/flagrant FT%, but this way is cleaner and clearer.

Looking through a revised leaderboard below, there are no major changes, but there are some notable differences. For instance, shooters like Stephen Curry and Kevin Durant are slightly downgraded, and it’s because they usually shot their team’s technical free throws while they were on the court. But DeAndre Jordan got the biggest downgrade, and it’s for an interesting reason: he was intentionally fouled or just plain hacked near the basket so frequently that he was well below average in his ratio of And-1 players to total free throws. Thus, the true shooting percentage estimate figured he had more And-1 opportunities than he did, and it under-counted the number of total opportunities he was actually using. LeBron, for example, had one of the highest ratios of And-1’s to total free throws, so his true shooting percentage was being slightly underrated by 0.3%.

Table: true-shooting percentage, 2016, source: stats.NBA.com

Player Est. TS% Real TS% Diff. Stephen Curry 66.9 66.7 -0.21 Boban Marjanovic 66.2 66.1 -0.18 Troy Daniels 63.4 63.4 -0.01 JJ Redick 63.2 63.2 -0.01 Kevin Durant 63.4 63.1 -0.33 Hassan Whiteside 62.9 63.1 0.17 Quincy Acy 62.9 63.0 0.11 Enes Kanter 62.6 62.7 0.09 Cole Aldrich 62.6 62.1 -0.48 Andrew Bogut 62.3 62.1 -0.21 Steven Adams 62.1 62.1 -0.02 Brandon Bass 61.9 61.9 0.02 Ed Davis 61.6 61.7 0.11 DeAndre Jordan 62.8 61.6 -1.22 Kawhi Leonard 61.6 61.2 -0.34 Tristan Thompson 61.1 60.9 -0.18 Jonas Valanciunas 61.0 60.9 -0.12 Tyson Chandler 60.6 60.7 0.04 Dewayne Dedmon 60.6 60.4 -0.16 Dwight Howard 60.4 60.3 -0.09

You may notice more of those differences are negative, and that’s okay: when you ignore technical or flagrant foul shots, the whole league’s TS% falls. You can, however, still include it in the team’s totals — the points still count, of course. By the way, the player with the largest drop in TS% with a significant shot volume was Ricky Rubio, sadly, by 1.5 percent because he didn’t generate many And-1’s and he shot 23 from 24 with technical free throws. That’s actually one provable instance where the advanced stats were overrating him, albeit by a small amount.

As a bonus, how has the league average FT% from these technical or flagrant foul shots changed over the years? We now have two solid decades of data, so perhaps there’s a pattern. Grabbing the data for the graph below, there’s no yearly pattern, except for a higher variation during the most recent seasons.

However, one of the reasons you do research in general is that you don’t know what you’ll learn when you dig into the numbers. I suspected that technical FT% was lower than most would expect because players shoot worse on their first free throw, and more tech’s are just one shot, but this was a lot lower than expected. And I never would have looked into it if I hadn’t graphed the data by season. It’s not far from league average. I would guess that this had something to do with how different these free throws are from any others, since the players are isolated on their side of the court, and it messes with their perpetual cues just enough to result in a lower conversion rate. So, I guess if you want an opponent to miss a crucial free throw, just clear the floor.