Nylon Calculus Week 6 in Review: Bucks, Vucevic, Kings and Elo ratings

Welcome to week 6 in the NBA. Somehow we’re getting far into the NBA season, and we’re moving past, “Is this a blip or the new normal?” and into, “How will team X deal with the disappointing season?” Teams not only have less time to turn things around and perform better, but they have 20 or more games that already count in the standings. That makes the gap even larger because if you want to be a 50-win team and you’re well under that pace now, you have to play as a, say, 60-win team the rest of the season. It’s time for some teams to hurry. And with that. let’s look back at the last week in the season.

A new contender emerges: Milwaukee

The Bucks are dancing around the top of the Eastern Conference behind only the Toronto Raptors, with a record that’s superior to anyone in the west. This is the breakthrough everyone was waiting for, given Giannis Antetokounmpo’s enormous potential and the tantalizing glimpses from him the past couple seasons. As we’ll see with the Kings, they made this leap without much pressure from external forces, save for one subtle pick-up and one obvious change: they changed coaches. Will the Bucks regress to their former selves as a weak playoff team or are they truly contenders?

Let’s start with the tangible forces. The most obvious change is the addition of a goofy comic book fan in the form of a 7-foot veteran center. Brook Lopez has been an absolute positive, clamping down a position that was a weakness last season. Thon Maker has not been the young center the team envisioned when drafting. Lopez, actually, is a reflection of what they had hoped Maker would become. He’s providing ample spacing for Antetokounmpo to drive inside with one of the most 3-point happy seasons for a big man ever, and his rim protection, which has long been underrated due to his slow feet outside the paint, has stabilized their defense. He’s also aiding the team in rebounding by boxing out — witness Antetokounmpo’s career marks in rebounding and how Milwaukee is suddenly first in defensive rebound percentage.

There were a few other personnel changes. Ersan Ilyasova came back, and he’s been having another fine, Ilyasova-esque year with 3-pointers and a few boards while looking like an enlarged James Franco. They brought in even more shooting with rookie Donte DiVincenzo, an athletic combo who has yet find his footing with his accuracy but nonetheless is helping space the floor. Finally, Pat Connaughton was another major addition. He can also — stop me if you’ve heard this one before — space the floor, and he’s supplanted Matthew Delavedova in the guard rotation.

The biggest change, however, is with the coaching. Mike Budenholzer, who spent five years as the head coach of the Hawks and was part of the coaching tree from the Spurs and Gregg Popovich, replaced Joe Prunty as head coach. But Prunty was an assistant under Jason Kidd, who was ousted mid-season after a tumultuous tenure. He was essentially just an extension of the Kidd-coaching regime and had no time to change anything significantly. Looking at the new roster additions, there’s are some obvious areas of interest that seem to align with the new coaching: they’ve updated their offense to space the floor and build around Antetokounmpo, and their new defensive scheme aims at sealing off the paint and giving more space in the mid-range.

I know all of this is obvious now and has been discussed at length in other places. But this all leads to one point I wanted to make: there were a lot of heated arguments about whether or not the Bucks should have fired Kidd last year, and if he was the central issue of their under-achievement. Those concerns were validated, as the team was clearly playing a style not suited to its strengths. And yes, there are legitimate questions about their current defensive scheme, but Budenholzer is a professional who’s had success before and the offense has definitely improved. I could see some of the team’s shooting percentages regress downwards, but they are indeed the real deal, and, as others noted, firing Jason Kidd is starting to look eerily similar to Mark Jackson being let go by the Warriors.

The future of the Warriors and Draymond Green

Speaking of the devils, there’s been a lot made about the discontent among the Warriors with Kevin Durant and Draymond Green. With Durant’s looming free agency in the summer, and Green’s own contract coming to an end soon, Golden State will need to make some tough financial decisions. And as one of Draymond Green’s biggest supporters, even I’m saying Kevin Durant is definitely the one you should focus on. That should go without saying, but the reason why is crucial.

As important as Green has been to their defense and identity, many people have noted, including Kevin Pelton last week, that he may not age well. He’s undersized for his position, and losing a step can severely hamper his utility because he doesn’t have the size or skills to cover the deficiencies. He had one wondrous season where he competently hit 3-point shots with slightly above average accuracy, and he hasn’t been close since. As Green has said himself, only old age will get us, and the Warriors need to be careful about structuring his contract.

Nikola Vucevic’s rim magic in Orlando

As a few people have probably noticed by this point, Nikola Vucevic, who not long ago was considered to have reached his potential, has had some eye-popping advanced stats that push him into the upper tier of the NBA. He’s 15th on ESPN’s Real Plus-Minus ranking, and eighth in BPM among high-minutes players. So he’s been killing it in the box-score and in terms of team impact (by raw on-off numbers, by the way, the Magic have been best with him on the court.) Why is this happening now at 28-years-old?

First of all, let’s do a cursory search through his stats to see what’s changed. The only career high he’s setting right now among the primary stats is his assist percentage, but it’s not by much. He’s shooting as much as he’s been in five previous seasons, and his rebounding numbers are excellent, as they’ve always been. Even his steals and blocks are within career norms. The most apparent substantial changes have to do with his shooting numbers: his true-shooting percentage, which factors in free throws and 3-pointers, and has always been near or under league average, is now at 61.5 percent (the league average is 55.6 percent.)

Like many modern centers who still have their jobs, Vucevic learned to shoot from outside the arc and first started shooting a significant amount of 3-pointers just last season. He’s actually shooting a smaller portion this year, but he’s hitting nearly 40 percent. Also helpfully, he’s near his career-high for free throws per field goal attempts, and he’s at a career high for free throw percentage with 85 percent. However, the most interesting development is with his field-goal percentage at the rim: he’s at 79 percent, which is a mark even LeBron James has only beaten once in his career.

Vucevic has not magically changed. He’s still rarely dunking for a 7-foot center. He’s still being assisted on roughly 64 percent of his 2-point shots. But he’s added enough to his game, and the Magic have increased their ball movement and spacing, to where he’s not a lot more effective. You can see what happens here when there’s movement and the defense has to switch: a smaller man has to cover Vucevic and gets burned. He’s also got a real outside/inside game. You can see him here receiving the ball at the 3-point line, where he can’t be ignored, and driving all the way to the rim. That kind of versatility is difficult to fully cover.

Generally, when a player has an anomalously high shooting percentage, especially one in his prime seasons, expect some regression to the mean. That’s not to say Vucevic didn’t improve or that the team didn’t improve; all of the above can be true even with some regression. The team has had a lot more movement this season, and it’s paid dividends for the big man in the middle. Watch that shooting percentage at the rim as the season progresses, but some credit should be given to Vucevic.

The Rockets and Bucks

For an informative and unique point of view, I want to link this analysis of shooting trends in the NBA with respect to the Rockets and the Bucks. I don’t think it got enough attention. Basically, while Houston has regressed on its off-the-charts shot selection last year, the Bucks have become disciplined at where they’re shooting on the court. That’s a significant improvement for the Bucks, as I also discussed earlier. And the article also showcases a novel way to evaluate shot selection.

Are the Kings real?

I’m not asking if the Kings exist in this physical dimension; this was figurative. The team is, currently, bobbing around the 0.500 mark, flirting with the playoffs in the ever-competitive Western Conference. This is without any injection of free agency talent or a star coming back from an injury. There’s a collection of young players, yes, but also a number of players in their late 20’s. This appears to be a massive amount of internal development, but is there more here going on underneath the surface?

First of all, I’ve been a little disingenuous here. There is some external source for improvement: their rookie, a second overall pick, has been by some standards pretty decent and provides more value than you’d think for a 19-year-old. Marvin Bagley’s been scoring well and blocking shots, playing real minutes. For what it’s worth, his plus-minus numbers have been awful, but this early in the season (and his career) I’d take that with a whole block of salt.

However, most of the improvement for the Kings has been internal. You can see that in the table below. Most of their heavy-minute players have improved with the exception of Willie Cauley-Stein, who was worse in 2017, and their rookie Marvin Bagley. De’Aaron Fox has improved substantially; sophomores improve but not by this much. Even the guys who were on other teams the year before have been a lot better, like Iman Shumpert who had a miserable injury-laden season — and that is actually my cause for concern.

I don’t think the team itself is the primary cause here; it may just be pure chance and, thus, liable to regress downwards. Also note that their win percentage is well above what you’d expect for their point differential, which is currently at -2.6. No surprise here, but the Kings are probably playing over their heads.

Elo and you: How the system rates NBA teams

The Elo rating system, an algorithm to rank players or teams in competition, has gotten some prominence in the league thanks to its use in FiveThirtyEight’s NBA team ratings. It’s a system developed for chess years ago by Arpad Elo. Using an arbitrary starting point (i.e. you can set a new player, or the average team, at any number you wish and it doesn’t matter), a team can gain points from winning games, the difference in team ratings, and other factors, even the margin of victory. Essentially, it’s like other adjusted rating systems, but there is one unique feature: recency matters.

In the NBA, the standard has been to take season results and use their measures (average wins or point differentials, or player stats like points per game and assists per game) without a time-based adjustment. In other words, a game in November is worth as much as a game in March. Is that wise? There are some recency issues with NBA stats, but in terms of team performance some of those can be mitigated by other measures, like adjusting for new personnel. It’s all about how you deal with recency. As others have noted, the Elo system weighs so heavily to recent games there’s some cause for concern. But let’s dig into how it’s calculated first.

The Elo algorithm frequently introduces the autocorrelation concept. To understand this, let’s take the root of the word: auto is coming from the Greek word for self, so this pertains to data correlated with itself. Think about what happens when you find a pattern to residuals (i.e. the errors from the model are not random noise but exhibit some sort of pattern.) This means there’s a variable that is unaccounted for. When time is involved, autocorrelation is likely because the full effects of the data being time-series were not considered. To put this into simpler terms, think about a chess player’s performance when aging — that is not static and can be thought of as autocorrelated data.

Now let’s get into the basics of how Elo is calculated. I’ve got the general formula below referencing this helpful post; there are many good resources online for understanding this. Basically, it’s an iterative function that changes based on the last game’s results modified by a K-factor. That K-factor will vary based on the sport and sometimes within the sport itself. For the NBA, FiveThirtyEight decided 20 produced the best results (using autocorrelation.) The actual result gives a full point for winning, and the expected result is just odds from 0 to 1.

New Elo rating = Previous Elo rating + K*( Actual result – expected result)

For a simple example, let’s turn to chess. The K-factor is 32 for experienced players, and we’ll go with 2400 for a previous rating — this player was quite good. The expected result is the odds of winning. We’ll pretend it’s 90 percent for simplicity, and let’s say this player actually lost. What happens with the formula? The chess player’s rating went down noticeably, but the player is still ranked high. With a higher K-factor, that rating would drop faster, so essentially the K-factor controls recency.

New Elo rating = 2400 + 32*( 0 – 0.9 )

New Elo rating = 2371.2

With that basic exercise out of the way, we can move onto how FiveThirtyEight calculates Elo for an NBA team. Their formula is a bit more complex and not fully spelled out, but it follows the same basic principle. The actual result, the win or loss, has to be modified by a factor for how much teams win or lose by — that’s important information not seen in chess matches. The expected result uses a basic odds formula with previous Elo numbers and homecourt advantage, which is given as 100 points from FiveThirtyEight.

New Elo rating = Previous Elo rating + K*( Actual result*m – expected result)

where:

m is the margin of victory multiplier = (MOV + 3)^0.8 / (7.5 + 0.006*Elo_diff)

Elo_diff = Elo team 1 – Elo team 2 + homecourt advantage

Expected result = 1 / (10^(-Elo_diff/400) + 1)

That’s a lot to digest, but it’s easy to unpack going step by step. We can use the first game of the season here. The Celtics at home defeated the 76ers with 105 points to 87. According to FiveThirtyEight, their pure Elo ratings were 1562 and 1607, respectively. That’s all you need. Let’s plug in values for Boston.

New Elo rating = 1562+ 20*( 1*m – expected result)

Now we have to calculate the specific terms one by one. Remember, homecourt advantage will factor into the Elo difference and will add into Boston’s numbers (the home team.)

Elo_diff = 1562 -1607+100

Elo_diff = 55

The margin of victory factor considers the point differential of the game.

m = ( 105-87 + 3)^0.8 / (7.5 + 0.006*55 )

m = 1.46

Now let’s calculate the odds of winning based on both team’s previous Elo ratings plus homecourt advantage, which is the “55” term.

Expected result = 1 / (10^(-55/400) + 1)

Expected result = 0.578

Boston had a 57.8 percent chance of winning. And now, putting it all together….

New Elo rating = 1562+ 20*( 1*1.46 – 0.578)

New Elo rating = 1579.6

By the way, doing this for the 76ers is very similar from what I understand. You flip the sign for homecourt advantage of course so it’s negative. And I believe the expected result defaults to 0; that’s at least how it works with other Elo systems.

Thanks to an 18-point win on opening night with homecourt advantage over a slightly better team, however, Boston increased its Elo rating by 17.6 points. Is that reasonable? I’ll analyze that over the coming weeks, and for next week, at least, I’ll provide a script to calculate Elo for yourself. (I believe I figured out all the terms and the formula completely, and if not, I’ll hopefully find the error by next week.)

There’s nothing wrong with using a new algorithm to quantify teams in the NBA. But this type of analysis only works if we can replicate the values ourselves and scrutinize them with testing. And if anyone would agree with that philosophy, it’d be Nate Silver himself.