Showing posts with label eastern conference. Show all posts
Showing posts with label eastern conference. Show all posts

Wednesday, January 29, 2014

The 2014 Eastern Conference All-star Game Picks

One idea floating around about the all-star game that has picked up steam is to do away with teams by conferences, pick the 24 "best" players, and let two captains pick sides. During a historically bad year for the east, this has gained traction, and I'd be fine with it since it's always a glorified pick-up game. I say this because I had to seriously consider the candidacy of guys like Afflalo and Lance Stephenson. Meanwhile, guards like Tony Parker and Mike Conley could miss the all-star game. Nevertheless, I had to attempt to scrabble together a competition eastern conference team.

Speaking of Lance Stephenson, a campaign has spread for his inclusion in the all-star game, and I'm not sure what people think they're accomplishing. First of all, insisting that Indiana should have three all-stars is weird and misguided; an elite team will be awarded by winning (by itself it's a reward) and by playoff success. And Indiana's strength is its well-balanced starting five, not having three stars. In fact, you can have a 60+ win team with only one all-star or, theoretically, zero. Think about this: a great team will have a point differential of, say, +7. The top players in the league will be around +4 to +6 overall just by themselves (but not this is if they played an entire game of 100 possessions.) A player that's a +2 is likely a good role player or a fringe all-star.

So let's say our fictional team has one great star who's +6, and he's surrounded by four solid starters who average +1.5. That's 6+4*1.5, equaling +12 overall, if the starters played the entire game. Bench players, especially the guys who ride the end of the pine, are typically "negatives," but if the bench is decent enough, like Indiana's this year, that +12 overall won't be depressed by a huge amount. Last season, Indiana's starters played 64% of their total regular season minutes, so let's pretend this team gets 60% of their minutes from their starters and 40% from a bench that averages a -1 impact (a poor player, but nothing horrific.) That means you have a weighted average for a point differential of +6.8, which would make them one of the best teams in the league. But we gave them only one star. It's evident that there's no perfect relationship between team strength and number of all-stars. As John Hollinger said, the all-star game is not about parliamentary representation; just pick the best players!

(By the way, that works even with other metrics like basketball-reference's Win Shares. The best non all-stars average like 5 to 8 Win Shares a season, and even Indiana's bad bench last season had 14.2 Win Shares. That means you could build a non all-star team with a poor bench that could win, say, 50 games, and if you add one superstar you can close in on 60 games, which is a reasonable facsimile of the LeBron-era Cavaliers.)

And realize we're constructing this edifice for a guard with a usage rate under 20 for an offense on a slightly below average offense. Lance is lauded for his "playmaking," but the results haven't been extraordinary, he turns the ball over too much, and he definitely has useful offensive players around him. Also, note that usage rate includes turnovers, so Lance is an even smaller part of the offense than it looks. As Kevin Pelton noted, the only two guards who made the all-star team with a usage rate below 20 and less than 7 assists a game since the turn of the millennium have been legendary shooter Ray Allen and Andre Iguodala, who's both a better playmaker and defender than Stephenson. If you go back to the 90's you'll see a couple more super-role players like Dumars, but you'll also see some of the worst all-star selections ever like BJ Armstrong. Basically, unless you're a top-tier distributor, defender, or shooter (Majerle and Ainge made the cut), you're unlikely to make the team. (If you go back further you'll find more guards, but as the league got smaller it meant there were more all-star spots for each player.)

If people want Lance to make the team because of his defense, I'm not seeing it anywhere, at least without a great deal of certainty. Indiana's defense is scary, but Hibbert and George are the best defensive players. Stephenson has cut down his mistakes, but I don't think he's good enough as a perimeter defender that he's a lock. Yes, the east is historically weak, but what are we doing with this campaign? All we're essentially doing is making Stephenson more expensive for his team to sign him after his rookie contract expires, and in their small market it might make keeping him impossible. So this strange obsession people have with proclaiming him an all-star will just have the effect of dismantling the dominating starting lineup of one of only two great teams in the eastern conference and the only bump on the road to the finals the Heat will face.

And, finally, here are my picks for the all-star team....

Starters:

Guard: John Wall

There are a few impassioned debates about who's the best point guard in the east right now, driven by the fanbases of Cleveland and Washington. Wall's case is more traditional than one would expect, given his errant jump shot and his flashy dunks -- he controls Washington's offense with his passing, and their offense falls apart without him. He's fourth right now in assists per game, or fifth if you include Kendall Marshall (i.e. the D'Antoni surprising, resurgent point guard du jour.) He's also fourth in "hockey assists" per game and moves up to third in the league in assist opportunities per game, per SportVu, basically implying that Wall's teammates are deflating his assist totals. Washington, meanwhile, has an offensive rating of 106.9 when Wall is on the court, and that plummets to an unfathomable 93.8 without him. This is the intersection of two strains of data types in this information world, and without juxtaposition they could be meaningless. But together it shows the large amount of control Wall wields -- he's, in fact, leading the league in time of possession per game, again from SportVU. However, since he plays heavy minutes and hasn't missed a game, his raw on/off differences are likely to be dramatic because a large portion of those off minutes consist of garbage minutes without any starters or only one. More nuanced metrics, controlling for teammates and the strength of the opponent, are more modest with their appraisal of Wall, but this is a historically dreadful east and there are few guards even approaching "star" status. For the last stat explaining how Wall sets up his teammates, Bradley Beal's TS% without John on the court is, via NBAWOWY, 43.6.

Guard: Dwyane Wade

I'm not entirely comfortable putting Wade in the starting lineup since he's missed a large number of games, but based on pure quality he's still the best shooting guard in the east (dubious award though) and, hey, Wall-Wade-George-LeBron looks like a really fun quintet. The rumors of Wade's decline have been exaggerated. Wade's motto is: always play hard. This will impress some people, and astonish the rest. But after years of falling down hard (or embellishing contact), and after years of injuries, he's no longer a sure thing on the court. Yet he's still generating a lot of shots on very good efficiency while passing well and finding players at the rim. He's a terror in transition, and he gets a pass for some missed games here because he's made three straight finals. They're keeping him fresh for a reason. I could see an argument for Lowry over Wade in the starting lineup, sure, but I prefer not to have two point guards starting, and Wade has the requisite box score stats and the "impact:" an RAPM version, free of box score stats, has Wade in the top 20 at +3.3.

Forward: Paul George

The reigning Most Improved Player, he's once again a viable candidate. In fact, last season was an odd case: he locked up the award playing for a good team and increasing his minutes by nearly 8 per game. His largest improvement came from his perimeter defense, so in a backdoor way he did deserve the award, but the media typically neglects defense unless it's propped up by gaudy block/rebound stats. He's maintained his status as an elite perimeter defender, but he's surged to stardom thanks to a legitimate high-scoring game. His shooting percentages have risen on virtually every area of the court, depending on how you slice it up, even though he's taking more shots, including difficult fadeaway jumpers. There should be absolutely no qualms about George being an elite player now. He's scoring efficiently on a fairly high volume without much help; it's not like he's being set up by one of the best playmakers in the league. And coupled with his defense, and he's a two-way force. Indiana's offense is overrated because their win total hides the fact their offensive efficiency is below average even with outstanding offensive rebounding, but that's through no fault of George and he's a key part in a defense that's putting everyone else to shame. The Bulls' defense is closer to the 9th rated Clippers than the Pacers.

Forward: LeBron James

I don't need to spend much time explaining why LeBron should be in an all-star game, even when he's "LeCoast." For one fun fact, with a usage of 29.9 via b-ref and a TS% of 65.9, he's literally off the charts in terms of usage and efficiency. (And actually, so is Durant.) Even though he's dialing back the effort on defense and his turnovers are up, he's breaking the laws of basketball -- he's second in the entire league in post-up efficiency at 1.17 points per game from Synergy, and it's not on a trivial amount of plays either; he's posted-up 156 times. He's also tailored himself as an excellent spot-up shooter, as SportVU ranks his effective field-goal percentage third out of 195 players with at least 20 games and 2 catch-and-shoot attempts per game. He's shooting 51% on those three-pointers. Once derided for his lack of finesse skills, his versatile skillset is a nightmare in a variety of situations.

Forward: Roy Hibbert

I should take more credit for defending Mount Verticality in the first half of the 2013 season, explaining that his shooting percentages were likely an aberration due to an injury and that his other stats held steady. Then in the playoffs the Indiana defense lurched into high gear against the Miami Heat, taking them to seven games. They have nearly perfected their own brand of defense and are currently 9.5 points better than the league average on defensive efficiency per 100 possessions. For people unfamiliar with these stats, that is unprecedented in modern basketball. The Ewing-Oakley-Riley Knicks peaked at 8.3 in 1993. The Duncan-Popovich Spurs peaked at 8.8 in 2004. The Garnett-Perkins Celtics peaked at 8.6. Outside of Bill Russell's Celtics, this could be the most impressive defensive season we've ever seen, relative to one's peers. The historically weak east takes a little oomph out of their stats, but this is still mighty impressive, especially since this is an age with an unprecedented amount of information and a wave of people trying to emulate the defensive success of guys like Thibodeau and Popovich. His box score stats may seem modest, but it's the tip of the iceberg -- the defensive stats of the Pacers are gargantuan, and Hibbert is their most important defender, guarding the restricted area. His defensive rebounding looks anemic, but Indiana leads the league in DRB% and their perimeter players get in on the action. He's also has a decent utility on offense for a center, more usable than types who can't create their own shots. If you were to take one center for the game, Hibbert is the choice if you want to win.

Reserves:

Guard: Kyle Lowry

The point guard competition in the east is seriously weak, as one could argue probably two players from the west who won't be picked over any point guard here. With Rose injured again, Irving failing to take a leap forward, and even Rondo limited, Lowry has unexpectedly put his hat in the ring. Offensively, he's taken on a healthy share of his team's offense with his shot creation and assists, and his shooting percentages have been excellent. He's taken care of the ball too with a 3.4 assist/turnover ratio. As a result, the Raptors have an offensive rating higher than Indiana, even with Rudy Gay's epic shooting problems -- if Gay had shot at the league average, he would have had 50 more points over only 18 games. In the blight that is the eastern conference, Toronto has been one of the few bright spots and Lowry has played a central role. Not only is he good offensively, but when properly competing he's one of the best defensive guards too. He's averaging 1.6 steals and 1.2 charges taken a game, which is the highest mark since 2007 from Varejao and Andrew Bogut, via Hoopdata. He's a bulldog defensive point guard who's a plus when he's motivated and not excessively gambling. He's definitely the best guard on the Raptors; let's hope everyone won't be distracted by DeRozan averaging 33% more points ... because he's taking 50% more shots. DeRozan is an "empty calories" scorer who offers nothing else of value and doesn't even score proficiently. Somehow Lowry's on the trading block, according to some people, but their reigning GM of the year will be smart enough to keep him.

Guard: Kyrie Irving

Like Wall, even though his team's offense is disappointing, it's better when he's on the court and better is an understatement: they score at a pathetic 96.8 points per 100 possessions without Irving, compared to 103.4 when he's on the court. Having a real NBA small forward helps, as they've been better with Deng on board. However, I'm still not sold on him as a player with his weak defense, and I think his crossovers and his dribbling skills don't lead a team to results that are as good as one would think. Unfortunately, there is no viable candidate to replace him, and I'd rather bet on a player who's probably just had a weak slump at the start of the season to a role player who doesn't belong in the game or a fluke season. For instance, Afflalo has gotten a lot of attention for the all-star game, but I feel like we're going to look back years from now and view him like we do Mo Williams. Last season in a similar role his shooting efficiency was poor with how large a chunk of the offense he shared. His TS% has risen 6.2 points.

Looking at his playing style, Afflalo takes a heavy amount of baseline jumpers, especially turnaround shots, usually contested. He's shooting over 50% in a couple of these midrange zones, and my instinct screams "fluky shooting percentages." He was a pretty decent midrange shooter last season, however, and the other reason his overall numbers are up is that his three-point shooting has bounced back from 30% last year (he's near 40% for his career) to 42%. Given his high minutes, he's averaging nearly 20 points per game, but beyond that he's not contributing at all. His overrated defense is now fairly porous given all the energy he expends on the other end, and he provides nothing else of significant value including playmaking. As for Lance Stephenson, I've said my share, and another serious candidate thrown around is ... DeMar DeRozan, a one-dimensional scorer whose only fame to claim is shooting a lot. Otherwise you have to consider guys like Deron Williams, who makes Kyrie Irving look like an MVP, and Joe Johnson, who's already been awarded far too many all-star games after that pact with Satan. So Kyrie Irving gets the selection here, but if someone wants to perform a Freaky Friday with him and Goran Dragic I wouldn't mind.

Forward: Carmelo Anthony

If there were more competition, I could have a nuanced discussion on Carmelo, how he's used in an offense, how we shouldn't judge him based on the disaster surrounding, his aloof defense, etc. If you're going to keep him out of the game because the Knicks are losing most games and you think he's a chucker, then you have to consider guys like Luol Deng or Joe Johnson. We all know his faults, but that means he's not an MVP candidate. A TS% of 55.3 isn't special, but it's not bad either; it's above average. He does this without turning the ball over, and his rebounding is underrated: a 21 DRB% is good enough for a center (although starting next to Bargnani helps a player's rebounding numbers, Carmelo has always been great.) I don't want him starting because of his poor defense and how he can stall an offense -- he averages 17.4 frontcourt touches for every assist -- but he's a lock here.

Forward: Chris Bosh

Bosh is a somewhat forgotten piece now, more known for his goofy antics and video-bombing, but he's still an excellent player on both ends of the court. He's only playing 31 minutes a game, but it's through no fault of his own: the Heat have gone the distance in the playoffs three years in a row and they're resting key guys to be fresh for another title run. Per 36 minutes, he's average 19.5 points with superb shooting percentages and a tiny turnover rate for a big man, stretching the floor for LeBron and Wade. His rebounding and post defense against behemoths is disappointing, but his DRB% is good for a power forward, his natural position, and he takes a pounding from enforcing Miami's strategy of smallball and space/pace. Miami's defense has slipped, but it's not Bosh's fault: when he's on the court their defensive efficiency is 103.0, which would be sixth in the league (currently 11th overall) even though he often plays in smallball lineups. In fact, Bosh has the largest raw +/- on the team, and adjusted RAPM method (non-prior informed) estimates his impact at +4.2, one of the best in the league. His scoring stats would be more impressive if he had a larger role on offense, which is a luxury some of the other guys in the east have, but his accurate midrange shooting is a boon for Miami's offense and he's one of the best pick and roll defenders in the league.

Forward: Paul Millsap

Millsap would have likely been ignored for the all-star game if Horford didn't get injured while Atlanta kept winning. He's long been one of the league's most underrated players without a single flashy strength or style. However, he did add one asset rendering him unique -- he's a good three-point shooter now, taking 2.6 per game at 37%. He's also been a larger part of the offense than he's ever, and he's performing well, including a surprising amount of assists. So he's an accurate big man who can stretch the floor, hit a jumper anywhere, he's not a ball-stopper, he can pass, he rebounds well, he's a good defender, he picks up a lot of steals -- he's just a well-rounded power forward. And he's not leaning on anyone here either. The attention is now on him without Horford and without a Joe Johnson-type on the perimeter.

And while I'm talking about the candidacy of a frontcourt player, let me slam have an opportunity to slam Al Jefferson -- I've seen him on people's ballots over guys like Chris Bosh or Millsap, and I have no idea why. They're averaging a similar amount of points, but Al needs over three more field goals per game to reach his totals. Jefferson's percentages are significantly below average and he's a black hole on offense. The Jazz were always better off with Millsap over Jefferson. People complain about people who overuse things like TS%, but Millsap gives you more points in less shot attempts -- why is that bad? And he's doing it more in the flow of an offense, even shooting from further away and stretching the floor. I'll commend Al's improved defense and that of Charlotte's, but guys like Bosh are still better defenders. You can see this with the "eye-test," you can see this with stats -- it should be obvious.

Wild cards:

Forward: Joakim Noah

Once again, the Bulls are without Rose, and once again they're near league average with an excellent defense and an awful offense. There was no Plan B with Rose -- he was going to be their only scorer, besides Boozer and ... Mike Dunleavy. The team has no business hovering around .500, but they get there with a stifling defense and more ball movement than one would think for an inept offense. Noah represents their strengths, and years later I hope people realize he's a multiple-time all-star because of his defense, rebounding, and passing. His offense is better than most centers; he's not a negative here. A team can play through him in the high post, he has a usable jump shot, and he's unselfish. But as a highly active center, he's the key pivot point of the second best defense in the league. The game today involves lots of switching and pick and rolls, and that's Noah's defensive strength. He's allowed 0.65 points per play in isolation via Synergy ranking 26th, which has involved a few perimeter players, and only 0.74 points per play as the pick and roll defender, ranking an impressive ninth.

I understand that people will argue defense doesn't matter for the all-star game, but the way people talk about all-star appearances, and what it means to the fans, the history of the game, and the players, I'm going for best player. If he were in the west, I could see arguments for Duncan or Dragic over him -- for one, Chicago's defense is better when Noah doesn't play, but I don't think that's accurate -- but I'm more certain taking Noah here than any of the other candidates, like the injured Chandler or Al Jefferson.

Forward: Andre Drummond

This is basically me saying "screw it" and picking someone I'd want to see because I don't think there's a 12th candidate who's deserving anyway. David West is a valuable piece for Indiana, but his scoring stats have slipped: he's not getting to the rim like he used to; it's not fluky jump shooting percentages. Afflalo certainly has a case, but I'm not sure I trust his offensive game right now, which might be unfair but he's really not overwhelming. Jeff Teague hasn't been shooting well, and besides his passing, well, it's Jeff Teague. I'd really like to sneak Dragic across the Mississippi, but alas, I gotta choose someone else.

Detroit is a mess defensively, yes, but I don't think it's because Drummond is a horrible defensive player. Even Asik-Howard was a bad combination, and those two are better than Monroe and Drummond. Drummond without one of those guys on the court still doesn't fix the defense, as when he's paired with Monroe or without both opponents are scoring at a high 111 points per 100 possessions rate, but it's worth noting the Josh Smith-Drummond pair allows only 104.2, which is decidedly above average. He's still learning the subtleties of NBA-level defenses, but he's destroying people on the boards, even with a crowded frontcourt. A defensive rebound rate of 27.8 is truly elite, and an offensive rebound rate of 16.5 is Rodman-esque. And you want him off the boards, because he's one of the best at put-back dunks. They don't run plays for him, ever really, because he's still raw and unskilled, but he still manages to score 14 points per 36 minutes on high efficiency. He's not the most deserving pick, but at least he's super young and could turn into a legitimate star, meaning the pick won't look so strange years from now. Let's enjoy this explosive big man while he can still get up.

The Darkhorse All-star Team

As a bonus, here are my crazy, darkhose all-star picks, filled with players who do not conventionally fit the definition of an all-star, but deserve credit for either being high-performing role players or fringe all-star candidates.

Guard: Isaiah Thomas

Before Cousins had a few monstrous games, I would have easily called him Sacramento's best player, and I honestly still think it's closer than people think. Per possession, his stats are on par with all the best point guards in the league, with the exception of Chris Paul.

Guard: Manu Ginobili

When people talk about the weaknesses of advanced +/-, it's because the results often bounce up and down from year to year, and that specific lineup rotation issues, and who's playing with whom, can drive the numbers. However, Manu is 36 years-old and is once again near the top of the league in advanced +/-, and, excluding Duncan and Parker, who don't even start alongside him, it's with an entirely different cast of characters than the players in the mid-00's. Plus/minus is just about outscoring your opponent -- it's all that matters, in the end. And Manu is the master at pushing the score in his team's direction.

Forward: Andre Iguodala

Iguodala was an actual all-star, but like Manu he's missed a few games due to injury and has a smaller role this season (his usage dropped by almost 5 points.) But he's the glue to Golden State's roster right now, keeping a top-notch defensive unit together, distributing well for a team without a real back-up point guard, and he's even hitting his outside shots, doing a laundry list of important tough tasks for a good team. The Pippen comparisons are apt.

Forward: Amir Johnson

With Rudy Gay and Bargnani gone, Toronto was supposed to be bereft of talent, but they actually improved and immediately after Gay's trade Amir had some monster games. Few people know his game, but he's an active defender who rebounds and blocks shots well, while on offense he actually spaces the floor to nearly the three-point line (he's actually been taking one per game this season) -- yet even with all those long two-pointers he's still a very efficient scorer, much like Bosh. The Raptors have been much better when he plays for a long time, and he deserves some credit.

Forward: Anderson Varejao

Like Noah, he's a highly active center on defense who works well as a high-post facilitator, but health problems have limited his career. He's being wasted on a terrible Cleveland squad, but if he's ever traded to a contender more people would understand his value. As a bonus, he sorta looks like Sideshow Bob.

Reserves

Guard: Wesley Matthews

He's the quintessential 3-D player. Shooting a high percentage behind the arc, even if you close him out he can drive to the basket with reckless abandon. He's also a good, feisty defender, and a key part of a surprising Portland team.

Guard: Lance Stephenson

He's rightfully in the right place here, in the land of role players and sub-stars. In the Pacers disciplined system, he's a tenacious defender and a dynamic offensive guard, rather than a player prone to weird, aggressive mistakes; he's the Stephen Jackson, circa 2003 Spurs, to Indiana.

Forward: Taj Gibson

As one of the game's best defensive players, he'll never receive much attention, especially when coming off the bench, but the value is there. Last year, for example, he allowed only 0.76 points per play on defense, from Synergy. He's strong, quick, blocks shots, rebounds, is fundamentally sound, and has learned from coach Thibs.

Forward: Nick Collison

Battier had a feature about being the "no-stars" all-star, but Collison has held that title for a long time now. Replacing Perkins in the rotation will do wonder for your +/- stats, but he's the role player every elite team would want: he sets great screens, he passes well, he defends at a high level on both pick and rolls and versus post players like Randolph, and he doesn't demand a large part of the offense.

Forward: Andrew Bogut

A former number one pick, Bogut, after years of injury, has turned into an underrated player. At the most important defensive position, he's one of the best in the game, and he's a useful complementary offensive piece due to his passing, finishing ability, and hard screens. Per minute, one could make the argument he's as valuable as all-star centers like Howard and Hibbert. Let's hope he stays healthy (unless he plays against my Blazers in the playoffs, however.)

Reserves:

Guard: JJ Redick

He'd probably make the all-star team in the east, but he certainly doesn't seem like one. However, his valuable shooting and playmaking has helped a Chris Paul-less offense stand the rigors of competition. He's second in the league in distance traveled per 48 minutes, among qualifying players. He plays like a disciple of Reggie Miller and Ray Allen, running around screen after screen for an open shoot, knocking them down with a high degree of precision, and putting an extra gear in an already great offense. I have an appreciation of this type of player and a theory that this is perhaps the best valuable type of offensive support for an elite team relative to its role on the team (i.e. adjusting for volume.) Redick's the piece that makes this Chris Paul team scary.

Forward: Kevin Garnett

Yes, I did say this was a crazy team. He doesn't play enough minutes anymore to deserve an all-star spot, but once again he's quarter-backing the defense and helping the crew in Brooklyn rise to 0.500 basketball while trying to put out wildfires everywhere. Lopez is gone, Deron has been hurt, and the coaching has been ... troubling, but they play better with Garnett. As I said, this is my crazy all-star team.

Tuesday, January 31, 2012

NBA Team Alignment

Introduction


Seven years ago, the NBA added its newest team, the Charlotte Bobcats, and realigned the league with three divisions in each conference. A few years after the Grizzlies moved to Memphis from Vancouver, Seattle lost its basketball team to Oklahoma City, and the new Northwest Division featured only one team truly in the northwest quadrant of the nation and one in Minnesota and another in Oklahoma. There are other oddities as well -- the aforementioned Grizzlies are in the "Southwest" Division, the desert city Phoenix is in the Pacific Division despite being hundreds of miles away, and likewise Toronto is in the Atlantic Division even though the closest they get to the Atlantic is raptor-filled lake Ontario. Next year will feature the New Jersey Nets moving to Brooklyn, and although it's akin to moving to a house down the block in the NBA landscape it hints at future developments.

Isn't there a better arrangement of NBA teams? What happens when a city like Charlotte or Sacramento loses their team? Or Seattle and Las Vegas gain one? With even a modest computer like mine, these questions can be tested with a little ingenuity.

Methodology

Teams typically play the same schedule for 58 out of 82 games because they play every other team at least twice. They also have to play division opponents four times, and other teams in the division three to four. There is a significant difference between conferences, but divisions are essentially meaningless in terms of scheduling. Therefore, for computational simplicity, I will set the conferences first, and then organize the divisions.

In order to find the most efficient alignment of teams, first I had to calculate the distance between every NBA arena. This was surprisingly easy thanks to the internet and programming. The latitude and longitude of every arena was found online, and the distance between was calculated using the spherical law of cosines -- basically I found the length of an arc on two different points on a sphere using trigonometry. Teams, obviously, don't travel on perfect paths from on arena to the next because they need to access airports and hotels, but over large distances the effects are small. With some nice logical statements and programming, I compiled a 30 by 30 matrix of distances between teams. I used the Brooklyn arena instead of New Jersey, although it doesn't significantly matter, and for computational efficiency the calculation was for 29 teams and the Lakers' results were copied for the Clippers.

The next part was surprisingly difficult. A fifteen team conference doesn't sound all too large, but there are 15,510,000~ unique combinations possible. (As a side note, combination is a specific mathematical term to describe the scenario. A permutation cares about order, so a conference with teams X, Y and Z would be different than X, Z, and Y, while combination only cares about unique groupings.) I wouldn't be able to crank out that many calculations with ease without the aid of the Jeopardy! computer, so I locked in 11 teams on each coast to their respective conferences and left eight teams in conference purgatory, waiting for their ultimate judgement from the program.

Next I found the minimum number of total league miles between arenas giving a 1.8 weight to teams in the same conference and a weight of 1.0 to those in different conferences. The weighting is basically just saying teams play 2 games against teams in the other conference, but because one of those will be at home they only travel once, and at least an average of 3.6 games within conferences, but again they only travel on average 1.8 games. Note this simulates 80.4 games, which makes it apparent how little divisions matter, and essentially that any efficient method of organizing divisions only affects 1.6 games half of which are at home.

I also included scenarios for teams relocating to different cities -- the Grizzlies, for example, moving back to Vancouver and restoring the sanity of the team's name. Looking at the smallest metropolitan areas and which cities already have many professional teams along with population growth, another candidate for relocation is the Bucks in Milwaukee, and I had them move to Seattle, which is currently the largest metro area without an NBA team. The last scenario tested was a major relocation with the New Orleans Hornets moving to Seattle to become the Sonics, the Sacramento Kings to Las Vegas, and the Memphis Grizzlies to Tampa and hopefully changing their name (Tampa Panthers after the elusive Florida cat?) Those three organizations are having trouble attracting enough fans and keeping their business above the profit line.

Las Vegas doesn't have a pro team, has hugely growth, and the Las Vegas Kings is a great name; Seattle deserves its team back and New Orleans had negative population growth last decade and became the smallest market besides Salt Lake City; and Memphis is another small market while Tampa is another warm weather city athletes love with plenty of people and growth. These choices, however, were mainly an exercise in seeing how the league's alignment would change if teams moved. For the geographical coordinates, the old arenas were used for Vancouver and Seattle, while the city's coordinates were used for Las Vegas and Tampa Bay.

Results


For reference, using the same conference alignment presently except with the Nets in Brooklyn, if every team traveled to every other team in its conference on average 1.8 times and once to teams in the other conference, they would have traveled 1,272,633 miles in total for an average of 42,421 miles per team. This does not include the extra games within one's conference, but again that amount is negligible for these purposes (only 1.6 games more on average per team per season.)

The most efficient conference alignment from the algorithm was Minnesota, Memphis, Oklahoma City, and New Orleans in the west, and Milwaukee, Chicago, Atlanta, and Indiana in the east ... which is exactly how it's already set-up. Basically, the conferences were already efficiently arranged. The entire operation wasn't fortuitous, however, since there's nothing wrong with proving the current system is best, and the best results are usually surprising.

The first alternate scenario also did not feature a shift in the conferences when the Grizzlies migrated back to Canada in Vancouver, although it's not surprising because Memphis was already in the Western Conference.  The total miles for the league was 1,329,218 miles, which was an increase of 4.4 percent from the present order, and an average of 44,307 miles per team. The Blazers would be happy for another team in the northwest, but the overall effects are fairly significant because Memphis is a centrally located city and Vancouver would be the furthest team from the center of the country. For minimizing travel, the most efficient placement of a single team would be near the center of mass, so to speak, of the conference teams and shifted to the center of the country for all the travel to the other conference. Memphis is in an ideal location in this respect.

The Bucks to Seattle scenario had a shift in the conferences, which is obvious since the Bucks were in the east and Seattle's a ways from the Mississippi. Only two teams would change conferences -- the Bucks to Seattle, and the Memphis Grizzlies to the east. The total miles from the league was 1,323,964 increased by 3.9 percent and an average of 44,132 miles. Once again, a team moving from the central of the country to one of the coasts would increase the total miles traveled by every team.

The Kings to Kansas City, predictably, decreased the total number of miles league-wide by 4.0 percent for 1,221,952 and an average of 40,732 miles. Surprisingly, teams didn't change conferences, as the Kings would stay in the west. Kansas City is geographically the center of the country, and even in the Western Conference it would still have a center location with Minnesota, Memphis and New Orleans east. A rule of thumb seems to be if you move switch teams from the center of the country to the outer edges league-wide traveling between cities would change by roughly 4 percent.

The most radical scenario with the Kings to Las Vegas, the Grizzlies to Tampa Bay, and the Hornets to Seattle featured again only one conference switch. The Hornets would stay in the west by going to Seattle, the Kings would also stay in the west because of Las Vegas, but Milwaukee would interestingly join the western conference while the Grizzlies in Tampa would join the east. The total miles increased by 3.7 percent to 1,320,134 with an average of 44,004 miles. Divisions would have to be completely changed, but that's a story for another section.

Conclusion


The NBA schedule is heavily dependent on which conference team occupies, but little about the specific division. 80.4 games are comprised of two with each opposing conference team and an average of 3.6 within the conference. The extra 1.6 games are added to teams within your division. The present conference alignment is the most efficient system in terms of minimizing travel distance between cities tested against seventy different combinations of eastern and western conference teams. The total travel distance of every team in the league was 1,272,633 miles (not including the extra 1.6 games.)

A few different team relocation scenarios were tested, and the results suggested that moving a team from the middle of the country to the outer edge would increase total travel distance by a fair amount but nothing too large (around 4 percent based on where the teams are.) Pairing a lonely city like Portland with Seattle wouldn't decrease travel distances for the league because of how far Seattle is from every other city. All four scenarios tested only switched at the most one pair of teams from each other's conferences, suggesting that the NBA's current alignment is mostly static.

This article is a little late in arriving, but I had trouble sorting the teams by division and as a result part two of this article will test for the most efficient alignments for divisions, their importance, and how relocations change those.