Since we're on the sports theme, and since this has been a big summer in sportsland, I'm going to stick with the topic for at least one more post. I've got, among other things, a post on my erstwhile poetry workshop in the works, and have been putting off a particular music post for far too long.
Also, you'll notice the blog has widened. I think it looks better this way, plus it let me fit my graphs whilst keeping them readable in this post.
Undoubtedly you've heard about LeBron James joining the Miami Heat alongside Chris Bosh and Dwyane Wade, making the team prohibitive favorites to win the NBA title for the foreseeable future. Not everyone agrees that the Heat will be good, of course, but there is no doubting that, individually, the Heat now have three of the best players in basketball. LeBron James is a back-to-back MVP, and he and Wade have finished first and second respectively in John Hollinger's "Player Efficiency Rating" two years in a row. In fact, LeBron has led the NBA in PER three years and a row. Add to that Bosh's fourth place finish last season, and it's reasonable to say that the Heat are getting three of the top 10 (if not top 5) players in the NBA right now.
The new "Big Three" are not "top 10" in some bizarre, backwards way like the context-dependent statistics "assists" and "points," either. Rather, they are in the top 10 in efficiency, in turning shots and possessions into points, and likewise stopping other teams from doing the same. That sounds to me like a lot of wins waiting to happen.
Anyway, having three such great players on a single team got me thinking about how NBA teams construct their rosters. Of course, the established narratives are obvious: the Cavaliers, while they had James, were a one-trick pony. The Nuggets much the same, relying on Carmelo Anthony. The Boston Celtics have their "Big Three," with a bunch of role players besides. Meanwhile a team like the Utah Jazz or the Atlanta Hawks tends towards more balance, a distribution of responsibilities among a talented collection of non-superstars. Those narratives are over-exaggerations, admittedly, but they are also, generally speaking, not true.
What do I mean? Well, I plotted each NBA team's roster by Win Shares of the best, second best, third best, and so on player against league average. Before we move on, Win Shares, in basketball, is still a young and rough statistic, but it's about as good as anything we have. In short, it tells us how much a player's performance has been worth to his team - based on a number of offensive and defensive factors - in terms of Wins. Great players like Lebron are worth 15 or more in a season. Most players are in the 4 or 5 range. Again, it's not perfect, but it's pretty good, and moreover it really does tell us something about how roster's are built and how they play out.
Consider this graph of NBA Finalists Boston and Los Angeles:
The black line represents league average at each rank (i.e. the average best player on an NBA team was worth 9.3 wins last season). The yellow line represents the Lakers players in order of production (that is, Pau Gasol, then Kobe Bryant, then Andrew Bynum, etc), while the green line represents the Celtics (Rondo, Pierce, Allen, and Garnett lead the way).
The first thing to notice is the so-called "Big Three." For one thing, Paul Pierce, Ray Allen, and Kevin Garnett were second through fourth on the Celtics this season, leaving the heaviest lifting to Rajon Rondo. The other big thing to notice, however, is that those big four were worth fewer wins than the Lakers' top four players, namely Gasol, Bryant, Bynum, and Lamar Odom. Now, that may be in part due to injuries and the way that coaches ration playing time, but that's exactly the point. Over the course of the every game of the whole season, the Celtics were built to win in a different way than the Lakers were built to win.
The Lakers were a great team one through eight. Their top eight players were all above league average in Win Shares for their rank on the roster. That's fairly remarkable, and goes a long way towards explaining the team's success. The Celtics, on the other hand, were great one through five, AND ten through thirteen (if the graph continued, they'd in fact be great ten through seventeen). That means, over the course of the season, the Celtics had great starters, and an extremely deep bench. Their second line was not exceptional - indeed, was below average - but their third line, which they used much more than many teams, was exceptional.
You can see, already, why the Lakers had the advantage come playoff time. In the regular season, it benefits a team to have useful players thirteen men deep on a roster. In the playoffs, the top eight are going to do most of the work, as coaches consolidate and put only their very best players on the floor. It is at exactly the ninth roster spot where the Celtics become better than the Lakers. Though it seems clear that, even with the crossover, the Lakers were the better team overall.
This method, however, isn't built for looking at playoff performances. Let us turn our gaze, instead to some notable teams, starting with Eastern Conference regular-season powers Cleveland, Atlanta, and Orlando.
So Lebron James is the one at the tippy top on the left, with 18.5 Win Shares. Yeah. The Magic, for comparison, were lead by the quite capable Dwight Howard at 13.2, while the Hawks Al Horford collected 10.9.
What is most striking here, I think, is how well-balanced the Atlanta Hawks were. And not just well-balanced, but excellent. While Horford was far from the best star of a team in the NBA, few number two players were better than Josh Smith. Moving down the roster, the Hawks had the best number three guy in the entire NBA in Joe Johnson, and Jamal Crawford at fourth bested everyone but the Lakers' Odom. It's clear from their comparatively even distribution of contribution that the Hawks were doing something right last year, something the Heat undoubtedly want to emulate next season (though at an even higher level).
The Magic come across very strong here as well. Unlike the Hawks, they displayed depth well beyond their starting lineup. Coupling that with one of the best players in the NBA in Howard, and it's no wonder that they took the Southeast division from Atlanta easily. Consider that the Magic used only twelve players all season, and that every single one of those players was above league average in Win Shares for his rank on the team. That's the kind of recipe that leads to 58 wins.
The Cavaliers are interesting, because they are not nearly as one-dimensional as they are made out to be. Without a doubt LeBron was their best player and the difference between a mediocre and a great regular season, but the much maligned players surrounding the King were more than adequate to get the team to 60 wins (considering that even the great LeBron "only" delivered 18.5 of those wins; even without the King, this was a .500 team). But the cautionary tale for the Cavs comes if you take each of those barely-above-average players and slide them one slot to the left to account for James leaving. The result is not pretty, as the entire starting lineup goes from above to below league average. The bench stays strong - indeed, the Cavaliers were a deep team behind LeBron, believe it or not - but without someone to anchor the starting lineup, Cleveland is looking at a mediocre season next year.
While I have data for all 30 NBA teams (I can send you the spreadsheet, if you like), they don't graph well in groups of more than five teams, so let's finish up here by looking at the Northwestern Division, the most competitive in the NBA last season. Here are the Utah Jazz, the Denver Nuggets, the Portland Trailblazers, the Oklahoma City Thunder, and the lowly Minnesota Timberwolves.
The first thing that jumps out, here, is how truly awful the Timberwolves were. Their two best players - Love and Jefferson - would be fifth on the Nuggets and sixth on the Jazz. Yikes.
It's also clear here that Oklahoma City's success has a lot to do with Kevin Durant, much more so than Denver's has to do with Melo (who, actually, didn't even lead the team in Win Shares) or Utah's with Deron Williams. While OKC had some decent players to complement Durant, their starting five is barely above average without him, which would certainly doom the team in this division if not for Durant's absurd season.
The Nuggets and the Jazz are quite comparable, with a slight edge to the Jazz as you get further down the roster. The irony, here, is that the accepted basketball narrative come playoff time was that the Nuggets - who have tremendous depth - couldn't match up with the best players from the Jazz. I suspect the apparent depth of the Nuggets is, much like the apparent hitting skill of the Rockies, an illusion perpetrated by the altitude of Denver. In reality, Nene (10.8 WS) was every bit as good as Carlos Boozer (9.9 WS) this season, and Billups (9.5 WS) very close to Williams (10.3 WS). Where the Nuggets struggle, in fact, is further down the roster, where the inefficiency of Kenyon Martin, J.R. Smith, and Anthony Carter is far too costly when matched up with the likes of C.J. Miles and Kyle Korver.
The Trailblazers, lastly, are a study in injuries and trades. Because they saw so many players play regularly at different times in the season, they seem to have tremendous depth. And for good reason. Had they been healthy over the course of the season, there's a good chance their graph would look more like Utah's, but as it was, when they needed to get wins out of players 10 and 11 men down the roster, they did. The plateau from their 7th to 11th Win Shares contributors is unmatched by any other team in the NBA last season. Appropriately, that plateau is bookended by up-and-coming Jerryd Bayless and the oft-injured Greg Oden.
A closing note, here, about the "league average" line. Most teams we looked at were above the line, of course, because we looked at good teams, but it really is the average, and it really is as smooth as it looks. The equation of the best-fit logarithmic regression line is f(x) = -3.5 ln (x) + 9.33, with an r-squared of 1(!). That is the Win Shares of a player is, on average, equal to -3.5 times the natural logarithm of his rank on the roster plus 9.33. Still mumbo-jumbo, so try this. The best player on a 2009-2010 NBA team is worth, on average, 9.33 Wins. Each subsequently ranked player is worth decreasingly less, but in a highly predictable way.
On its own, this equation doesn't tell us a whole lot. Without looking too deeply, I'm guessing it represents some well-known statistical law about skill distributions and ranking (something like Zipf's law, though it doesn't quite fit). More interesting would be to look at previous years, as well as other sports, to see what, if any, relationships hold. But that's all for another time.