The European sailors who "discovered" Australia were stunned by the island continent's black swans. All European swans were white. In their language, the expression that something was "as rare as a black swan" meant that it was impossible.
Black swans existed, but because no European had ever seen them before, there was no way for their models of the world to account for them.
In his award-winning book "Black Swan," Nasim Taleb characterizes major scientific breakthroughs and historical shatterpoints as "black swans"—completely unpredictable. Two recent examples he gives are the 9/11 attacks and the collapse of the housing market in 2008.
These "black swan" events are statistical outliers—they don't occur within the normal bounds of historical behavior, but they have an out-sized impact on the course of history.
Taleb's main point was that a statistical model for the American economy that perfectly predicted the events of 2001-2007, but completely missed the housing bubble, was of far less value than we realized. Even if a model predicted events with 99 percent accuracy, if the one percent of events it missed were of sufficient importance, than it really wasn't worth all that much.
He's no academic dilettante either. Taleb, a hedge fund manager, has run some of the biggest investment firms in the world and made himself a small fortune based on his analysis of the unpredictability of risk.
** It has become somewhat fashionable to bash the New Yorker's Malcolm Gladwell as his work (Blink, Tipping Point) has become increasingly popular and influential in American society. But if you are just looking for an interesting magazine article to read, check out his archives. Every article, even if it is based on a dubious premise, is interesting and thought-provoking. **
In the basketball world, many people have been trying to construct statistical models that can capture, explain and (most importantly) predict what's happening on the court.
One of their first discoveries (which has held true in all major team sports) was the importance of point differential. Their counterintuitive conclusion was that a team's win-loss record told us less about how good the team was than its average scoring margin.
Or as Aaron Schatz of Football Outsiders put it: "Championship teams are generally defined by their ability to dominate inferior opponents, not their ability to win close games."
But what about that other one percent?
A single basketball player can have a much larger impact on a team (one out of 12) than a single baseball (one out of 25) or football (one out of 53) player.
** This is why I'm fairly dubious of the value of a quarterback being a "winner". **
So are there any "black swans" in basketball?
Are there any historically unique players who impact games in new and different ways than the players before them?
In 2008-2009, the Cleveland Cavaliers had the best point differential in the NBA at +8.9. But the results of that year's playoffs—a resounding six-game loss to Orlando in the Eastern Conference Finals, who the Lakers proceeded to trounce in five games in the Finals—make it pretty clear that they were not the best team.
In 2009-2010, the Cavs had the second best differential at +6.5. But after Game 5 of their second round series against Boston, it was obvious they had no chance of becoming champions.
So what happened? Why do LeBron James' teams under-perform their regular season point differential in the playoffs? And what does that tell us about the 2010-2011 Miami Heat, who currently lead the NBA with a +9.5 scoring margin?
The conventional interpretation of this statistic is that LeBron does not have "the heart of a champion." I disagree strongly.
Instead, I'd say that LeBron is such a good player based on his ability to completely dominate bad teams, that it tends to distort his team's point differential and disguise how good (or bad) they really are.
If someone gave a basketball player a ball and told them they had to make their next shot or they would kill you, what shot would you want them to take? You would want them to dribble it up the court and dunk it.
And has anyone in the history of the NBA been better at that than LeBron James?
He's listed at 6'8", 250 pounds, but many people believe he's really somewhere in the range of 6'9, 270. Combine that with a 7-foot wingspan and a vertical easily north of 30 inches, and LeBron is one of the best athletes in the history of the NBA.
Add an all-around game superior to most of the league's point guards, and you've got a "black swan." There's no one who would have predicted a player like LeBron James could exist in 1995.
While the media has been fixated on the tabloid circus around South Beach, the Miami Heat have been an incredibly predictable team. If you don't have a seven-footer who can protect the paint and stop LeBron from dunking on your head, you are going to lose. If you do, and you have either a low-post player or a dominant point guard (the two types of players the Heat cannot guard), you have a good chance of winning.
** Of the nine NBA games I've bet on so far this year, my only three wins have come in Miami Heat games. But I've been able to stay even because the Heat games were such easy calls ("Clay Davis" games). People just refuse to analyze them rationally. **
This is a bad sign for the Heat, who have been shellacking the NBA's worst teams en route to winning 19 of 20 games and accumulating the league's best point differential.
Boston has a shot-blocking center (Perkins) and a great point guard (Rondo); Orlando has a shot-blocking center (Howard) who doubles as a low-post threat and Chicago has a shot-blocking center (Noah) and a great point of their own in Derrick Rose.
The main reason why a team's scoring margin predicts their future performance better than wins and losses is that performance in close games can be attributed mostly to luck:
NBA stat mavens such as ESPN.com's John Hollinger will tell you that pretty much no team in history has shown sustained year-after-year success in winning close games, even when keeping most of the same personnel. History says that good teams and bad generally tend toward .500 as the games get closer.
Yet in 2008-2009, the Dallas Mavericks went 18-5 in games decided by five points or fewer. In 2009-2010, the Mavericks went 18-7. This year, they are 10-5. Since 2004-2005, they are an astounding 103-49.
Hollinger calculated that Dallas would have a one in 150 chance of compiling this record. He dismisses it as a statistical fluke, but isn't it possible we've found another black swan?
In this case, a seven-footer with a fundamentally perfect jump shot.
Dirk Nowitzki has the 15th highest career free throw percentage in the history of the NBA at 87.6 percent. No other seven footer is in the top 40. His mentor Holger Geschwindner believes he should shoot 95 percent from the line ever year. And his percentage has been steadily increasing as he has gotten older.
Who is the most unique player in the NBA?
What makes this skill so valuable is that's impossible to deny a seven-footer on an inbounds pass. Even if you double him on defense, the offense can just throw it high in the air and let him grab it over the smaller defenders.
So if you have a seven-footer who is automatic from the free-throw line, you have a huge advantage in closing out basketball games. If the other team is trailing with less than 24 seconds left, they foul and hope you miss your free throws. If you're playing Dallas, that's pretty much not going to happen.
So when the Mavericks give the ball to Nowitzki and Jason Terry (a career 84.4 percent FT shooter) at the end of the fourth quarter, they are shortening the game. A one-run deficit against the New York Yankees in the ninth inning is about as insurmountable as missing a shot in the last fifteen seconds and giving the Mavericks the ball with a two-point lead. Dallas will make all four free throws they are given, so the other team has to knock down two contested threes in the span of ten seconds.
** It's easy to underestimate how skilled NBA players are at knocking down open shots. When I was working for the Dallas Morning News, I watched Jason Terry take about 200 3's after practice one day. He missed about ten and grazed the rim no more than a quarter of a time. **
Long story short, I think the Miami Heat are worse than their point differential (+9.5) and the Dallas Mavericks are better (+4.1).