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Kobe Bryant, Tim Duncan, and Making the Impossible Probable

Audiences know what they expect, and that is all that they're prepared to believe in.

A good friend of mine went nuclear on my productivity the other day through a stream of Twitter links to articles on Berfrois, an extremely interesting (though dense) site that I'd never had the pleasure of browsing before. One article in particular that demanded my undivided attention was this one, outlining the Kierkegaardian perspective on the concept of theodicy. Fully unpacking the ideas at play in Aylat-Yaguri's article is somewhat beyond the scope of this blog, and frankly, beyond my depth as a thinker. I don't intend this to be a discourse on a thinker I've always found difficult to parse, and as such, there will be little more mention of Kierkegaard today. Instead, I'd like to discuss an old Aristotelian prescription parenthetically outlined in that Berfrois article.

In Aristotle's Theory of Poetry and Fine Art, he prescribes that poets should in all work "prefer probable impossibilities to improbable possibilities" while excluding entirely all that in the realm of irrationality. It's been quite a while since I've read any Aristotle -- at least two years, probably more -- but I distinctly remember being impressed by that quote when I read it the first time. It distills the heart of writing a serious fictional narrative into a simple either/or statement, and manages to encapsulate the real reason many writers flounder when pushed into action with their readership's imagination. It's not that they are poor writers, or that their ideas aren't excellent -- it's that they simply never get that inherent buy-in from the reader. They can't ford the gap between the improbable and the impossible in a way that satisfies the reader. And they leave many readers wanting, knowing the story lacks that simple buy-in that improves everything. Despite the brilliance of their work, oftentimes, they simply can't bring the reader in. One of the best writers of the last decade was a basketball player. His rival? Lesser in the eyes of the populace, greater in his own mind's eye, free from the audience at hand.

Yep. We're talking about Kobe Bryant and Tim Duncan, once again.

• • •

In basketball, there are three levels of possibility. The first is obvious -- the truly impossible, the things that can never be done because the rules of basketball simply don't work that way. You can't have a six point single shot (although you can have a six point possession). You can't score from the opposing baseline -- you'd need to pass it to someone first, you literally aren't allowed to shoot the ball from the opposing baseline with no time off the clock. You can't punch other players in the face, unless you want to be suspended for the rest of the game and the rest of the season. And -- perhaps most importantly -- you can't defend every possession perfectly. There will always be some ghost of a chance that the shot is made, and as a defender, you have to live with that.

Where things get a bit trickier to describe is after you leave the comforting warmth of the absolute. The impossible not because it's logistically against the rules of the game, but because it defies the viewer's prescribed notions of possibility. There are the patently possible high-percentage plays -- the simple layup because of a blown defensive assignment, a wide open corner three from a good shooter, a Steve Nash free throw. Et cetera. There are also the virtually impossible nil-percentage plays -- a Dwight Howard three point shot, a triple teamed hail mary halfcourt shot, a post-up play against a prime Tim Duncan with less than two seconds on the clock. These aren't impossible, nor are they always going to happen -- they just seem like it. If you were to assign probabilities to them, the virtually impossible would probably happen less than 5% of the time. A patently possible play would be converted over 90% of the time. In-between those two? It becomes the province of the viewer to determine how probable a play is, and whether or not it's possible at all. That's where Kobe comes in.

• • •

Consider: the Duncan Spurs achieved the improbable with some regularity over the previous decade. Duncan carried one of the worst supporting casts in the last 30 years to an incredible title run in 2003, and he did so averaging 25-16-5 on a team that averaged just short of 95 points per game and 60 rebounds per game. As well as being the team's defensive backbone, and consistently guarding some of the best big men in the game throughout the entire playoffs. The issue is, from a narrative standpoint, that Duncan never made any claims to the impossibilities of his actions. Nor did he make it a media showcase over how dominant he was, a la Shaq. Duncan simply played incredible, generation-defining basketball.

He did not seek deification for his actions or absolution for his sins. He just wanted to play the game, and in his plodding consistency, he convinced the world that his feats -- while improbable for such a small market fan -- were all patently possible and even expected for a man of his talents. Duncan is content to simply be the best at his position to have ever played the game. He's content to consistently pull off the improbable -- but well-agreed upon possible -- feats of greatness that typified some of the other all-time greats like Bill Russell, Moses Malone, and Oscar Robertson. There is no shame in that. Kobe Bryant tries to style his game after the elusive probable impossibilities that the fans eat up. Tim Duncan simply does the improbable, night in and night out, with no concern for his fans or ego. There is a fundamental difference in approach in the games of Kobe Bean Bryant and Timothy Theodore Duncan.

Understanding this is key to the heart of the true philosophic rivalry between the perennial foes.

• • •

I am not a probabilist. I had several wonderful professors in my undergraduate education who were, but I quickly discovered that I simply wasn't cut out for it. I don't have the mental faculties to calculate probabilities on the fly, like only the best probabilists can. I'm more of the slow and steady type of statistical thinker -- the model builder, the experimentation enthusiast, the ever-considerate analyst.  But there's one excellent anecdote that sticks with me from my probability lectures. One example that my probability professor was fond of involved Shaquille O'Neal and free throws. I walked into class one day only to see a giant picture of Shaq projected on the board, and a random event simulator my professor had programmed beside the picture. I don't remember most of what he said, but a reasonable facsimile of what stuck with me follows:

"Today's lecture begins with an applied example. Shaquille O'Neal is an NBA player. He used to play for the Los Angeles Lakers. He is terrible at free throws. Absolutely awful. In 2001, in just 74 games, Shaq shot 51.3% on 972 free throws. Relative to the NBA average of 74.8% in 2001, that's abhorrent. Still, given that he's essentially shooting a coin flip for each free throw, and shooting a ridiculous 13 free throws per game, what would one expect his best performance to be?"

A brave soul pipes up. "I'd expect him to have a 75% game at some point, professor."

"Interesting. Let's run the simulator a few times. I've programmed the simulator to generate all 972 free throws over and over, giving us the longest streak of made free throws Shaq has assuming that he's truly a 51.3% free throw shooter." He ran it the first time. "In this run, he made 17 straight free throws." Again. "Now, 25 straight." Again. "Now, 15 straight." Again. "Wow. 32 straight makes from Shaq. That's certainly going to have the L.A. Times waxing poetic about his free throw stroke, won't it?"

"How does this compare to reality, though?"

"Glad you asked. Shaq's best performance in a single game was a 100% performance, where he made 13 of 13 free throws in a April 17th win against the Denver Nuggets.  In fact, Shaq actually had 12 games of 75% or better free throw shooting, if you count his three in the playoffs. He also had 12 games of 33% or worse.  Had he coupled two of his best games from the stripe, he could've gotten 25 straight free throws in a year where he shot 51% overall from the line. We all know the law of large numbers, here -- we know that in the long run Shaq is going to hit that 51% line. After all, we programmed the simulator that way, and he's a career 50-50 shooter. But how he gets there is neither prescriptive or predictable. In the long run, you are more and more likely to see random streaks of sustained performance dramatically better than the average. Or dramatically worse than the average. Shaq also had games of 0-11 and 5-19 in 2001 -- had he chained those together, Shaq could've MISSED 25 in a row in the same season.

"Probability is a funny, tricky mistress. You know you'll be right in the long term if you go by the numbers, but when you're looking at a granular short term in a long string of draws, you're just as likely to be right in a short term prediction as you are to be horribly wrong. That's the curse of being a probabilist. You may have the greatest probability model on the planet, and you may have the perfect probabilities of every event you aim to predict. You're still going to get things wrong, and you're still going to have completely inexplicable streaks. They aren't impossible, and though they are improbable in the long term, they're probable in the short term if you consider the fact that you're looking at a long-run game. Perhaps you can claim them to be unlikely in theory. But in practice, they'll always happen. And as you try to reassure people you know what you're doing, you need to keep this in mind, and realize that you're never going to convince everyone. You will always stop short of a truly perfect prediction. That's the peril of our art. As well as the promise, if you look hard enough."

• • •

Given the subjectivity of probability, then, and the preponderance of temporary dispersions from the long-run average, there should be little question as to why Kobe Bryant is the most popular player of the recent decade, while Duncan finds himself rarely discussed. As I noted earlier, everything between a Steve Nash free throw and a Dwight Howard three is essentially a glorified gray area of what is varying levels of possible. The greatest trick Kobe and Jordan ever played on the world was convincing the commentariat that their shots are impossibilities, but regardless of that probable makes for a true clutch player. Tim Duncan's fatal flaw as an NBA player, if there is one, is that he didn't follow Kobe and Jordan's new world order. It is now required for NBA players to convince the public that their impossible feats are -- while still impossible -- altogether probable when they're in control.

That is the art of clutch basketball, as it stands today. The concept of clutch is aesthetically a concept most akin to painting a picture. As Duncan's Spurs and the Moses Sixers demonstrated time and time again, simply being clutch isn't enough. Simply being a dynasty isn't enough. Not anymore. Bird, Jordan, and Kobe changed the game. In order to be "truly" clutch, or to dominate the ESPN narratives that make the NBA tick, you need to put on a show, and paint the picture that what you're doing is something akin to Sisyphus finally rolling his stone up the hill. It is your responsibility to not only make improbable shots, but to make the audience believe that your exemplary clutch performance is a probable and predetermined success.

Kobe's exaltation of the self and his accomplishments have driven his fans -- and, as a whole, the basketball community -- to simply accept his contradiction.  We all know that it's absolutely impossible for Kobe to be as good as we imagine him to be in the clutch, and as Henry Abbott has often pointed out, the numbers indicate that he simply isn't that good. But with the story as he's told it, and the image as he's built it, we have a tough time really grasping that. We have a tough time separating the Kobe of our imaginations from the Kobe that exists in reality. Kobe has positioned himself to, like Jordan, forever straddle the divide between what we all know he'll do and what he can't possibly do. Kobe's image has been carefully developed over the years he's played. And Kobe has, more than anyone, successfully created the air of the probable impossibility around his every action.

Their careers represent the parallel poles of Aristotle's prescription. As stated, Aristotle has always preferred the narrative strength of a Bryant, Jordan, or a Bird. But as Duncan and Kobe suit up for one last mutual grasp at a overwhelming triumph of their ideals, I find myself wondering just how accurate the prescription really is. Duncan may not have sought his audience as Kobe did, but in the end, his accomplishments and philosophy towards his career left its mark on history all the same. And as they cruise towards the end of their respective careers, the prospect is slowly dawning on us. As things stand, the Spurs and Lakers are the 2 and 3 seeds in the west, respectively. How better, then, for one last rodeo to come before the new age fully replaces them? Kobe vs. Duncan, the two philosophers collide once more. The audience sees Kobe, and expects him. Duncan has always been content with idling in obscurity. And as he rallies his troops and prepares to focus once more on a winning formula, I wonder just how long he can keep churning out improbable season after improbable season before we realize that he too has been fording the impossible, vintage 1999.

He just gave us a few years to realize it. Good guy, that Duncan.

• • •

The long day wanes: the slow moon climbs: the deep
Moans round with many voices. Come, my friends,
'Tis not too late to seek a newer world. 

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Aaron McGuire
Editor in Chief at Gothic Ginobili
Aaron McGuire works as the lead mathematician and CTO for a small financial consulting firm in Richmond, VA. As a basketball writer, he's primarily known for Gothic Ginobili's 2012 Player Capsule series, where he wrote the equivalent of 1.5 Russian novels about every NBA player around. Nowadays, he writes a weekly column on whatever he damn well feels like.

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