A Substitute for War

Basketball philosophy

Kobe Theory: Adventures in Distorted Probability

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We saw some fantastic, hard-hitting articles this week about Kobe Bryant‘s clutch reputation. I’ll go over them briefly, and then just talk about what people’s perceptions say about people in general, and running a basketball team specifically.

Henry Abbott at ESPN’s TrueHoop does a great job of just summarizing the fact that despite Kobe‘s reputation as the ultimate clutch performer, all the evidence says this is not the case.

Kelly Dwyer at Yahoo’s Ball Don’t Lie shows some moxie in making clear that he’s quite comfortable saying that if NBA GM’s don’t see the problem with Kobe’s stats, then the GM’s are in the wrong.

Zach Lowe at SI’s The Point Forward chimes in, but also emphasizes the larger trend that NBA offenses in general do terrible in the clutch. Scoring at far lower rates than they do in the rest of the game.

All very cool stuff. Here’s the most telling fact as I see it: People who reject the numbers here do it by dismissing statistics as not being as valid as what they see, which is an argument that often has merit, but is not valid at all here. So, Why isn’t it valid? and Why are people like this?

Statistics have limitations, but this is a straight forward question

Relying on statistics causes problems when the statistics themselves don’t sufficiently describe the the situation they are being used to analyze. For example, using a player’s assist totals to say definitively how good of a passer he is, is flawed because much team context has a major impact on a player’s ability to get assists, and there’s more to passing than making the passes that get credit for the assist. So using assists as part of the evaluation process is fine, but you’ve got to go beyond that stat, or really any stat to get a complete picture.

However, when people talk about Kobe being clutch, they always focused on some simple attributes that are easily translated into a statistic. A complete description of what clutch is might be difficult to put in statistical form, but evaluating these people’s basis for calling a player clutch is not. Kobe’s clutch, they say, because he makes the tough shots when it matters. So all we need to do to evaluate their basis, is actually get data of how Kobe’s shooting efficiency is when the game is on the line. This has been done by a variety of people, and the conclusion is always that Kobe doesn’t show any major ability to shoot clutch shots with unusual efficiency.

That doesn’t mean that Kobe is not clutch, but it does mean that people are concluding Kobe’s clutch based on some kind of flawed thinking. So what’s the problem? Well, there’s more than one. For one, people reject the statistical refutation of their thinking based on flawed arguments, this happens because people don’t understand stats, they feel ridiculously overconfident in their own judgment, and they’re too stubborn to look objectively at a clearly superior argument.

Human Beings have limitations, and that causes a distorted sense of probability

The root problem though is that human beings aren’t good at working with gradually accumulated large numbers without technological aids of some sort. People thus have a distorted sense of the probability that Kobe’s going to make that tough shot, because they don’t accurately remember how often he’s made similar shots in the past, compared to how often he’s missed similar shots.

And this is also why it absolutely makes sense for someone like Dwyer to say, “No, I don’t care if someone else is a millionaire because of his basketball knowledge, he’s wrong”. Because the flaw here is not one that is basketball-based at all. It’s just a human problem, and so we should expect that anyone analyzing the situation without the use technological tools is going to have problems with this. When NBA GM’s join the general chorus and exult Kobe his clutch abilities then, if they are being honest, they are unwittingly telling us that they have not properly used the tools that all humans need in order to properly analyze the situation.

Chamberlain Theory + Kobe Theory = Everybody’s Wrong Sometimes

Recently, I wrote an article describing what I called Chamberlain Theory.  Here’s how I put it:

There is more to judging the effectiveness of a scorer, or a player in general, than simply his most obvious related statistics, and pursuit of those obvious statistics without proper awareness for the rest of the court can erase most if not all of a scorer’s positive impact, even when those obvious statistics are as great as any in all of history.

So here’s a counterpart to that I’ll call Kobe Theory: Ability in sports is typically based not on the ability to successfully complete an action once, but on the ability to successfully complete actions consistently and reliably. Because human beings are not good when analyzing consistency and reliability, it is not possible for anyone, even the greatest of experts, to make precise judgments about such things without the use of tools. So everyone should be using such tools, and if they do not, or do not use them properly, then there will be flaws in the strategies that they prescribe. Thus if the decision makers on a team don’t use such tools, and use them properly, there will be related flaws in how their team plays.

In other words, the combined takeaway of Chamberlain Theory and Kobe Theory: Whether you’re a jock or a nerd, if you aren’t actively and objectively making use of every perspective and every piece of data, you’re conclusions will often be flawed.

13 Responses

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  1. This time, you beat me to it Matt – I have something similar in the workings, although nothing like Kobe Theory. Very interesting stuff, and a well written thesis. I think there’s a lot of availability heuristic involved here…which is precisely why tools to gauge large data sets are helpful, *regardless* of the expertise of the judger.


    January 29, 2011 at 5:32 pm

  2. Hehe, thanks man. Yup, can’t stress it enough, we’re in expertise independent territory here.

    Matt Johnson

    January 30, 2011 at 6:28 pm

  3. […] there are more reasons, of course. Matt Johnson over at A Susbtitute for War delves more into this pretty nicely, explaining why in-field experts like coaches can still be wrong when it comes to judging the […]

  4. This is absolutely not about confirmation bias.

    This is pure semantics. No one is arguing that Kobe Bryant is 6-22 when his team is tied or down 1 or 2 points. They are saying that that fact does not mean he is not clutch, nor does it mean that he’s not the guy you want to take the shot in that situation.

    Unless you define clutch to mean “makes shots when your team is tied or down 1 or 2 points with 24 seconds or less”, then yes he is not clutch.

    Take tonight’s game for instance. A quick look at the play-by-play shows that Kobe did not take a shot with less than 24 seconds and his team tied or down 1 or 2 points, mainly because that situation did not occur. From the purview of the “clutch stat” Kobe was neither clutch nor un-clutch tonight. Yet, you would be hard pressed to find an objective viewer who would say that Kobe did not hit the “dagger” type shots to close the game.

    If I’m sick, you can bet I’m going to look to medical research to find out what my best outcomes are. But the difference between those statistics and the ones in basketball are that the medical research is carried out in carefully controlled experiments, so that any variables affecting the outcome are ruled out. This is not the case in any basketball statistic. “Who has made the highest % of “clutch shots” as defined above?” is a much different question than “Given a choice of any player who should I want to take a clutch shot?” The answers to each are not necessarily the same.

    Gil Meriken

    February 11, 2011 at 12:29 am

    • Hey Gil,

      You definitely seem like you’ve got a good head on your shoulders but your dismissal of my argument as semantics seems pretty wide of the mark to me.

      1. If I were to simply say “Kobe is clutch, but others are more clutch.”, do you seriously think people would be okay with that? Nah, there is a huge contingent dead convinced that he is far more clutch than any other current player. Don’t try to make them more rational than they are.

      2. If you were to ask people before these game winner statistics were coming out how Kobe did on those shots, these same people would largely say that Kobe gets in a zone and makes shots in the clutch with higher accuracy than in the rest of the game, and they would say that *that* was the main proof of Kobe’s clutchness. Don’t try to debate that man. I live in LA, and I still hear people saying this all the time. So again, don’t try to make people out to be more rationale than they are.

      3. As Abbott has linked to previously, it’s not like there’s just one study that says these things. There are tons of them going as far back as the last 5 minutes of close games. And no it’s not that they say Kobe’s not clutch, it’s that really no matter how you slice it, Kobe doesn’t come out on top.

      If you want me to say Kobe’s ice cold veins and killer instinct, I will. The man is where he is today partly because he’s got oodles of drive and never gets nervous. However, there are much, much more grandiose claims about his clutch-ness that are entirely without basis.


      Matt Johnson

      February 11, 2011 at 12:43 am

      • Well it’s tough for me to debate what other people think, but for every guy who thought Kobe was 90% on game winners, I can show you someone who thought he was 10%.

        Humans are fallible and cannot keep track of large sets of numbers on their own. I completely agree with this.

        But I obviously didn’t delineate my argument very well, because that’s not what I am arguing against. There are two factors here: (1) the strict definition of “clutch” in this instance and (2) the very unscientific nature of basketball statistics like FG%, as compared to say FT%, or other statistics used in scientific research. With FT% I can safely compare someone who shoots 33-50 on free throws, and another player who shoots 33-50, without any extra information, and make a fairly confident statement about that they are roughly equivalent free throw shooters. I cannot do the same with two players who both shoot 13-22 from the field, without any extra information. The very fact that if you have two data points (59% FG, 59% FG) that are the same, and yet you can’t equate the two says that I can’t make good comparisons based on those two numbers alone. So why would I even try, or build a system or model upon those data points? There is are too many variables built-in, and too much context to decipher.

        Interesting that when it comes to this sample of 22, the contextual analysis seems to fall away. But mention something that shows Kobe in a “better” light than Michael Jordan (say, the fact the he scored more points in one game than MJ ever did), and suddenly we have all sorts of contextual adjustments: lack of hand checking, lack of physical defenses, lower quality of talent pool, poor Toronto offense, etc., etc. Anyway I’m veering off again, because this might not be what you do (but other people do, don’t debate me on this! 🙂 ), point is it’s tough to use the statistics generated in basketball in any scientific way (except of course FT% – shot 15 ft from the hoop, on a ten foot hoop, unguarded – it’s very controlled).

        Gil Meriken

        February 11, 2011 at 9:26 am

      • Fair points on how I spun the argument. It was late, and I was in a particular mood. I can’t expect you to answer for the sins for all fans everywhere. At the same time, I don’t accept your 90%/10% statement in the slightest.

        Re: FG% in context. To me what’s so damning here is the specific nature of what people talked about Kobe’s clutch-ness in terms of.

        When someone says someone is a good scorer or a good shooter, they typically aren’t tying this a particular efficiency. It’s understood that Ray Allen’s drop in efficiency in Seattle didn’t come because he forgot how to shoot, and it’s understood that Kobe Bryant’s shots are going to be more contested than Kyle Korver’s.

        However, while clutch-ness is absolutely something too complicated to be measured by simply by FG% at a particular time, the basis for Kobe’s clutch-ness has always been the perception that he has a clear separation in performance compared to other superstars. So if we can’t find that separation based on any statistic that Kobe clutch supporters would naturally identify, then that’s a clear sign that they are developing their opinions strongly influenced by a perception that isn’t accurate.

        This is my point, along with talking about the backlash that comes when this fact is brought to conversation.

        Re: 81. I do still think you and I tend to be set off by different groups of people, but there is absolutely a tendency to refuse to acknowledge the superiority of an accomplishment by people who view a player as inferior.

        My issue with people who trumpet the 81 game is that it’s not something you can rely on Kobe to do in future games. However, I absolutely consider it the single greatest performance in basketball history. I think when Kobe’s “on” he’s better than Jordan, I just think he tends to rely on a game that’s more risk/reward dependent than peak Jordan, and I don’t like that. (Incidentally, I would not give 2nd 3-peat Jordan that nod over Kobe.)

        (And incidentally, I think people’s fuss over Wilt’s 100 game is silly. Give me Kobe’s 81 any day, despite the fact that I do consider Wilt’s ’67 season superior to any of Kobe’s season.)

        Matt Johnson

        February 11, 2011 at 12:57 pm

  5. *I mean “IF you define clutch to mean …” not “unless”

    Gil Meriken

    February 11, 2011 at 12:31 am

  6. I guess you can’t infinitely reply.

    You are right on, Kobe is more of a gambler and risk taker than Jordan (and actually seems to want to entertain the crowd – not that Jordan didn’t do this), so his game has more lows and more highs. This is complete speculation, but I tend to think he experiments more in regular season games, taking those risks you mention, and he straightens up to play the “right way” come playoff time.

    Gil Meriken

    February 11, 2011 at 6:08 pm

    • Yeah, detailed conversation seems to overload WordPress’ code here. It’s weird.

      I can’t go with you about Kobe straightening up for the playoffs. It’s actually Jordan’s game that shows the real improvement come playoff time which is really something.

      I think that with Kobe, he doesn’t really see anything wrong with his game on offense (I have no doubt he knows when he’s extending more or less energy on defense, and that when he’s coasting, he’s doing so to conserve resources). And to be honest, I think Jordan thought the same way – and I think both of them were wrong sometimes.

      Jordan has the overall edge because he’s got the sturdier, stronger frame, along with a truly awesome motor and bigger hands. Kobe though has some edge as simply the superior outsider shooter with superior skills on that front. However I think both of them have a tendency to just want to take over situations and to have not quite enough faith in others. This isn’t a horrible trait to have – far from it, it’s mostly quite good, but it’s not a perfect match with the ideal mindset in some situations.

      Matt Johnson

      February 11, 2011 at 6:20 pm

    • Kobe’s game definitely has more variance in the regular season — just wrote a post about it: http://elgee35.wordpress.com/2011/02/10/variance-volume-and-elite-wings-part-i/

      I might follow up by looking at the playoffs as well. I do know the last time I looked at FG% in the playoffs Kobe was at least equally as hit or miss as he was in the regular season, so your theory doesn’t sound right at first glance.


      February 11, 2011 at 6:55 pm

      • I didn’t say his FG% straightened out. Actually, I think he mostly he starts playing real defense, instead of the half-assed sort of regular season defense.

        Gil Meriken

        February 11, 2011 at 10:38 pm

  7. […] previously and pretentiously wrote an article on what I dubbed “Kobe Theory”. The full article is here, but to give the briefest possible […]

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