A Substitute for War

Basketball philosophy

Letting the Lamppost Illuminate

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He uses statistics as a drunken man uses lamp-posts…

For support rather than illumination

Andrew Lang (1844-1912)

I’ve been rather crucified lately for having Kobe Bryant so low on my MVP list, and I completely understand why. He’s the player many consider to be the best in the game, his team has an elite record, and as we approach the final stretch of the regular season, both he and his team appear to be entering back into their familiar, championship-winning groove. How can he be not anywhere near the top 5 in the MVP race?

And I answer, knowing that my response hurts my credibility among quite a few not simply because they disagree with me, but because a significant influence on where I place Kobe is his poor performance in adjusted +/- statistics (APM).

Remaining Sober

Oh sure, I can and do mention the fact that he has played less this year than in previous year, that his efficiency is down from peak, that there was evidence from previous years that the Lakers could be quite good even without Kobe, and that the Lakers’ peak level of performance (which requires Kobe’s peak levels of performance) is far above what the Lakers have achieved this regular season. In the end though, if Kobe had a great APM right now, Kobe’s place on my list would be higher, and many people think it’s crazy for me to take a fringe stat so seriously.

The quote above makes a powerful point that I always try to keep in mind as I use stats. The reality is that all serious basketball watchers come to their use of a particular tool set of stats at least partially based on their own understanding and intuition of the game. Thus on a broad strokes level, we are all arguably guilty of being Lang’s drunken man. This behavior is not an inherent problem as long as it does not extend to fine scale analysis, however it’s quite easy to make that leap because doing so is very tempting and often times quite subtle. Were I to ignore Kobe’s APM, then I truly would be the drunk Lang seeks to condemn for I’d then clearly only be using the stat when it fit with my pre-conceived notions.

Let me clarify the situation with Kobe’s numbers here in a set of preemptive statements to the thoughts I think will come to your mind based partly on the arguments I’ve already seen come my way:

Kobe’s APM isn’t simply weak for an MVP candidate, it is horrendous by any standard. I’m not talking about something minor.

What about APM notoriously having a lot of standard error (essentially, randomness) which requires a huge sample size before you make confident statements with it? The standard error is a quantified number, and it is large, but not large enough to make one consider Kobe’s APM insignificant. I realize that Dave Berri said it did indeed make the APM insignificant, but that was in comparing Kobe’s numbers here to average players which isn’t a very useful question to ask. We’re talking about the MVP, let’s compare him to their APM’s according to basketballvalue.com:





As you can see, even when you give Kobe every shred of the benefit of the doubt that standard error provides, he still lags behind the major MVP candidates. (Of course, standard error isn’t any perfect thing either, but for anyone saying that the gap here isn’t significant, c’mon now)

Now I’ve actually got some people telling me that the mere fact that Kobe’s doing so poorly by this metric this year means we need to toss the stat out entirely. Literally, if he had mediocre numbers that would be defensible and thus perhaps usable, but with the level of discrepancy so strong, that tears it, APM is no longer welcome at the party. I’ve had people say this simply because Kobe is Kobe, and Kobe is known to be great. I’ve had people say that because Kobe’s done great in this stat basically his whole prime and that somehow calls into question this year’s result.

All of these are arguments for letting one anecdote completely over turn my previous thinking, despite the fact that there actually are reasons to believe that Kobe’s having significantly less impact than in previous season. I don’t see any reason to change my previously established thinking though. The numbers are what they are, and having such a massive discrepancy essentially kills the low sample size argument. What makes the stat look ridiculous to others, is precisely what makes it impossible to ignore for me.

How I apply adjusted +/-  to evaluate Kobe Bryant’s MVP candidacy

This however, does not mean that I need to rank Kobe Bryant as one of the least valuable players in the league because of what this stat says at the most superficial level. As with so much of analysis, whether it be statistical in nature or not, nuanced thinking is required. So let me explain how I interpret these stats into relation to Kobe’s season, and why I rank Kobe as I do.

People tend to have confusion about exactly what APM says, and actually I’d argue, they tend to have confusion about what all stats say. They like to think a stat says which players are better and which are worse. However, all stats come from the 5-on-5 basketball the NBA plays, and are thus influenced by the context in which they were achieved. With +/- statistics this distinction becomes much more pronounced.

Consider a tweener role player whose set of strengths and weaknesses can be exploited by certain types of opposing players but not others. If his coach only puts him in in situations where such opposing players are off the floor, either because the opposing team has no such players, or those players are on the bench, then the tweener the team may end up doing very well with him on the floor.

We’ve seen times in the past where a player who plays role player minutes has an APM among the league leaders, which makes a tweener interpretation like I’ve presented plausible. Does that damn APM as a stat? Well, depends on how you look at things, let me put it another way: Does that mean that APM is meaningless? Here the answer is a resounding “No”. There is meaning, it’s just a question of whether people will grasp the meaning.

Let’s go back to Kobe. People tend to look at his negative APM right now and think that it’s implying that Kobe’s going out there and scoring points for the opposite team, which makes the stat awfully hard to swallow. In reality, when Kobe is on the court, the Lakers are typically beating their opponents by a good amount, the poor APM comes simply because the team is doing so unexpectedly well with Kobe off the court.  For Kobe on the floor then, there’s nothing glaring about the team performance that shouts “this isn’t working”. To put it another way: If the goal of the game was to beat your teammates’ performance by as much as possible, and the scoreboard was showing Kobe was routinely underperforming relative to stars on other teams, then these numbers would mean something very different to Kobe than they currently do, and I don’t really have any doubt that he’d find a way to kick up his intensity. That’s not the goal though, the goal is to play well enough to earn a high seed, and if you’re an aging superstar, conserve enough energy so that you have a full tank come playoff time.

So how should one look at the current numbers? Well, I look at it from a supporting cast perspective. In an MVP race, players do get judged implicitly and sometimes explicitly based on how good their supporting cast, otherwise we’d always give the award to the top player on the top team. And hence, Manu Ginobili, the current star of the San Antonio Spurs, is not in many people’s top 5 MVP ballot.

The players ranked ahead of Ginobili then are considered to only be on teams with inferior supporting casts compared to what Ginobili has. The salient question about Kobe’s candidacy becomes: How can one move Kobe Bryant ahead of a star on a team with a superior record, when his supporting cast is so strong that they actually give him a terrible APM – something I don’t believe we’ve never seen in the half dozen years we’ve had this type of advanced stat?

And my current answer is: I can’t. This isn’t a reflection Kobe’s capabilities, but simply based on what we’ve seen this season, Kobe’s got a supporting cast as solid as anyone else, and yet there are teams with better records. That puts a ceiling on how much credit I can give him in the MVP race.

Now last, all of this probably begs the question in the minds of some: “Okay, I get that given what you already believe about +/- statistics, your reasoning about Kobe Bryant follows, but how did you get sold on +/- statistics to begin with?” Very reasonable question, for another post. In the next week, or maybe two, I’ll write more on why I feel it’s necessary to use these stat, and how I do, and do not, use them.

Written by Matt Johnson

March 19, 2011 at 9:52 am

22 Responses

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  1. So, basically what you’re saying is that APM is showing that LA is still really good without Kobe, *regardless of how good they are with him.* And that’s relevant in the MVP discussion…even with the noise in the stat.


    March 20, 2011 at 5:11 pm

    • What you didn’t like the pretty picture ‘n stuff? 🙂

      Your summary is quite correct, and might actually convey my point better than the wall of text I put up.

      Matt Johnson

      March 21, 2011 at 5:40 pm

      • I’m not sure that I exactly agree with what ElGee wrote in entirety, which means that either his explanation was a tidge off, my thinking is a tidge off from what Matt was saying, or I’m picking nits. All 3 are in play.

        To me, the APM story isn’t that LA is really good without Kobe *regardless of how good they are with him*…it’s more that they are really good without Kobe, and *when he’s in there he doesn’t add any extra value to the mix*.

        For instance, the Lakers would also be really good without either Bynum or Gasol. But APM doesn’t hold that against them, because when they DO play the team plays dramatically better in a way that the stat attributes to their presence.

        If what I said made any sense, that second condition is what makes it most relevant to the MVP race IMO. I don’t think you should hold having good teammates against an MVP candidate…but regardless of how good they are, the MVP should take them to an even higher level when he’s present.


        March 25, 2011 at 1:46 pm

      • drza, I do prefer your choice of words to ElGee’s. I tend to let small things slide when I think I’m on a similar page with someone, but I do appreciate you being so precise.

        It’s true, literally I don’t “punish” a guy for having good teammates, they are just part of the context of helping to develop a conclusion about what net impact that guy is giving to his team.

        Matt Johnson

        March 25, 2011 at 11:17 pm

  2. […] letting the lamppost illuminate […]

  3. I agree with a lot of your larger points. But Kobe is exactly the wrong kind of player to judge with APM…

    As far as I know, there are two ways to get a APM sample to have smaller standard errors – either add more minutes (larger sample) or more diverse lineups.

    Thus when you see the standard error is large relative to other values with a similar amount of player-minutes, you know the player has been in the same lineups and combinations of teammates than most players.

    Take the Lakers, for example…

    Gasol, Pau
    2,555.75 minutes played +10.63 APM, 6.19 SE

    Bryant, Kobe
    2,325.78 minutes played
    -6.43 APM, 6.99 SE

    When I check how much court-time they’ve shared with each other (I have to got to NBA.com’s +/- page since I don’t know of anywhere to get this information easily) I found that Gasol has played in 87% of the minutes that Kobe has played, and the two starting lineups they’ve used this year account for a whopping 60% of Kobe’s total minutes played.

    Basically, Kobe is an extreme example of co-linearity, with Gasol specifically. APM only has a tiny amount of data to decide whether Gasol or Kobe are responsible for the pair’s success, and probably not enough data in the one-year sample to untangle the starting lineups that dominate LA’s rotations.

    You find the same thing’s going on with Derrick Rose and Luol Deng. Typically over the course of an NBA season injuries, trades, promotions and demotions are enough to provide the diversity in lineups that APM needs. In some cases one year of data isn’t enough.

    We have standard errors to clue us to when this might be happening. And hopefully one day soon we’ll have lineup details like player pairs and trios in a searchable, public form for use alongside adjusted +/- data.


    March 21, 2011 at 2:54 pm

    • What a well thought out comment. ‘preciate that, and welcome Greyberger.

      The thing I keep going back to is that low sample size should mean you require a more massive distance before you use it, and that you shouldn’t let that distance lead you toward ridiculously bold conclusions.

      Yes, Gasol & Kobe have a lot of overlapping time. And yet, Gasol’s raw +/- is at +446 and Kobe’s is at +367. That’s kind of a huge difference and APM is telling us we can’t chalk that up to Kobe playing with weaker teammates against tougher competition in general.

      I don’t use this information to say “Kobe’s killing his team”. Indeed I still have Kobe on my list and not Gasol. However, using that data to help make the statement, “Uh, he’s clearly not doing this alone, I’m not going to give him the nod over a ton of other stars where it assumes essentially that he has a weaker supporting cast.”, doesn’t seem that bold to me.

      Being shy about using 1-year APM is one thing, refusing to let it influence you at all even when the numbers are glaring is quite another. And we do have other signs that Kobe is contributing less value than in previous years, we already had evidence that Kobe had a very strong supporting cast, and we know that despite every indicator that says the cast is even better this year, the team isn’t racing toward 65+ wins.

      To take all this information and still treat Kobe like the top 3 MVP candidate he’s been in the past is to me simply saying we’re not going to re-evaluate Kobe’s candidacy each year.

      Matt Johnson

      March 21, 2011 at 5:38 pm

      • Right and well-said. One-year APM does have something to say about Kobe and players in the same situation. It just calls for other +/- information (raw +/-! regressed +/-! Four factors on-court-off-court splits!) to be included in the reckoning to me.


        March 21, 2011 at 9:23 pm

  4. […] Letting the Lamppost Illuminate (asubstituteforwar.com) […]

  5. […] Letting the Lamppost Illuminate (asubstituteforwar.com) […]

  6. Kobe fans are convinced that his mere presence inspires the Lakers to victory. If you didn’t figure out the Lakers were a good overall team when they beat Orlando, you should’ve when Kobe’s 6-24 night won Finals MVP.


    March 22, 2011 at 8:14 pm

  7. I think you’re still the substition patterns combined with limited minutes has on the statistical result. Three of the top 4 rotations for the Lakers this year courtesy of 82games, all with Blake-Brown-Barnes in the lineup w/:

    Walton-Gasol 32.4 min 87.5 win%
    Odom-Gasol 138.6 min 80.7 win%
    Walton-Bynum 23.5 min 80 win%

    Also, those three + Bryant-Gasol played 24.9 min for a win % of 85.7%.

    What is the significance of all of this? Well, for starters, the Lakers tend to outscore their opponents with those three on the court (and Bryant on the bench) in very, very limited minutes–only 8% of the team’s total minutes this season. The sample error here, which is not directly reflected in Bryant’s standard error, is huge, and it should be pointed out that the APM success of these units in limited minutes is very nearly a zero sum game vs. the APMs of the guys sitting on the bench when these lineups are on the floor.

    What is the next thing that stands out here? These lineups look like mop up lineups to me. Note the two oldest starters (Bryant/Fisher) aren’t on the court, presumably resting. Also note that the players on the floor are generally the very best free throw shooters among rotation players. Actually, excluding the team elders, over 75% of the floor time in these lineups is held by the 4 best FT shooting rotation players on the club. The worst FT shooting regular (Artest) isn’t to be found.

    These very successful in limited minute lineups are precisely those that you put on the court when you’re up 10 with 3 minutes left. The opposition starters are still in out of desperation, you pull your aging vets and drop in your free throw shooters. You hit your FTs, the opponent bricks desperation treys, and the 10 pt lead is suddenly 16 very quickly. The system only understands +6 in 3 minutes against starting caliber competition. What it can not understand is game situation.

    Lastly, we need to take a step back and understand what the -6.68 for Bryant means. APM is adjusted for quality of competition and represents that player’s contribution on the court in a neutral manner. It IS in fact saying that Bryant is a below average player in the league. Even giving him the full benefit of the SE, he is merely average according to the system. Does this bear any semblance to reality?

    This isn’t to say that I necessarily think he’s an MVP caliber performer this year, but there is so much noise in the Laker sub numbers that Bryant’s numbers are impacted beyond the SE term.


    March 22, 2011 at 10:34 pm

    • Some good thoughts here Nat.

      I do think though to some degree you’re overthinking things a bit. You’re breaking it down, and breaking it down, talking about how all of this is based on such a tiny sample size, but the numbers are where they are because in the 30% of the team’s minutes that Kobe hasn’t played, the Lakers have done very, very well. Not that I’m against you doing more detailed analysis than that to get a more nuanced picture, but to dismiss the time a 33 MPG guy doesn’t play as mop up time just doesn’t seem reasonable to me.

      The reality is that Kobe’s resting a lot more this season, and that resting isn’t coming from hanging out on the bench late in blowouts. It’s happening all through the game.

      Re: “Even giving him the full benefit of the SE, he is merely average according to the system. Does this bear any semblence to reality?”

      You’re looking at this too rigidly.

      Say I’ve got a furniture moving company where one guy is actually a world champion weight lifter.

      Say I’ve got the champ and a mere mortal lifting a couch together, and they are both lifting the same amount of weight when they do this.

      Say I can replace the champ with another mortal and they still successfully lift the couch.

      Does that say anything negative about the champs ability to lift weight? Of course not.

      The real moral of the story is that the goal of a basketball player isn’t to maximize his +/-, it’s to make his team successful. Yes, winning by more is good, but if you’re not desperately worried about your regular season record, it’s completely understandable why you’d be satisfied with just winning and conserving energy. And so if the supporting cast makes that job easy, then it’s entirely understandable if the star’s +/- doesn’t set the world on fire.

      This of course does beg the question, “Well if the star isn’t trying to maximize his +/- because that’s not really his goal, why use it against him?”

      Well if the world champ furniture lifter isn’t actually lifting more weight than the mortal, why would we pretend otherwise? Anointing a player as MVP based on what he could have done if needed doesn’t make sense to me. If you have a different philosophy, well, live and let live.

      Matt Johnson

      March 22, 2011 at 11:31 pm

      • I don’t think the 2011 Lakers are a great example when talking about how to use APM.

        Their starting lineups (Fisher, Bryant, Artest, Gasol, Bynum_or_Odom) account for 42% of the total minutes played by the team. Most teams don’t have one single lineup that’s played for 500 minutes this year, but the Lakers have two.

        Fisher only ever plays when Bryant, Gasol and Artest are playing. That’s not much of an exaggeration – it’s 1518 minutes so far for that quartet, 1959 for Fisher – 77.5% of Fish’s minutes are in the unvarying company of better players.

        That’s just an unusual situation for APM this late in the season.

        By the way that 4-player combination leads all quartets in minutes by a healthy margin:

        Fish Bryant Artest Gasol…. 1518 min +347
        Rondo Allen Pierce Garnett.. 1283 min +321
        Battier Scola Martin Lowry.. 1198 min +165
        Miller Aldridge Batum Mathews 1140 min +131


        March 23, 2011 at 11:20 am

      • I suppose I’d agree.

        If it were a model example, then I’d be talking about how a particular player’s APM is actually a better indicator for his value than other stats. A la Carmelo Anthony.

        Here I’m clearly giving far more wait to other factors than APM, and thus I’m in a debate where I argue you should give non-zero weight to the stat while others don’t want to use it all.

        I understand that I come off like I’m making bold statements, but I really don’t think I am.

        Matt Johnson

        March 23, 2011 at 2:35 pm

      • Sorry I don’t mean to make it sound like APM is all you’re looking at. I don’t get many opportunities to talk as nerdy as I’m getting here, so apologies if it all comes tumbling out into incoherent or off-topic paragraphs.


        March 23, 2011 at 9:32 pm

      • @Greyberger, no apology necessary, but you making clear your intentions wearing your geekdom on your sleeve is appreciated.

        You’re communicating fine, and I hope you stick around.


        Matt Johnson

        March 29, 2011 at 10:16 pm

  8. This post (and the responses) highlight my main problem with APM, which is the horrendous number of confounders that attach to the team-derived end-statistic.

    I don’t say this as a Kobe fan (quite the reverse, really), but I just don’t have a lot of confidence in APM as a consistent measure of overall impact. This isn’t to say that on-off stats don’t have a place, only that to put such a heavy store in it (as you appear to have with Kobe) seems fraught.

    You indicated you were going to put up a post with your thinking on APM, and I’m really looking forward to that.


    March 25, 2011 at 7:56 pm

    • Does it really seem like I’m putting so much stock in APM after I explain it? I realize with the emphasis of my discussion it *feels* like it’s my primary statistical source, but if I just went buy that I’d be arguing Kobe wasn’t top 100, and instead I have him in my top 10.

      As for the follow up, putting finishing touches on it. It’s massive…and yet it’s still not covering everything. I will definitely welcome feedback because of what’s missing, and because when my posts are too long, I really feel like they don’t communicate the salient points as well.

      Matt Johnson

      March 25, 2011 at 11:20 pm

  9. […] felt the need to write this as a result of the article I wrote on interpreting Kobe Bryant’s +/- this season. That article showed my perspective as someone who uses these stats – this one […]

  10. Interesting post. Even as a Lakers (and Kobe) fan, I don’t think he’s a good MVP candidate this year. However, I also think that APM–as much upside as I think it has–still retains some fundamental flaws when used as a metric for individual players (as opposed to line-ups, where I think it has substantial value).

    My main beef with it is that it makes an assumption that APMs add linearly–that ceteris paribus, a team with Player A instead of Player B will have a relative margin, over the course of 48 minutes, of APM_A – APM_B. This assumption is a natural one to make, but it largely goes unexamined, I think (at least in the sports world). Winston’s APM does try to account for this, in pairwise fashion, but I’m not sure that the noise level is sufficiently low to do it reliably.

    All that being said, I like APM. I think it just needs to be more rigorously examined so that it can do what it sets out to do.

    Brian Tung

    March 29, 2011 at 2:46 pm

    • Brian, I enjoyed your post over on Hoopspeak. Glad you made it over here, and welcome.

      First, you might want to check out my Nash Disequilibrium post when talking about the fundamental flaws of APM. By no means does it answer every you talk about, but you’d probably find it interesting, and possibly insightful.

      The linear aspect of APM is clearly something to be aware of. Obviously a player’s ability to impact depends on context, which means giving him a single weight is not a complete answer, so I’d say I’m with you there.

      As far as Winston trying to account for this, I’ve actually not seen him elaborate on the details of his methods. I’d be very interested, but I don’t believe that a bigger, better APM is the answer. The answer is diving into the lineup analysis, which makes it tough for us armchair guys, who want to come up with a formula for insight that we can run to infinity.

      Matt Johnson

      March 29, 2011 at 10:14 pm

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