What You Measure Matters

Henry at TrueHoop had a post today on the Celtics and offensive rebounding that I think is interesting for a variety of reasons.  One interesting point is that the Celtics were the worst offensive rebounding team in history; any time a recent team is the best/worst anything in history, it’s kind of interesting.  The strategic idea of going for offensive rebounds is also interesting.  But I’m not going to chat about that one today.  What I thought was most interesting was how Henry jumped from one measure, offensive rebounding, to another, shots per possession, and in the process completely messed up his thinking.

So, like we said, the Celtics were the worst team in history at offensive rebounding, and thus obviously the worst team last year.  Also in the John Hollinger article that Henry is working from is the tidbit that the Celtics were last in the league in shots per possession.  That also sounds bad.  But what Henry notices is that teams 2 and 3 on that list are the Thunder and Heat.  They obviously did pretty well overall.  So now Henry says that some of the best teams in the league don’t emphasize offensive rebounding, and then he’s off to talking about rebounding and defense and the Blazers.  But what was skimmed over is that shots per possession is not offensive rebounding.

A possession can end in one of three ways: a defensive rebound, a turnover, or a made shot.  So if a team were to have a low number of shots per possession, it could do it in one of three ways.  One would be to turn the ball over a lot.  Good teams obviously don’t do this for the most part, although we can turn to bball reference and see that the Thunder actually were bottom in the league at turnover percentage.  The Heat and Celtics were also below average, as it turns out.  So all three of these teams happened to hurt their shots per possession by simply not getting a shot off more than most other teams.  The second way, as Henry has covered, is to not get offensive rebounds.  If you get an offensive rebound the possession continues, and so you can get extra shots on the same possession.  That same bball reference page tells us that the Thunder were in fact above average and the Heat average at offensive rebound percentage.  So they were not hurting their shots per possession because of rebounding.  The third way (and perhaps more important?) way to reduce your shots per possession is simply to make your shots.  If you make it the first time, you only get one shot per possession.  And if you turn to Hoopdata and sort by true shooting percentage, you’ll see that the Thunder and Heat were first and fourth in the league at making their shots last year.

So to sum up: offensive rebounding is only one piece of shots per possession.  As it turns out, the Heat and Thunder were perfectly competent at offensive rebounding.  Instead they were good at shooting and bad at holding on to the ball, and that is probably what put them at the bottom of the shots per possession list.  The Celtics were 8th at shooting, which would also limit their shots, and 6th worst at turnover percentage.  Put that all together, and you have the worst team in the league at getting shot opportunities.

Henry’s mistake reminded me of another one in an old article by Neil Paine (here if you have insider).  He was talking about how the Celtics were increasingly running their offense through Rondo and how that was a bad idea.  He notes that Rondo was third in the league in pure point rating and that his touches per minute were second in the league to Steve Nash.  Obviously Rondo had the ball a lot and was a big distributor.  But then Paine points out that as Rondo’s usage increases, the Celtics tend to be worse on offense and lose more games.  But do you see what happened there?  Paine moved from touches and point rating to usage; usage doesn’t include assists.  If Rondo had a relatively high usage rate in a game (or season), it means he either had more shots or more turnovers.  Turnovers are always bad, and Rondo is a poor shooter so more shots is also bad.  Those are not good things for the Celtics.

So was it bad for Rondo to have more usage?  Probably.  Was it bad for the Celtics to run the offense through Rondo?  Probably not.  The raw on/off numbers say that Rondo was a huge plus for the Celtics, Rondo’s offensive RAPM was low but positive, and he made the Celtics 7 points better on offense than his main line-up counterpart.  It’s tricky to parse these things out and line-up data isn’t perfect, but if we had to guess it seems like Rondo helps the Celtics offense on the whole.  But he apparently does it with ball movement, which doesn’t show up in his usage (in fact, it measures his ball stoppage to some degree).  By making a point with one set of numbers and then shifting to another set that sounds the same but isn’t, Paine can make a point that probably doesn’t exist.

Hopefully both of these examples make sense and illustrate the importance of knowing what you’re talking about when you use a certain measure.  There are a lot of options in the sports world, let alone the ‘real’ world, and a lot of them get at the same or similar things without actually being the same (or occasionally even similar).  When you read something and the author changes his measure mid-stream, be sure to ask yourself if he’s telling the same story or what exactly has changed.  And it would be good to remind authors, including myself, of the occasion dangers of having too many options.

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13 Responses to What You Measure Matters

  1. Pingback: Is there a Cost to Offensive Rebounds? | The Wages of Wins Journal

  2. Guy says:

    Clearly, Abbott messed up in accepting Hollinger’s premise that shots-per-possession is an inherently good thing. Good catch. But I hope you’ll return to the issue of offensive rebounds, which seems like a more interesting question. Dave Berri’s “analysis” of the issue — finding no correlation between team oreb% and team defensive rating — barely scratches the surface of a complex issue.

    • Alex says:

      Yeah, I think there are a lot of moving parts there. Teams who shoot well may not even try to rebound, purposefully or not, because they’re just used to making shots. Generally small/poor rebounding teams may not try because they can do better with a set defense than they can with another shot opportunity. Some coaches might tell their team to go for rebounds, and thus get them, even against their best interest. But I think the correlation at least starts the story. If you wanted to claim that offensive rebounding hurts your defense, it doesn’t seem to be true at a gross level.

      > Date: Thu, 11 Oct 2012 18:07:25 +0000 > To: akonkel@hotmail.com >

      • mystic says:

        “If you wanted to claim that offensive rebounding hurts your defense, it doesn’t seem to be true at a gross level.”

        I think that is a point where the issue starts, because I hardly believe that Abbott wanted to say that a player should just run away from a potential easy offensive rebound. Thus, I don’t think that his message was: offensive rebounding is hurting your team.
        It is rather the question whether the explicit strategy “crash the offensive board at all costs” is actually helpful, or would it be better to just “go back on defense” instead? The simple correlation analysis of ORB% vs. DRtg will not give the answer to that question. Thus, it is not a good way to start the story, imho.

        • Alex says:

          Here’s his follow-up post: http://espn.go.com/blog/truehoop/post/_/id/50284/follow-up-do-offensive-rebounds-hurt. He says “My knee-jerk thought: Maybe being really bad at creating more shots, primarily through offensive rebounding, isn’t the worst thing.

          Then my next thought was: I know for a fact a lot of coaches, including some of the best, harp on their players, including big men, to hustle back on defense quickly.

          It just might be true that hanging around to battle for offensive rebounds is not a smart tactic. That’s what I theorized, based on this scant evidence. ”

          So I guess we can argue about if that goes so far as to say that he thought players should run away from easy rebounds. I doubt he meant that if the ball bounces straight to them that they should drop it and get back on D. But it did sound, to me, like he thought there was probably a somewhat obvious connection between offensive rebounding and defensive performance. Maybe even the kind of connection that would show up in a simple correlation. You might think this because Henry says “Finally David Berri got to the heart of the matter by querying his massive database to see if there was any correlation, as I had suggested there might be, between giving up on offensive rebounding in the name of playing better defense”.

          So to echo what Guy said and my response to him, I think the correlation is a reasonable first-shot thing to look at. Put it this way: had the correlation revealed an obvious negative correspondence, I don’t think we’d be having this conversation. But it didn’t, and so now we can think deeper and come up with other analyses.

          > Date: Thu, 11 Oct 2012 21:04:23 +0000 > To: akonkel@hotmail.com >

        • Guy says:

          There is nothing wrong with looking at the team correlation as a starting point. But Berri treats it as an end point — seeing no correlation, he’s ready to conclude there is little or no tradeoff. This is the kind of simplistic analysis he brings to most issues, which is to be expected since he has said many times that basketball is a simple game (get possessions, keep possessions, put ball in basket).

          You need to begin with a theory of what the relationship might look like. The theory is that making an extra effort to get ORBs will cause you to give up more fast breaks on defense. So first we need to isolate “extra effort” (or below-average effort) on ORBs, which is presumably only 1 of several factors impacting ORB% (along with player talent, distribution of offensive shots/misses, opponent DRB talent). On the other side, many factors obviously influence defensive rating, so allowing more fast breaks — even if it does happen — will have only a modest effect on Def Rating. So already we can see the correlation is likely to be small, even if the effect exists.

          And what if there are confounding variables that make it hard to see even a weak correlation? That seems very possible here. For one thing, there is basically no correlation between ORB% and DRB% at the team level. Assuming certain player attributes help on both ends of the court (height, speed, ability to anticipate location of missed shots), that strongly suggests the rebounding story is much more complicated than can be seen in simple correlations.

          I would also note that ORB% has a very low correlation with wins (at least in last few years). If ORB% is an obvious plus on offense, doesn’t that seem to suggest there is some offsetting cost on defense?

          • Alex says:

            I think the lack of a simple correlation implies, as you say, that the effect (if present at all) is likely to be small. And I agree, as I said before, that it’s still just a first move and not definitive. But it certainly puts some constraints on what might be going on, right? We didn’t see a large positive or negative correlation, so we learned at least a little something.

            In regards to your comment on the low correlation between offensive rebounding and wins; it still exists, right? Given the rest of your discussion on the number of factors involved and the confounding variables, one might conclude (even if just to play devil’s advocate) that finding a significant, positive correlation suggests the offensive rebounding is pretty important. But obviously you’d want to do a little more digging before making a blanket claim like that. Similarly, if we accept the results that mystic and Kevin Pelton have posted in other spots, I don’t think you’d make a blanket claim that “offensive rebounding hurts defense”. All they seem to be finding so far is a relatively small effect, and defense is obviously impacted by a large number of things, as you say. There would also be circumstances in which you would want to make that trade, potentially getting more rebounds while potentially hurting your defense. It seems like the best description so far would be, better offensive rebounding helps your offense, maybe hurts your defense a bit, and overall maybe helps you win.

            > Date: Fri, 12 Oct 2012 14:43:25 +0000 > To: akonkel@hotmail.com >

          • Guy says:

            “I think the lack of a simple correlation implies, as you say, that the effect (if present at all) is likely to be small.”
            No, I said that the correlation between ORB% and Def Rating will be small. That’s not the same thing. In fact my point is precisely that the effect could be quite significant (in basketball terms) even while the correlation appears small.

            “But it certainly puts some constraints on what might be going on, right? We didn’t see a large positive or negative correlation, so we learned at least a little something.”
            No, I don’t see why that necessarily needs to be true. The impact on Def Rtg could be “small” (depending on how one defines that term) and still big enough to make crashing the boards a neutral or even counterproductive strategy.

            “In regards to your comment on the low correlation between offensive rebounding and wins; it still exists, right? Given the rest of your discussion on the number of factors involved and the confounding variables, one might conclude (even if just to play devil’s advocate) that finding a significant, positive correlation suggests the offensive rebounding is pretty important.”
            I’ve only looked at a couple of seasons, so I may be off here, but I see an R^2 of only about .01. So if offensive rebounding explains only 1% of wins, is that “pretty important?” I suppose that depends on what you mean by “pretty important.” Let’s be more precise: is that as important as Wins Produced says it is? No, not even close. However, to do this right we need to control for other factors, and perhaps confounding factors are disguising some of the importance of ORB%.

          • Alex says:

            Let’s say that the correlation between ORB% and def rating had turned out to be .8. That would be something, right? We couldn’t say much about causation and there would obviously be other factors, etc etc, but that’s still a strong finding. It would be hard to argue that offensive rebounding hurt your defense, wouldn’t you agree? Now say it had turned out to be -.8. Same deal, but it would be hard to argue that it does *not* hurt your defense. We can argue about what that .8 really needs to be for any given person to feel one way or the other, but given that the correlation actually turned out to be small (in my book) implies that it is not obvious that offensive rebounding hurts defense. The size of the possible connection has been constrained. Maybe you can provide a concrete, clear example to the contrary? Where something strong and meaningful is occurring but the correlation ends up near 0?

            I implied from your statement about the low correlation between offensive rebounding and wins that it existed but was small; I would have described an R square of .01 as the non-existent relationship between offensive rebounding and wins. I’ll renege on that last comment for now.

            > Date: Fri, 12 Oct 2012 17:08:03 +0000 > To: akonkel@hotmail.com >

          • Guy says:

            “The size of the possible connection has been constrained. Maybe you can provide a concrete, clear example to the contrary? Where something strong and meaningful is occurring but the correlation ends up near 0?”
            Sure. In football, the correlation between passing yards and wins is statistically insignificant, while the correlation between rushing yards and wins is very strong and significant. That would seem to suggest that running is much more important for offensive success in the NFL, while in fact the reverse is true.

            That said, I agree that a zero correlation seems to suggest that getting ORBs is likely not a terrible thing to do. But who would ever think it was? The relevant question is whether a team should make an above-average attempt to get ORBs. This is where you and I often disagree. I don’t necessarily care if the R^2 is .2 or .4 or .8, while you often do. I care more about the coefficients. How many extra ORB/48 will I gain? And how many extra points/48 will I give up? It’s entirely possible that this could be a harmful strategy — i.e. costing you 3 or 4 wins because of the harm to defense — while still generating a “low” correlation. Statistical significance can be a poor indicator of basketball significance.

          • Alex says:

            As someone with a large NFL database, I can tell you the connection between passing yards and winning is very significant. But I get your general point; running appears more important than it might be (and passing less) because teams who are winning start to run the ball more.

            We do often seem to be at odds over the R squared versus the coefficient issue. I think one of Phil Birnbaum’s posts from a while back would be a useful talking point. Let’s say I collected the net worth of a bunch of people, and noted whether that person had ever won the lottery or not. The lottery predictor is significant and has a huge coefficient; winners on average have a higher worth by $5 million or whatever number you like. But the R squared is very tiny, say .03, or something most people would agree is tiny. Do you decide to play the lottery? My point of view would be that you could but it’s unlikely to matter. Yes, the coefficient is huge, and if you have enough data it might even be significant. But the lottery has so little effect on where your worth ends up, you could just as easily focus your attention in a hundred other places. In the end, it is unlikely to make a big difference.

            > Date: Sat, 13 Oct 2012 16:18:30 +0000 > To: akonkel@hotmail.com >

          • Guy says:

            On correlation of wins and passing yards, I was relying on a study Brian B. did. But it was a few years ago. I would guess the correlation is stronger in recent years, as offenses have shifted toward passing. In any case, I think we agree that the observed correlation greatly understates the real importance of passing success, so indeed there are cases where the overall correlation doesn’t come close to telling the real story.

            On the lottery, the variable you need is not “lottery winner” but “lottery player.” The coefficient on that and net worth will be negative, which tells you what you need to know (although it will exaggerate how bad an idea lottery playing actually is).

            Let’s forget R^2 for a moment and return to the example at hand. What I would want to know from a study is, if I tell my players to crash the boards, then:
            A) on average, how many ORBs per possession will I gain?;
            B) on average, how many points/possession will I lose on defense (if any)?
            C) what is the value of A-B? (I can do that part myself!)
            (Of course, any given team then has to evaluate what they think these values would be for their specific players, but this provides a good starting point.)
            Do we really disagree on this? If you were hiring researchers to address this issue for an NBA team, would you give them a different assignment?

  3. Pingback: How a Shot IS a Turnover

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