What’s the Use?

The first principle is that you must not fool yourself – and you are the easiest person to fool.- Richard Feynman

For an engineer like me , unintended consequences are a way of life. Someone comes up with something fancy and we see some new way to apply it. Getting from point A to point B is the goal but somehow serindipitously we wind up at point X.

Let me explain. You may have noticed that it’s getting a little crowded in this space. This is all prelude. We are working on something. As part of that, I’ve been going thru some projects I had pending. One of them was continuing to breakdown and reverse engineer all the advanced stat models out there. I finally finished most of that this weekend and I will be writing it up at some point in the future.

But this post is not about that.

It’s about this:

Usage Percentage (The percentage of a teams plays a player uses while he’s on the floor): 100 * ((FGA + 0.44 * FTA + TOV) * (Tm MP / 5)) / (MP * (Tm FGA + 0.44 * Tm FTA + Tm TOV)).

And this:

And maybe a little of this:

Before we get too crazy here, feel free to go to the Basics for background. The numbers are courtesy of Nerdnumbers and all the stats,tables and madness that follows is based on 2010-2011 data for the NBA thru 03/26/11.

Let’s get started with some background:what’s usage and what are usage curves? Usage is the % of the available offensive possessions a player uses when he’s in the game. Usage curves come from Dean Oliver’s Basketball on Paper (which I may or may not have spent an inordinate amount of time perusing recently).In chapter 19, Oliver goes over “skill curves” that plot a player’s offensive efficiency when compared with usage . In the book, he does this on a player by player basis to show that players who take fewer shots become more efficient and as they take more shots their efficiency drops. He doesn’t  quite explain this other than with some hand waving voodoo magic which is something that could be frustrating to someone who was trying to understand what he was doing and trying to …. Really need to stop with the inner monologue.

Quick, Here's a picture of a kitty to distract you!

So anyways, the theory, based on Dean’s skill curves (or usage curves) goes goes as  follows:

  • Certain players need to take all of the shots because their teammates can’t
  • There are diminishing returns on shooting. Taking lots of shots is not easy, the more shots you take the harder it gets.
  • Each player has an optimal range of shooting and players like Kobe are good with 15-25 shots a game but other players wouldn’t be.

The usage argument boils down to teams need a guy (like say Melo) to take shots (i.e. become high usage guys) and that this is the way to succeed in the NBA.

The counter argument is that you can always find someone to take that shot because the supply of shooters far outweighs the supply of shots (see Denver).
So we have a clear difference of opinion and the biggest problem has been the lack of a clear data set to attack it.
Funny thing that I have just the data set for it.
If I take every player game for 2010-2011 with more than 30 MP (about 7300 data points so far) and I plot Points per 20 Possesions vs Usage Rate it looks like so:
Can you see what I see? No? What if I sort every point by usage and work out 100 point averages and standard deviations and plot it again:
Ok, Let’s put it in Layman’s terms. Avg Points per possesion does not change based on usage. It stays about the same. Rather than a curve what I found is that it’s more like a usage line at about 20 pts per 20 possesions (The equation I get is y = 0.1921x + 19.638).
Variability does however change significantly and inversely proportional to usage. So more usage less variability. This implies selection bias and diminishing returns. So you get more shots only if you make at around an average rate and it becomes increasingly difficult to score at a better than average rate the more of a ball hog you are.
What if I look at Wins produced?
If I look at Wins per 48 minutes the higher my investment of possessions in a player the higher my wins but this is deceptive. First my risk is also higher because my variability skyrockets. Second, if I normalize to wins produced per 20 possessions I get:
Lower usage has a higher average rate of return but a higher variability (or risk).
For WP48, the implication is that increased usage implies higher wp48 (again typically higher return replies higher investment) but the downside is that it implies higher risk.

High usage is a high risk strategy for the most part. We want a good spread going to players who are at above average at the needed usage.

I’ll leave you with a look at some players:
We’ll get into this one later.



  1. Some Dude
    March 31

    ” Avg Points per possesion does not change based on usage.”

    This is a weird interpretation, IMO. What we’re seeing is a lot of of data points of high usage, medium usage, and low usage players. What we expect is that the majority of the data points with high usage points are from high usage players. So while the average PPP is the same at all the usage levels, it is not the avg PPP is necessarily unchanged. This is OVB in the sense that you’re not isolating who is doing the data points (you actually mention it).

    Point being, if high usage players average the same PPP as low usage players, this does not mean PPP is unchanged when you move up the usage ladder. Maybe it does or maybe it means high usage players are players who would have higher PPP if they were lower usage players but because they know this they use more possessions. The STD seems to be hinting at this and as you point out, there is selection bias going on. if you can’t maintain average PPP at higher usage, you won’t be allowed to shoot (unless you play for the Warriors).

    An interesting insight to this is the STD shows more variability among low usage players. What we see are guys who are being very efficient or terrible This makes sense. Guys like Joel anthony suck at offense no matter what, whereas other players (like say Ariza) greatly benefits from the attention a combo like Kobe and Gasol receive. hence, players who can maintain average PPP at a high usage are extremely valuable to a team because it allows others to be more efficient at a lower usage.

    In other words, as long as the marginal increase in efficiency from dropping lesser players’ usage is greater than the marginal decrease in efficiency up upping star player’s usage, it makes sense to keep upping star player’s usage til we get to the pareto optimal point. In fact, it might make sense to have the star be below average in PPP!


    As for WP, I don’t think it means much. At the low usage end you’re going to end up with a bunch of rebounders who don’t do much else or defensive wings who don’t do much else, so by the time they hit 20 possessions, they’re going to have a lot of rebounders with high WP per 20 pos or guys who don’t contribute much to the box score and probably don’t shoot well. Hence the variability.

    “High usage is a high risk strategy for the most part. We want a good spread going to players who are at above average at the needed usage.”

    Wrong! As mentioned above, it’s the marginal PPP that matters. Take Kobe for example. He’s below average for his usage. Okay, so to whom does he transfer? Well, not Ron and Fish we can agree, they’re more below average (okay Fish is basically tied, but still). So there is Lamar and Pau. But look at how much above average they are! If we transfer 5 percentage points from Kobe to them equally, are the Lakers better? It depends on how much Lamar and Pau’s drops are as a result and how much Kobe’s gain is (now don’t get me wrong, I DO think Kobe could drop his usage IRL for Pau’s sake, but ignore that).

    being a bit below average at 35% usage might be better than being average at 30% usage. It depends on whether the teammates are any good and how much the good ones will drop.

    Also, I don’t see the point of looking at WP48 above average STD at usage rate when WP48 has non-possession stuff in it like rebounds and assists and steals. What do any of those have to do with usage? If your rebounding is driving usage, we can’t say to give him the rock more. Look at Rondo, great in WP48 but horrible in PPP.

  2. Some Dude
    March 31

    One last thing, I get why you looked at 30 minutes, but I think it should have been 24. You’re losing a lot of quality games in the data set. Kobe shouldn’t be penalized for playing well blowing out opposing teams (his WP48 is over .200 but under .18 here). Same for Duncan, Ginobili, Odom, Martin, or whomever. Way too few games for some of these legit NBA players. It won’t change the conclusions much (may reduce some high end risk, though) but it would be better for the player stuff, IMO.

    • John R.
      March 31

      So run that then. I’ll go to your blog and read about it.

  3. Rashad
    March 31

    One thing I would be interested in is if and how individual players’ usage curves change over time. Also, it is clear from the data that for some players more shots help them, and for some more shots hurt. Who are these players right now? And are these tradeoffs consistent over careers, or something with super high variance?

    • Very good questions. I actually have some cool followups lined up but I can add this as well.

  4. ilikeflowers
    March 31

    Arturo, do teams with 0, 1, 2, etc… high usage players systematically over or under perform their team’s expected wins-losses based upon efficiency differential? What about the same for low usage?

    • The historical angle is very interesting. I think you’re pitching if this explains some of the prediction error we see in the model for teams. Very interesting as well. Need to build a bigger data set 🙂

  5. Westy
    March 31

    Arturo, this is fantastic stuff! Thanks as always for this work.

    So basically, the potential statement you quote, “…that you can always find someone to take that shot because the supply of shooters far outweighs the supply of shots.” kind of only tells half the truth.

    Yes, the shots will be taken, but in short time [in an ideal team economy], the most efficient players to do so will rise to the top, because “…selection bias and diminishing returns [ seem to exist]. So you get more shots only if you make at around an average rate and it becomes increasingly difficult to score at a better than average rate the more of a ball hog you are.” Therefore, as who should be taking the shots settles itself out, shot quality should go up.

    Am I interpreting your conclusions correctly?

    • Westy,

      You’re arguing invisible hand? Cool. Problem is information assimetry. You’ll see in the followup. The market does not tend to optimization.

      • Some Dude
        March 31

        I don’t see how you could prove that unless you devise a way to measure marginal efficiency of individual players.

        And to that end, you’re going to have to factor in the opponents strategy as well to do so. What Westy is actually referring to is not the invisible hand, it’s best response functions. Unfortunately, to find optimization, we’d probably have to find Proper Equilibriums (or at the very least trembling hand perfect) and this would require way too much guessing on our part.

        • Westy
          April 1

          I look forward to the follow-ups. Even if assimetry exists, though, don’t results speak volumes? If teams are about winning, one would suspect that even by trial and error teams would arrive at optimal solutions. I don’t think that any team is putting forth purposefully suboptimal strategies (unless they’re ‘building’ for the future and hoping for lottery luck).

          As to which economic theory fits this search for ideal winning conditions/makeup, I’ll probably have to leave that to the experts.

          • Some Dude
            April 1

            Oh, I agree that for the most part teams are finding their sub-optimal levels. I just don’t think we can statistically measure that.

            i do think there is some error done by the players so that they don’t play the game perfectly suboptimal (hence the trembling hand subgames), and we see this ourselves. We call them the “NO NO NO YES” shot/play (or often a 4th NO), but they get pretty close in most cases.

            On the other hand, I do think some coaches do screw up strategies like last year with Carlisle not playing roddy against the Spurs in the playoffs. Now the players on the floor played optimally, but the coach didn’t put out the optimal lineup for the series enough.

            But back to measuring. In order to know if player A should shoot more we’d have to know the elasticities of functions of the players conditional on the opponent and then we’d have to know if they’re capable of even shooting more at all.

  6. marparker
    March 31


    I’m sure you have a ton of projects, but I was getting curious about the difference between average wp48 and average championship team participant wp48. If we’re interested in predicting the champion each year or building a championship team wouldn’t we be more interested in the latter?

    Secondly, I’m am waiting around for someone to call into question the true genius of coach K. We keep hearing that Kevin Love must not be that good because the genius wouldn’t allocate any minutes to him in the World Championships. I have my own numbers but kind of figure that noone cares about the MarParker Opportunistic Player Evaluation System(MOPES). I have some conclusions but would be curious to see what conclusions can be drawn from similar metrics.

  7. Here’s a guess – average championship team participant wp48 will be higher than everyone else’s in the Finals.

  8. marparker
    April 2

    Yes, i know that but what is the average production they get from each position during the regular season?

    For an example, Kobe may rank behind other shooting guards in wp48 but in my as yet to be quantified ch48 I bet he is 1st or 2nd each and every year.

    Shouldn’t we be more curious about championships produced?

  9. […] average of 52.2%. That’s especially difficult to pull off when taking so many shots. There is a natural trade-off between shooting percentage and usage percentage, because a player taking more of his team’s […]

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