The Payoff

Cost–benefit analysis is tool used by governments, companies to evaluate the desirability of an action. The goal of the analysis is to see whether the benefits outweigh the costs. The trick for applying this analysis is to figure what constitutes value and what exactly is your cost.

The game of basketball is about turning possessions into points. It is thus extremely easy to identify possessions, the currency of the game, as cost and point margin creation as value. The word margin being the critical one in that equation because we know that the ability of a team to generate point margin is the truest measure of the quality of a team.

Over the past week, I’ve spent a lot of time looking at usage or the percent of the possessions available that a player uses for his team. You might ask me why? It may seem like a devout jew preaching the glory of bacon. I might even answer you.

I think this'll end better than that. (Image courtesy of xkcd.com)

Simple enough. Wins Produced (go  here for details) gives me the value produced by a player (or a reasonable approximation). Usage tells me the cost of that production. In essence it gives me a sense of perspective. If a player produces .2 wins in a game it’s generally a good game but if he uses 40% of the possessions for his team? Not quite so good.

Let’s get some numbers on the table.

Total Wins Produced for the Season so far (thru April 1st): 1126

Total Points for the Season so far (thru April 1st): 225,240

Total Possessions for the Season so far (thru April 1st):238,102

Points per possession: .942                                 per 20 possessions: 18.856

Wins Produced per possession:  .0047          per 20 possessions: .0942

What do these numbers mean? Remember what I said about point margin? The goal for the NBA is to generate more points than the opposition and to do it consistently. The more you do it the more you win . This is why scorers get all the love. The problem lies in the fact that if we focus just on scoring (i.e. value) and not on usage (i.e the cost) we can miss the boat.

Let’s address that. We want to win games over .500. The end goal is then to be better than average.

Thus I came up with the above average rankings.Using all game samples >= 24 Minutes Played and looking only at players with more than ten games, I worked out:

  • Average of Usage Rate
  • Sum of Player Possesions
  • WP48 & Wins Produced
  • Break even win return on 20 possesions (see above)
  • Expected Break Even Wins Produced return on Possesions: this is the player possessions used times avg wins produced per possession
  • Marginal Wins (Wins over .500 generated) : Wins Produced -Expected Break Even Wins Produce
  • Break even point return on 20 possesions: this is the player possessions used times avg points per possession
  • Point Return on 20 possesions: Points Produced by player over Break even per 20 possessions
  • Points over average generated: Points Produced by player over Break even total
  • Estimated Marginal Wins over .500 from Scoring: Points over average generated divided by 31.1 (full explanation for that is here)
  • And I ranked everyone by WP, Usage, Marginal Wins  and Marginal Wins  from Scoring

How does that look? Let’s look at it three ways:

First comes use:

Now comes points:

And finally marginal wins:

Heh. You’ll note that use does not track to winning (or even wins from scoring). You’ll also note that Melo and Amare are both high usage above average scorers. The problem is that they don’t do the other things that help you win.

The point to this? Simple, to win in the NBA you need guys from the top of List #2 (efficient scorers) but you need to pair them with guys from the top list three (marginal win producers) . Guys on both lists? Superstars. Too many from List #2 ( scorers) and your team becomes one dimensional (NY). You can survive guys from the bottom of list 2 (Rondo,Kidd) if they bring enough else to the table and you have stud scorers (Allen,Dirk,Pierce) on your team.

Oh and if you have a high usage, borderline efficient scorer who brings nothing else to the table?

Go Raptors. :-)

24 Comments

  1. Crow
    4/4/2011
    Reply

    When a shot goes up that is assisted did 2 players use that possession or did each use part of it? When a offensive rebound occurs is it divided again with the offensive rebounder and the next actor(s)?

    I know how possessions are calculated elsewhere, I just what to be clear if it is exactly the same here or different.

  2. Crow
    4/4/2011
    Reply

    Points per possession break-even of .942, does equate with an Offensive Rating of 94.2 per 100 possessions or a TS% of 47.1?

    • Crow,
      Close.
      I get .942 and 94.2 per 100 poss (league avg thru saturday)

      but TS% is PTS / (2 * (FGA + 0.44 * FTA)) not PTS/(2*(FGA+.44*FTA +TOV)
      so it’s 54.2% not 47.2%. But this is why I went to points per possessions, I wanted to include the TOV.

      I’m counting possessions straight to the final actor. At least on the points side. Other win producing actions (like off rebounding and assists) are being counted in Wins Produced.

  3. Some Dude
    4/4/2011
    Reply

    I don’t understand your possessions number. Milwaukee is the worst offensive team in the league, yet is averaging 1.013 points per possession.

    I didn’t count it up exactly, but total possessions seem to be in the 210,000 range. Minnesota has more possessions than any team and it’s around 7500. Even if all 30 teams had that many possessions, they’d still be just shy of your total.

    You are either double counting something or your formula is different from what I thought was an industry standard (for lack of a better term than industry).

    • Some Dude
      4/4/2011
      Reply

      correction. .984 points per possession for Cleveland (almost same for Bucks). Used outdated number I believe. Still well above the average in this post.

      So yeah, I’m confused.

    • SD,
      Huh? I think you’re confused.

      Milwaukee with just the players on the table is .932 points per poss (vs an average on table of .979). I’m only showing Players who played more than 24 minutes in a game at least ten times. That’s 173106 possessions out of 238102 (about 72%).

      • Some Dude
        4/4/2011
        Reply

        oh, I see. You only counted 24 minutes plus in your calculation of individuals, too. I guess this means benches are very efficient!

        I’m still not sure how you get 238102 possessions total. According to basketballvalue.com it’s closer to 2150000 or so. Your number puts the average team at around 8000 possessions so far (in total). But no team has even crossed 7500 using data including yesterday.

        Your possessions is not the same as the standard or something is being double counted. How did you calculate possessions or where did you grab it from?

        • EvanZ
          4/4/2011
          Reply

          Team rebounds may be an issue here one way or another.

        • SD,
          Here’s the walkthru:
          In the Table:
          Stats Thru April 1st
          FGA 183835
          FTA 55273
          TOV 30747
          Possesions (FGA+.44*FTA+TOV)
          238902.12
          Games 1132
          Pts 225240
          Pts per Possesion
          0.942812898
          Possessions per game
          211.0442756

          And the data thru 4/3 from Bref:

          Stats Thru April 3rd from Bref
          FGA 186404
          FTA 56010
          TOV 32743
          Possesions (FGA+.44*FTA+TOV)
          243791.4
          Games
          1148
          Pts
          228452
          Pts per Possesion
          0.937079815
          Possessions per game
          212.3618467

          There’s a slight difference (<1%). Not enough to skew the results at all. I probably just need to reload the games to make it go away.

          Please note that I am using the simple possession formula (FGA +.44*FTA +TOV) and not Oliver's more complicated formula (http://www.basketball-reference.com/about/glossary.html#poss)

  4. Some Dude
    4/4/2011
    Reply

    Hate to make another post, but BRef already lists points per possession (times 100). None of the ones in the chart are close to the website’s listing (yes, I can multiply by 20).

    Also don’t understand your marginal win formula. Not sure what that formula is called, but I don’t think it’s marginal wins. Marginal means what happens to Y when you increase X by 1. For instance, Kobe up top of the first chart has what you call a 1.76 marginal wins from scoring. This means if he increases his possessions by 1 more percentage point, he’d up wins 1.76. This obviously makes no sense.

    Marginal wins would really mean, if player X increased usage by 1 possession (or 1 percentage point to keep things clean), how many wins does he add? Players who are positive should continue to increase possessions until you hit 0 and below lower possessions til you hit zero. An ideal team would have all 5 players are MW = 0.

    You’re not measuring the elasticities of the point on the curves each player is on. You’re doing “Wins Produced -Expected Break Even Wins Produced” which is something that I’m not sure is measuring anything at all in relation to what you’re trying to accomplish.

    A very bad, but better approach, would be to regress each player’s individual games usage and PPP and measure the slope and that could be your marginal value, then transfer that to wins. Like I said, this would be terrible, but at least it would be some kind of start. I’m not sure if we should assume the curves are linear, hence why it’s bad. If you could regress each player within say a 3% boundary from their average, maybe it would provide us with a more accurate curve, even if still linear. This is why I mentioned earlier post of the difficulty in discovering elasticity. Need a lot of data here and it’s very possible different areas of usage have different shapes.

  5. 4/4/2011
    Reply

    Am I surprised by Bargnani’s showing? No. Maybe a little surprised to see his company in the usage department, but not about your overall conclusion.

    Bargnani is such an easy target. It wouldn’t be too much of a stretch to pull an Andres and mention how unproductive he is at least once per post.

    How about Jordan Crawford? He’s been jacking it up like crazy ever since he got traded to the Wiz.

  6. marparker
    4/4/2011
    Reply

    Some Dude,

    Arturo didn’t count individual rebounds or assists. I’m pretty sure that account for the difference between what we see here and the numbers you are referring to.

    • Some Dude
      4/4/2011
      Reply

      no, individual assists are not part of it. But yes, assists count in player possessions which should be obvious. But I now realize ORating counts that, so yeah I was wrong there (it’s points produced, not scored).

      Still, my point about marginal wins is on the mark. And I still don’t get how Arturo is getting so many more possessions than other websites.

      • tgt
        4/4/2011
        Reply

        I bet Arturo is counting a shot as the end of a posession, not a defensive rebound or score.

        • tgt,
          You are correct. I’m using shot or turnover as the end of the possession. So if the team shoots and gets an offensive rebound, I’m counting that as two possessions.

          • Some Dude
            4/4/2011
            Reply

            so you’re double counting. At the very least, you need to make it very clear what you’re doing, because virtually the rest of the basketball analytic world counts a possession differently, based on Oliver’s work. It doesn’t make sense to use the simple formula, anymore. You’re not capturing a lot of value. A possession does not end until the other team acquires the ball.

            What you’ve calculated is points per shot and turnover.

            • SD,
              I did explain repeatedly. I was trying very specifically to separate the rebounding out. You’ll see why in my next post :-)

              • Some Dude
                4/5/2011

                I’m confused, where was it explained? I didn’t notice it in any of the posts on this topic (I re-checked). If it’s in the comments, I think it should be added to the posts.

                Your definition of “possession” is different than everyone else’s. I believe this should be clarified in your posts (I don’t see it). Honestly, it shouldn’t be called a possession at all. it is like defining a meter as 130 cm for your datasets.

                I’m having a hard time following right now because the definitions of “possession” and “marginal value” are being misused.

                As for the rest, measuring points per FGA/FT/TO makes no sense to me. Since not all turnovers are on the ball, stuff is miscounted. That’s why points per FGA makes more sense in this scenario. And a lot of TOs come from passing the ball, which doesn’t figure into usage unless it’s a turnover. It should be points per shot or points per possession (the right kind).

                And then there’s assisted and unassisted points.

  7. Westy
    4/4/2011
    Reply

    So you note, “The point to this? Simple, to win in the NBA you need guys from the top of List #2 (efficient scorers) but you need to pair them with guys from the top list three (marginal win producers).” That is a little different than the WP mantra we’ve heard before. Any thoughts on this from Mr. Berri?

  8. Italian Stallion
    4/4/2011
    Reply

    There’s nothing I enjoy more than a discussion about scoring, usage, and efficiency.

    To me, the key issue is how to value a high usage scorer that’s not especially efficient like Carmelo Anthony.

    IMO, the value probably “depends”.

    Even before the trade with the Knicks, I would have argued that on a team with a lot of efficient scorers like Nene, Afflalo, Lawson, Billups, Anderson, and JR Smith, Melo’s very high usage was probably not adding much to the offense. You could probably even argue that at times he was hurting by taking a lot of poor shots.

    Swap in Gallo (lower usage but above average efficiency) and even though the team lost Billups (above average efficiency) and added Felton (below average) the team was unlikely to lose a lot on offense even though it game up a leading scorer even if a few players had to up their usage slightly.

    The more important question to me is what happens when you put a guy like Melo on the court with with guys like Landry Fields and Ronnie Turiaf (low usage high efficiency).

    IMO, neither of those players can up their usage enough at this stage to contribute their fair share of points without a negative impact. Without a guy like Melo teamed with them, IMO offense would suffer. Melo can get his 25 points at a good but not special TS% of 55% (give or take) and you can then get some scoring value out of guys like Fields and Turiaf on lower usage. So in that situation, his ability to really rack up points on high usage may have incremental value even though his efficiency is more in the average range.

    • Italian Stallion
      4/4/2011
      Reply

      Sorry about the grammar etc… I was typing and watching the NCCA finals at the same time. :-)

      • Some Dude
        4/5/2011
        Reply

        It was so bad it made grammar worse around the world!

    • Italian Stallion
      4/4/2011
      Reply

      Perhaps an easier way of expressing my point is to say that the reason it’s so hard to reach a consensus about the relationship between usage and efficiency and the value of shot creation is that it’s a variable.

      Put Monta Ellis on the same team as Melo and his scoring will probably be useless because you don’t need that high usage.

      Put Monta Ellis on the Milwaukee Bucks and his scoring might have some very good value because they struggle to score and get good shots.

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