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Layups: Nate Silver on Carmelo Anthony & the Usage-Efficiency Debate

Posted by Neil Paine on January 19, 2011

Nate Silver is primarily a baseball guy. (Or is that a politics guy?) But he weighed in on basketball last weekend -- specifically, the prospect of Carmelo Anthony joining the Knicks.

Some advanced stats underrate Anthony because they assume a quality shot can be created at will, every time down the floor. The logic is that if Anthony (an inefficient scorer) doesn't shoot, the team will just find someone else who can convert at a similar rate. And since Anthony isn't the most complete player in the world when you look beyond his scoring, it stands to reason that formulas which undervalue shot creation will see little reason to pay him top dollar.

But as Nate argues, Anthony is making his teammates better by taking the pressure to create off of them. His skills allow a team to surround him with defense-minded, low-usage players that compliment him, setting up something of a division of labor on the court. Silver lends credibility to this notion by showing that when players play alongside Carmelo, their offensive efficiencies increase.

I tend to agree with Silver's premise. This is why I constantly harp on "skill curves" and usage-efficiency tradeoffs, and why offensive statistical plus-minus contains a squared term for true shooting attempts per minute -- because there's a great deal of evidence that the marginal cost of possession usage declines as a player's offensive role increases. Unlike baseball, where "usage" is evenly spread out across all players and the only concern is an efficiency metric like OPS, the ability to create "at bats" is an important consideration.

In that way, Carmelo Anthony is just the latest in a long line of players who have been confounding statistical analysts for decades (before him, it was Allen Iverson). But as Silver, Kevin Pelton, and Henry Abbott are noting this week, one measuring stick for the evolution of basketball analysis is precisely how it deals with players like Anthony. I can't say he'd be the best fit for the Knicks specifically (New York -- 7th in offense, 23rd in defense, & featuring a player who already commands 31% of possessions -- seems a curious destination for an offense-only gunner), but in general it's useful to recognize his offensive value beyond pure efficiency metrics.

39 Responses to “Layups: Nate Silver on Carmelo Anthony & the Usage-Efficiency Debate”

  1. Joe Schaller Says:

    I understand the value of shot creators yet if you put up shooting percentage, assist and turnover stats of Carmelo and Iverson up against those of Jordan, Kobe, Lebron, Dwyane etc they don't come close to being amongst the elite. Some are great at creating shots yet poor at converting.... Latrell Sprewell? Stephon Marbury?
    It would be interesting to see a historical offensive analyis of "shot creators".

  2. huevonkiller Says:

    Neil you clearly "underrate" PER. The way you skim over defense when you are not comfortable using defensive rating, makes me want to just look at PER.

    I think PER is even better than Neil's usage efficiency tradeoff, because Neil dislikes using defensive rating. Lately he ends up disregarding defensive rebounds, steals, blocks, etc., completely when judging great perimeter players to each other, and so the picture he paints is incomplete compared to what Hollinger does. Hollinger can't account for defense but he gives me a better idea than just looking at offensive statistical plus minus. Or just looking at offensive rating against good teams.

    When Neil does use Defensive rating I'm not sure what to make of it.

    I know for example that the Cavs are trash defensively and that Paul Pierce struggled against them last year, but somehow Neil feels it unnecessary to make that distinction and blamed the entire team for their defensive problems. I know who deserves credit for playing well defensively, and who didn't play well defensively. It is puzzling why Neil is so down on Player efficiency rating when it not only passes the eye test, but actually has a box score component at least of defense. Overall it takes into account more factors than Neil's preferred method lately of O-rating and %possessions.

  3. Neil Paine Says:

    It's true that I'm no fan of PER, but what are you talking about w/ regard to me "skimming over defense", "disregarding defensive rebounds, steals, blocks, etc., completely when judging great perimeter players to each other", and "blaming the entire [Cavs?] team for their defensive problems"?

    Seriously, I have no idea what you're talking about.

  4. Anon Says:

    Melo still takes too many bad shots for my taste. At least players like LBJ, Wade, Kobe can knock them down and gets some efficiency returns from their shot-creation while not freezing out their teammates. I'm not even sold he's a more valuable player than Nene for the Nuggets.

    Also, Huevon - what are you talking about?

  5. Anon Says:

    Did I just type Kobe doesn't freeze out his teammates? Wow.

    Well, I think I mean he doesn't do that when he's playing at his best. He'll create by shooting some tough shots while also making them, and also get others involved when defenses rotate over to him.

  6. Jason J Says:

    "...there's a great deal of evidence that the marginal cost of possession usage declines as a player's offensive role increases." That seems to be the trick - incorporating usage into player efficiency metrics properly (another thing I love about SPM - the weight it gives to V.I.).

    Also, does anyone know what Huevon is talking about?

  7. AYC Says:

    In Anthony's defense, his efficiency this season might be down because he's mentally checked out on his team; I've always thought he was overrated, but I expect him to play better wherever he is next year.

    Anyway, count me among the critics who thinks WS overvalues efficiency relative to usage somewhat. I think PER does a better job in that regard (not that I understood what #2 was talking about either). All of these advanced stats overvalue a high FT rate IMO, by not recognizing the full value of a FTA. But since FT rate matters so much, why isn't it listed on the leaders page, or anywhere on this site?

  8. Nick Says:

    Nate kinda forgot to account for a bunch of important factors in his analysis, like the ages of the players Melo played with, as most of Melo's teammates have historically been at ages where most players get better, and the ones that weren't, such as Billups, declined as expected when playing with Melo.

  9. Anon Says:

    "I think PER does a better job in that regard (not that I understood what #2 was talking about either)."

    I'm not even sure PER does that, at least explicitly.

    In watching Anthony play, he seems to be a bigger version of Allen Iverson. On any given night especially when midrange game is on can be the best player in the league and help his team offensively. At other times, he can be a black hole on offense and a bit jumper happy. That kind of approach might suit off-the-bench "instant offense" guys like JR Smith fine, but when you're doing that as a player putting in alot of minutes? It can keep your team's offense from realizing its full potential. Nene isn't going to give you Hakeem production on the block but he is certainly able to be a presence down-low. I think shot-selection keeps Melo from being in that upper-echelon of best players. If he heads to NY it would be interesting to see how he works out with Amare. LeBron and Wade are high-usage guys but they're always willing to get each other and their teammates the ball; can Melo do the same with Amare?

  10. Anon Says:

    Also, it would explain why Nate frowned upon these kind of statistics if he was looking at Berri's metric. Bunch of flaws with that forumla, and it doesn't take usage/efficiency into account like WS and SPM.

  11. Bradley Says:

    Usage rate does factor into WS, though, doesn't it? For instance, last year, Varejao had a better offensive and defensive rating than LeBron (if I'm remembering correctly), but LeBron blew him away in WS48, because his Usage Rate was so much higher. Are you guys saying Usage still isn't weighted heavily enough in WS?

  12. AYC Says:

    I guess I should have said, it "seems" that PER values usage more; I say that based on the way high-usage players like AI, Isiah, Kobe and Ewing fare better in PER than WS48. Anon, based on WS, Nene IS more productive on offense this year than Hakeem ever was. Nene is averaging 8.4 OWS per 82g this year so far; Hakeem's single-season best was 7.9 OWS.

  13. Matt Says:


    The way I understand it, WS does incorporate usage in the sense that a player gets more win shares the more possessions he uses (unless you are below RL, of course). It does not, however, account for the fact that there is inherent value in using possessions beyond what a player produces because high usage rates theoretically allow the non-high-usage teammates to take shots they can convert at a higher rate (and conversely, it prevents them from taking shots they would convert at a very low rate).

    My question from all of this is whether it is more valuable for a player to create his own shots through ball-hogging a la Melo (tongue-in-cheek -- sort of) or through shot creation for teammates like a Rajon Rondo or something. I think to properly evaluate this question, we need a stat that I have been begging for forever: Teammate Assist Conversion Rate (or something like that). For instance, I would like to know how often a pass from Rondo turns into an assist. So if, in a given game, Rondo passes to his teammates 24 times that result in an immediate FGA (or foul), I would want to know what the Celtics TS% is off of those passes. I think that would be valuable information.


  14. Sol Says:

    Did you even see the rebuttals by Arturo, DBerri (to name a few)? They pretty much waylaid the argument that he made the players around him shoot better.

    Not to mention - TS%? What does FT% have to do with Melo in any way whatsoever? If anything Nate should have used FG% (and I say this as someone who has been a big fan of Nate for years).

  15. Anon Says:

    "It does not, however, account for the fact that there is inherent value in using possessions beyond what a player produces because high usage rates theoretically allow the non-high-usage teammates to take shots they can convert at a higher rate (and conversely, it prevents them from taking shots they would convert at a very low rate)."

    Not true. It's directly based on the Oliver stats that were made to explainthis phenomenon.

    The caveat is that while it works in the general sense, it may not fully explain the tradeoff for certain players with specific styles of play. That's where +/- data can come in to help to round out the picture.

  16. AYC Says:

    Sol, did you read Kevin Pelton's article?

  17. Neil Paine Says:

    Actually, Matt has it about right. The only bonus you get in WS for taking on more possessions is the greater marginal points for yourself, assuming your ORtg is above the margin. However, there is no mechanism to directly account for the potential increase in ORtg you bring to your teammates via the skill curve phenomenon.

  18. Jason J Says:

    Neil is there a way to "directly account for the potential increase in ORtg you bring to your teammates"? I can't see how one player's usage could be properly apportioned out to all his teammates. Does the next highest usage player get the max benefit because, theoretically, he'd be the one most likely to take those tough possessions that the high usage player does? Or maybe Pippen already has a high enough usage where he's not seeing as much benefit as Grant? It certainly doesn't make sense to distribute it evenly.

  19. Neil Paine Says:

    Well, you do kinda have to distribute it evenly.

    What I did with my WARP (and what Kevin Pelton does with his WARP now) was to add a player to an otherwise league average lineup and use the usg/ortg tradeoff to see how good the lineup is (adjusting the "teammates" ORtgs based on their new usages). Then you do the same thing, but you take the player out and put in a replacement-level player and see how the lineup efficiency differential changes. That way, you can calculate the difference in wins between the simulated lineups, which is the player's theoretical impact.

    That's how you take into account not only the player's own performance above the baseline, but also his effect on generic teammates' performance.

    I suppose you could do the same thing with specific teammates instead of generic ones, although it would make things more complicated.

  20. Sol Says:

    Read Kevin's stuff - it seems like him and Arturo come up with different #s:

    Arturo clocks in a lot less of an impact on TS/eFG.

  21. Sol Says:

    I would honestly love a roundtable where we can get some of these guys locked in a room and refuse to let them out until they arrive at a consensus :)

  22. huevonkiller Says:


    During the playoffs I thought you gave (I say this respectfully) an ignorant analysis of the Cavs defense. You used defensive rating as one of the barometers to be used against ALL of their players. When clearly one of them is a much better defender than the rest, stat plus minus supported my statement, PER supported my conclusion, and now this pathetic Cavs roster in 2011 is supporting my conclusion (you didn't, we argued about it back then). PER is better than your incomplete comparisons Neil, you're skimming over defense lately.

    Performances against top defenses, using only offensive statistical plus minus, I'm not sure that's quite a complete picture. I'd rather look at PER then.

  23. huevonkiller Says:

    Oh and sorry for being vague and unclear, but I was referring to a past discussion I had with him. Guess he forgot. ; ]

  24. huevonkiller Says:

    Also one more point, I usually agree with a lot of what Neil says. I just have yet to understand his explanation for PER, when it looks like it takes into account more factors and weighs the usage-efficiency trade off pretty well.

    A lot of people seem nervous when discussing defense, or are not quite sure. I think Neil was operating under the assumption that like the 1994 Bulls, the 2011 Cavs would retain their defensive prowess. Well I did not operate under that assumption and I don't think Varejao is such an elite defender either.

  25. Nathan Walker Says:

    But, PER doesn't describe players well at all. I don't understand why you like it so much. Maybe because it's marginally easy to calculate...or because it's on

    Try something, anything else.

    DSMok1 or Rosenbaum's ASPM, Basketball Value's APM, This Site's SPM, Win Shares and Win Shares per 48. Heck, even Berri's Wins Produced and Wins Produced / 48 are better.

  26. Greyberger Says:

    It's been a good discussion, but why it has to start with linear roll-up metrics (WP48! PER! cagematch!) is beyond me. These metrics are fine for generating attention and debate over the relative importance of basketball events, but it's twenty-eleven guys and it doesn't always have to be about A plus B plus 0.3 C.

    As for linear weight metrics and defense, they only include steals and blocks because it would be a little threadbare without them. Hollinger will be the first to tell you that PER doesn't capture defense because only three defensive statistics are recorded in box scores. And Oliver explicitly says that DRtg is an estimate, until such a time as the King returns and brings free defensive assignment statistics.

  27. Anon Says:

    Melo tonight: 35 points, 12-25 from the field, 11-12 from the line. No tovs.

    This is the player the Knicks THINK they're getting though. But with all the talk about Melo's volume-shooting helping his teammates (which have some valid rebuttals by the way) the goal at the end of the day is to put the ball through the hoop. Shot-creation has value, but you can't be chucking up shots and not scoring either. It's still potential points being given away to the other team when you miss and they get the board.

    Melo may take shots that others may not be as adept as making, but then again, he's not exactly FINDING teammates as much as other stars for the easy shots either. Unless he's now the greatest "triangle assist" man in history.

  28. huevonkiller Says:

    Sure I love defensive rating for someone like Dwight Howard.

    However Nathan we still disagree, defensive rating can be completely misleading and overvalues role players or bad defenders on great defensive teams. Or mediocre-ish defenders (Varejao) on good defensive teams. Looking at per by position like 82 games does, has already identified Varejao, Chris Paul, etc. as respectable but overstated defenders. There methods are supremely underrated here (again remember I agree with Neil plenty of times).

    Take a look at win shares per 48, and you'll see some dubious rankings precisely because of this. In contrast PER ranks all time seasons pretty well, even more so for perimeter players. has kind of exposed Varejao as the bland defender at his position, 07-08,08-09.09-10. He has a Udonis Haslem reputation, not really a great individual defender but he looks the part. This year the Cavs are absolutely garbage defensively and I tried to tell Neil last year that one player is much better defensively than the rest, but he failed to make a distinction. Again he was operating under a vague assumption that the 2011 Cavs would be able to keep their defensive skills like the Bulls after Jordan left but they simply don't have the personnel. Neil was not distributing credit correctly. in comparison did a much better job of identifying who was talented defensively on that team with counterpart PER.

    PER gave me a lot better analysis and is a much more useful tool than what Neil gives it credit for. If we're going to look at an incomplete picture in offensive rating and %possessions, then I'd prefer PER as it takes into account more things. Like I said though I think Neil usually does a great job around here, and no blog is perfect.

  29. EvanZ Says:

    Question...Neil, you said: "because there's a great deal of evidence that the marginal cost of possession usage declines as a player's offensive role increases." Could you mention maybe 2-3 pieces of evidence for this effect? Dean Oliver tried to construct some skill curves in BoP, but even he admittedly said it was a very difficult problem to address. It seems to me like the jury is still out, but perhaps, I haven't seen the same "evidence" you are referring to.

  30. Ed Says:

    Sorry but Nate's anaylsis was VERY sloppy and I'm surprised to see it being featured here. Dberri has posted a lengthy reply which details many of the problems with Nate's anaylsis.

    In the end, it COULD be that Nate is correct....but there's no way to draw that conclusion from his anaylsis.

  31. Neil Paine Says:

    Re: #29 - Dean later went on to expand on the BoP study of skill curves and even a basic (for the public's eyes) version of what he was doing for Denver showed an inverse relationship with a significance level at which there was no way it was due to chance.

    Eli Witus took a much more in-depth look using 5-man unit data and found that units whose members were forced to take on more possessions underperformed their expected efficiency before a skill curve compensation, while units whose members took on fewer possessions outperformed their expectations before a skill curve adjustment:

    Also, Dan Rosenbaum, Daniel Myers, and I have each consistently found a "diminishing returns" effect to true shooting attempts per minute when predicting on-court impact from box score stats.

    As for Huevon, care to link to any of the "ignorant" analysis I've supposedly done regarding defense?

  32. EvanZ Says:

    Thanks, Neil. Good stuff!

  33. AYC Says:

    Not even Hollinger thinks PER does a good job of measuring defense....

  34. Guy Says:

    Ed/30: I think you are right that Silver's analysis was quick-and-dirty, and far from convincing. However, Pelton's study (linked in Neil's post) was much better and deeper, and still found a strong "Melo effect." Because Pelton looks at players with and w/o Melo, he is controlling for the most important factors Silver didn't control for (coach, team, age, and -- to some extent -- teammates).

    Berri's study cannot yet be considered as evidence on the other side, because he declined to report his regression coefficient and standard error. He said only that Melo's coefficient was not statistically significant. It's entirely possible that his regression found a positive Melo effect similar in size to Pelton's (or even Silver's), and yet it was still not statistically significant given Berri's small sample. And despite multiple requests at this blog that he provide his regression results, he hasn't responded. So unless/until he does, his reported result should have no standing (or, if you're cynically inclined, you might take his failure to disclose results as evidence in favor of Pelton's/Silver's findings). And the truth is that Berri's seasonal w/ or w/o Mele data is methodologically far inferior to Pelton's on/off court data in any case.

  35. Jason J Says:

    Huev - I think another significant reason for the defensive collapse in Cleveland (aside from Bron and Delonte, their two top perimeter defenders, jetting to Miami and Boston) is the coaching change. Brown was a Pop disciple and a very good defensive coach. Not that Scott isn't a good defensive coach, but he's got a different philosophy and doesn't have the pieces to make it work. They also lost Moon who was a decent defender for them. And Z and Shaq, so they're undersized. You're right. They don't have the same defensive personnel at all.

  36. Crow Says:

    huevonkiller is being critical of the lack of individual ratings for shot defense in Defensive Rating and perhaps also that it is team average for all minutes and not for when they are actually on the court. I recognize these shortcomings as well though I don't blame them on Neil. It was a simplification that was better than no consideration of shot defense- at least for guys on different teams.

    Simple PER though had and has no shot defense component at all. Counterpart PER has such estimates. That however assumes all shot defense is counterpart shot defense and the data is inferred based on assumed match-ups and not from videotape so it also has issues and imperfection.

    Evan's EZPM has team shot defense divided among players actually on the court but at this point it is still even to all. Some weight to counterpart data might be an improvement. Evan and I batted the idea of differential credit shares for team shot defense perhaps based on shot distance at his site. Jeff Fogel and I also discussed whether the credit / blame of shot defense could be better modeled with variable credit by position instead of equal shares at hoopdata.

    Some improvements in linear metrics are possible on this issue / may happen / may gain support. Or perhaps the shot defense factor estimate of Adjusted +/- could be calculated and plugged into where either the boxscore metric hole for it is or the crude current estimate is.

  37. Crow Says:

    It is still an estimate but perhaps the fairest one? Blending one on one shot defense with help defense impact whereas Defensive Rating and counterpart PER each only have one. If you don't want to use this Adjusted +/- Factor then I'd think it would make more to sense come up with some blend of statistical data on team level opponent shot defense and counterpart defense than to continue with just one value. While the original authors may not want to update their metrics "officially" and in their own use, and they can have that view, it has become more common to see adjusted metrics such as adjusted PER (for other reasons) and adjusted WP48 (for rebounds) so some interested parties and users could also do an adjusted Defensive Rating, if they have the desire and time to put it together. Or if an adjusted old metric is an undesirable mash-up then a new metric may be the way to go. I am encouraged by EvanZ's EZPM.

  38. Crow Says:

    If a new metric were to try to supplement or replace existing ones it would be good to see the predictive performance comparisons.

    Perhaps the shot defense component should be a weighted multi-season estimate instead of just the current season. That too may raise flags with some, but if it gets you closer to modeling reality in a more stable / helpful way I'd be for it.

  39. huevonkiller Says:

    Thank Crow, those are some interesting conclusions.

    As for Shaq and Z? Yeah they're getting killed on last season, it isn't only because the Cavs are undersized.