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January 18, 2011
The Value of Carmelo Anthony
Measuring the Melo Effect

by Kevin Pelton


A fan who just began following the NBA in the last month could be forgiven for believing that Carmelo Anthony was the league's best player. Because Anthony is sure to be traded before next month's trade deadline, because said trade will likely include a team from the country's biggest media market (either the New Jersey Nets or the New York Knicks) and because there have been enough twists and turns in the rumors to sustain a miniseries, Anthony has been the subject of more recent discussion than any other NBA player.

One aspect of that conversation has centered on Anthony's value in a vacuum. Statistical analysts offer very different answers to that question, depending on which one is asked. The most recent take came from Nate Silver, who oversaw the creation of Basketball Prospectus before going on to fame and fortune as a political analyst. Silver looked at the history of player efficiency while playing for the Denver Nuggets and elsewhere, finding that players posted much better True Shooting Percentages when playing alongside Anthony:

"All but 2 of the players - Marcus Camby and Voshon Lenard - posted a higher TS% playing with Anthony than without him, and on average, he improved his teammates' TS% by 3.8 points (to 55.0 percent from 51.2 percent).

The effect of a player who improves the rest of his team's TS% by 3.8 points is extremely substantial: it is works out to their scoring about 5 or 5.5 additional points per game solely on the basis of this efficiency gain. That, in turn, translates into about 15 additional wins per season for an average team, according to a commonly-used formula. This is how Anthony creates most of his value - not in the shots he takes himself, but in the ones he creates for his teammates - and some of the “advanced” formulas completely miss it.

Essentially, Silver's argument is one in favor of the importance of shot creation. The tradeoff between usage and efficiency has been a common theme in my work for Basketball Prospectus, and my belief is the evidence strongly supports that it is real. However, the "Carmelo effect" found by Silver is much larger than the value the WARP rating system assigns him based on his usage. If Anthony used plays at an average rate (20 percent) rather than his actual 2009-10 usage (33.5 percent), his wins above replacement would have dropped from 8.6 to 3.5, putting a value of 5.1 wins on his shot creation. Even accounting for the fact that Anthony did not play a full season, that figure is much lower than the number Silver found.

Dave Berri, whose pessimistic assessment of Anthony's value helped spark Silver's analysis, responded by pointing out several factors uncontrolled for in Silver's study. In the case of players like Nenê, whose rookie season was compared to the rest of his career, aging could account for some of the benefit attributed to Anthony. Even when a player clearly improved while with the Nuggets, Silver's method is unable to distinguish whether that should be credited to Anthony's presence, George Karl's coaching or something else.

Fortunately, there is data out there that can help disentangle Anthony's impact from these other factors. Back in 2005-06, while writing for 82games.com, I used the site's player-pair statistics to evaluate how the performance of teammates of Kobe Bryant and Steve Nash changed with those players on the floor as opposed to on the bench. While 82games.com is no longer publishing detailed player-pair stats, I was able to break down the numbers from 2006-07, 2007-08 and 2008-09 to see if Anthony's presence on the floor improves his teammates' efficiency. (Note that I did not use 2005-06 because the consistency of Karl's rotations and Anthony's health meant many starters played few minutes without Anthony on the floor.)

In addition to True Shooting Percentage, the player-pair statistics allow us to explore the other primary way Anthony can influence his teammates' performance--by limiting their turnovers. This turned out to be a major factor in the case of Nash because of how much he handles the basketball. We'll then use these numbers to create a simple Offensive Rating of points scored per 100 plays used (statistically, FGA + .44*FTA + TO).


                   TS%                  TO%                   ORtg
Player     with    w/o   diff   with    w/o   diff    with     w/o   diff
Blake      .479   .571  -.093   .213   .183  -.030    75.3    93.3  -18.0   
Iverson    .558   .530   .028   .147   .152   .005    95.2    89.8    5.4   
Smith      .589   .580   .009   .125   .087  -.039   103.1   106.0  - 2.9   
Diawara    .517   .425   .092   .076   .121   .045    95.5    74.7   20.8   
Najera     .694   .504   .190   .139   .106  -.032   119.5    90.1   29.4   
Kleiza     .596   .535   .061   .121   .131   .010   104.7    93.0   11.7   
Evans      .551   .549   .002   .223   .263   .040    85.7    80.9    4.8   
Nenê       .651   .543   .108   .143   .209   .065   111.6    86.0   25.6   
Camby      .528   .511   .017   .149   .121  -.028    89.8    89.8    0.1

Average                  .046                 .004                    8.5
Weighted                 .041                -.001                    6.8

2006-07 was Allen Iverson's first partial season in Denver, which was also interrupted by Anthony's suspension for his role in a melee at Madison Square Garden. Because of all the changes, there are nine players who played appreciable minutes both with and without Anthony. Of these, only Steve Blake had a lower True Shooting Percentage when Anthony was on the floor. Even when we account for one of Berri's critiques by weighting the differences (in this case by the number of true shot attempts or plays used when on the court with Anthony, which will be useful later), the observed improvement in players' True Shooting Percentages is actually higher than Silver found--if, perhaps, not quite as consistent. Note that with turnovers, the positive sign on the overall average indicates turning the ball over less when Anthony plays.


                   TS%                  TO%                   ORtg
Player     with    w/o   diff   with    w/o   diff    with     w/o   diff
Camby      .489   .546  -.056   .140   .137  -.003    84.2    94.2  -10.0   
Carter     .539   .506   .032   .198   .173  -.024    86.4    83.7    2.7   
Iverson    .571   .558   .013   .116   .114  -.002   101.1    98.9    2.2   
Smith      .637   .575   .062   .107   .148   .041   113.8    98.0   15.9   
Kleiza     .619   .553   .066   .108   .106  -.003   110.4    99.0   11.5   
Najera     .502   .651  -.148   .119   .131   .013    88.5   113.0  -24.5   
Martin     .572   .485   .087   .104   .106   .002   102.4    86.7   15.7

Average                  .008                 .003                    1.9
Weighted                 .016                 .000                    2.9

2007-08 was the outlier of the three seasons I looked at, which may be instructive. With Iverson around for a full season, the Nuggets had a second go-to scorer, giving Karl the opportunity to make sure at least one creator was on the floor at all times. Despite that, most of Denver's role players were significantly more efficient when Anthony was on the floor. It was two of the team's lowest-usage players, Marcus Camby and Eduardo Najera, who bring down the overall numbers because they were far more efficient when playing without Anthony.


                   TS%                  TO%                   ORtg
Player     with    w/o   diff   with    w/o   diff    with     w/o   diff
Billups    .593   .596  -.003   .126   .132   .006   103.7   103.5    0.2   
Carter     .501   .487   .015   .244   .289   .046    75.8    69.1    6.7   
Smith      .603   .563   .041   .103   .137   .033   108.2    97.2   11.1   
Jones      .569   .468   .101   .141   .152   .011    97.8    79.4   18.4   
Kleiza     .567   .543   .023   .095   .102   .007   102.6    97.6    5.0   
Martin     .557   .479   .078   .130   .119  -.011    96.9    84.5   12.4   
Nenê       .653   .628   .025   .118   .177   .059   115.2   103.4   11.8
Andersen   .603   .610  -.007   .122   .179   .057   106.0   100.2    5.8   

Average                  .034                 .026                    8.9
Weighted                 .032                 .023                    8.4

The 2008-09 season presents the strongest argument in favor of Anthony making his teammates better. Despite a strong bench led by Chris Andersen and J.R. Smith, every Nuggets player was more efficient when Anthony was on the floor. The difference was sizeable in the case of everyone save Chauncey Billups, who replaced Iverson as the team's second star. In this case, the reserves in particular tended to turn the ball over far more frequently when they did not have Anthony setting them up for easy scores.

If we combine the three seasons, here are the averages:

              TS%      TO%    ORtg
Average     +.031    +.011    +6.7
Weighted    +.028    +.007    +5.7

Ultimately, this method shows Anthony having a smaller impact on his teammates' True Shooting Percentages than Silver found, especially when we account for the fact that his presence tends to make a greater difference for infrequent shooters. However, looking only at shooting ignores some of the benefit of Anthony reducing his teammates' turnovers. Since the average turnover rate without Anthony is 14.9 percent, a drop of even 0.7 percent is worth noting. Adding the two factors together, the player-pair statistics show Anthony improving the efficiency of his teammates by 5.7 points per 100 plays.

This weighted figure allows us to estimate the value of the Carmelo effect. During 2009-10, he was on the floor for 90 plays per game (this is more than the team's pace would indicate because there can be multiple plays on a single possession in the case of offensive rebounds). Anthony himself averaged 30 plays per game, leaving 60 plays a night used by his teammates. An improvement of 5.7 points in their simple Offensive Rating translates to 3.4 points per game that can be credited to Anthony drawing the defense. Using the rule of thumb that each point of differential is worth approximately 2.7 wins over the course of the season, the Carmelo effect appears to create 9.3 wins per 82 games, or 7.5 over the 66 games Anthony actually played last season--a figure 50 percent higher than the value WARP assigns his usage.

Using plus-minus statistics provides another way of checking Anthony's impact on the Denver offense. The Nuggets are actually scoring better without Anthony this season, but that is out of line with his plus-minus history (via BasketballValue.com and 82games.com). Prior to this year, Denver's Offensive Rating was at least 2.0 points better per 100 possessions in every year of Anthony's career. The average impact in this span was +4.6 points per 100 possessions. Despite the fact that his own efficiency has been middling at times, Anthony has consistently lifted the Nuggets' offense with his ability to create shots.

As Silver noted, there is still an important aspect of "fit" that cannot be removed from the numbers. Denver has been able to build a lineup around Anthony's high usage. The Nuggets have put a series of low-usage, defensive-minded shooting guards alongside him on the wings, for example. With another team already blessed with shot creators, like the Knicks, the value of Anthony's usage might be limited. In a vacuum, however, a variety of different numbers point to similar conclusions. We may not be able to put an exact number on how many wins Anthony's ability to create means for his team, but it appears to be larger than zero and substantial enough to make him an All-Star-caliber player despite his other shortcomings.

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Kevin Pelton is an author of Basketball Prospectus. You can contact Kevin by clicking here or click here to see Kevin's other articles.

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