## Is Melo in the top 5? Top 10? How high is he?

For several days as board has been debating the value of Carmelo Anthony as a basketball player. Is he a top five player? Top ten? Is he a gold, silver, or bronze level superstar? I'm going to approach this question strictly from statistics. It doesn't matter (for these purposes) that Melo has never gotten a ring. It doesn't matter how many times he's been an All-Star. It doesn't matter how famous he is and it doesn't matter that he was a legend as a college player. All that matters here is what he has been contributing that shows up in the box score. Now, it may seem that he should do well here, because he is always among the league leaders in points per game. But how do we balance his high scoring, low assist rate, fair rebounding, and so on? Glad you asked J

Over the past few years a number of statistics have sprung up that claim to measure the approximate value of a player with one number, much as on-base % plus slugging % serves as a shorthand for a baseball player’s value on offense. The basic idea behind composite statistics like Kevin Pelton’s WARP or Dave Berri’s Win Shares is to start with the team’s won-lost record.  Then find the relationship between that and the team statistics that also appear next to a player's name: FG, FGA, assists, steals, rebounds, etc. It turns out that these statistics are a very good predictor of wins and losses. Then the statisticians make something of a leap: they assume that an individual player's statistics (at least on offense) represents their proportionate part of the team’s record. There is no way to prove that this is the case, but it does make sense.   Maybe if we look at the top players in the league it will jibe with what we believe about who is the best.  If it does, then we got what the statheads would call convergent validity-- multiple methods of measurement that come out with the same result

So let's look at who the best players in the league are according to WARP (Wins Above Replacement Player). This formula is designed to measure exactly what it says: how many wins will accrue to a team who uses this player as the replacement for someone who is good enough to have a starting job, but is no better than that. I've chosen to use the *total* WARP scores from the past two years, so as not to excessively penalize someone who missed significant time  (Melo, Devin) and not to excessively reward someone who just happen to have their career year in 2009-10.  It definitely hurts Kevin Durant, as he was much better last year than the year before, but so be it. Let's start with the top five:

1-- James                     52.2  WARP

3-- Howard                 40.2

4-- Paul                        36.8

5-- Duncan                  31.4

Nothing surprising to anyone about the top three or the order in which they are ranked.  CP3 may be a bit of a surprise to some considering that he was out most of last year, but WARP rewards things like a shooting percentage better than .500, along with 23 ppg, 11 assists, and 5.5 rebounds, along with being the league leader in steals. On to the next five:

6-- P. Gasol                 28

7-- Rondo                    28

8-- Bosh                      26.8

9-- Durant                   26.2

10-- Bryant                  25.6

Deron Williams is #11.  Pau may be a little higher than some of you expect, but it's not really surprising that the best team in the league would have the 6th and 10th best players.  Rondo was something of a surprise to me, but like CP3, he shoots better than 50% and dishes out and hellacious number of assists.  I'd say that's pretty much the top 10 players in the league contained in those 11 slots.  Well, except those of you who believe that Melo should be up there.

So where’s Melo?  Now let me admit that I may have missed someone along the way: my method was to take the 40 best players I could think of and do the arithmetic with their numbers.

Using that, in total wins over the past two years, Melo comes in 32nd with 15.4 WARP.  That's not a typo.  OK, but he missed some time last year.  Maybe he moves up if we look at his record on a per minute basis. In fact, he does: to 31st.  FWIW, on a per 48 minutes basis the top 10 are:

1--  James                    0.416

2--  Paul                       0.375

4--  Howard                0.341

5--  Duncan                 0.304

6--  Ginobli                  0.264

7--  P. Gasol                0.249

8--  Camby                  0.248

9--  Rondo                   0.240

10--  Bosh                   0.236

Yes, Marcus Camby.  Let it rip on this one.  WARP does put a high valuation on rebounds, because a rebound means an extra possession, which is usually expected to be worth a little over a point.

Finally, a little somethin’ somethin’ for those who just have to see a Net in the stat line:

Troy Murphy, 17.5 wins, .174 per 48

Brook Lopez, 15.9 wins, .164 per 48

Devin Harris, 15.7 wins, .160 per 48.

Now, individual statistics don't tell the whole story, they don't count who defended you or how well you set picks. But I suggest you ask yourselves: why do the stats do right by all the other superstars, but not Melo?

---------------------------------------------------------

Some technical junk at the end:

Some of you may prefer to use John Hollinger's PER.  Please don't.   There are three points to make about that:

1--  PER is the only commonly used composite statistic that is not based originally in the team's wins.

2--  I’ll let Dave Berri say it for me:

“Hollinger argues that each two point field goal made is worth about 1.65 points. A three point field goal made is worth 2.65 points. A missed field goal, though, costs a team 0.72 points.

“Given these values, with a bit of math we can show that a player will break even on his two point field goal attempts if he hits on 30.4% of these shots. On three pointers the break-even point is 21.4%. If a player exceeds these thresholds, and virtually every NBA played does so with respect to two-point shots, the more he shoots the higher his value in PERs. So a player can be an inefficient scorer and simply inflate his value by taking a large number of shots.”

Clearly, someone hitting 30% of his shots is hurting his team by shooting.  PER doesn't see it that way.

3--  as a result, PER often wildly disagrees with WARP and Win Shares, while those two are generally in good agreement.  Convergent validity.

WARP scores can be looked up at http://www.basketballprospectus.com/cardindex.php

(This post is dedicated to Andres B, to whom I was very harsh during a certain draft-related debate.  Apologies)

UPDATE:  for reasons known only to the gremlins in my brain, I forgot to include Brandon Roy in my analysis.  Move Melo to 33rd overall, 32nd per 48 minutes.

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