The Left Tail of the Talent Distribution in the NBA

Posted on October 7, 2007 by


Sports fans tend to put athletes into one of three categories.  There are great players, such as Tim Duncan, Kevin Garnett, and Steve Nash.  Then there are good players, like Lamar Odom, Corey Maggette, and Ray Allen. And then there are average players. 

This latter category appears to contain all players who are not “great” or “good.”  In other words, sports fans tend to live in a place adjacent to Garrison Keillor’s Lake Woebegone.  In Lake Woebegone, “all the women are strong, all the men are good looking, and all children are above average.”  In sports we see a similar story.  All players are either average or above average.  In essence, no one is ever “bad.”

If we think about it, though, we know someone has to be below average.  Performance tends to follow a normal distribution. Most players hover around average.  A few players, though, are “great” and these can be found in the right tail of the distribution.  And just as we have a few players who are well above average, there also must be a few players who are way below average. Such players reside in the left tail of the distribution.  And one of these is the primary subject of today’s post.

The Impact of Willie Green

Last summer the Philadelphia 76ers were pre-occupied with Allen Iverson.  Should “the Answer” be traded or not?  While Philadelphia postponed their answer to the question of “the Answer, the team did make one move.  The 76ers re-signed shooting guard Willie Green to a five year contract. And Green responded to this new contract by posting a career high in points per game.  So although the 76ers didn’t do much last summer (they did a great deal during the regular season), the one move the team did make looks like it worked out.

Well, that would be your story if all you looked at was scoring.  If you looked at Green’s complete statistical profile it would be hard to find a reason to place him anywhere near Lake Woebegone.

Table One: Evaluating the Performance of Willie Green

Table One reports what Green did in 2006-07 per 48 minutes, as well as was what he has done across his career.  And for comparison sake, I also report the average performance of a shooting guard per 48 minutes played.

The aspects of Green’s performance where he is below average are marked in red. And yes, this table just bleeds.  Relative to an average shooting guard, Green is below average in his career with respect to shooting efficiency (both from the field and the line), rebounds, steals, blocked shots, assists, turnovers, and personal fouls.  The only thing he does at an above average pace is take shots from the field.  And this propensity to take shots allows him to score at an above average level.

When we put the whole picture together, we see that Green is not just a bit below average.  Last year an average shooting guard would have produced 3.8 wins in Green’s 1,842 minutes.  Green, though, posted a (-4.6) Wins Produced.  In other words, replacing Green with just an average shooting guard would increase Philadelphia’s wins total by 8.4 wins.  Such a change would have put the 76ers in the playoffs last season.

Let me put this performance in some perspective.  Andre Iguodala is the leading producer of wins for the 76ers.  Iguodala’s WP48 (Wins Produced per 48 minutes) was 0.195 in 2006-07.  Such production across 3,062 minutes was worth 12.4 wins to Philadelphia last season.  In sum, Iguodala is really good.

However, the combination of Iguodala and Green was only worth 7.8 wins.  Replacing both players with average performers would have given the 76ers 10.2 wins, or 2.4 more victories. This means that the distance between Iguodala and the average player is smaller than the distance between Green and an average guard. 

Okay, more perspective.  Green is 8.4 wins below average.  Replacing Kobe Bryant with an average shooting guard would have cost the Lakers in 2006-07 about 8.8 wins.  So Green is as far below average as Kobe is above the mean.  

The Least Productive

Alright, Green is clearly living in the left tail.  But he is not there alone.  Here are the ten players produced the lowest quantity of wins (or the most negative totals) in 2006-07.

Table Two: The Ten Least Productive Players in 2006-07

Leading the list is Adam Morrison, who I have discussed previously.  As Table Two indicates, if the Charlotte Bobcats had replaced Morrison with an average player the team could have expected to win 11.6 more games.  Yes, Morrison had a truly awful rookie season. There is hope (not much, but some) that Morrison can get better.  Other names on this list, though, are not likely to improve.  Jason Collins, Antoine Walker, and Brian Scalabrine are all veteran players who do not have much hope of turning their games around. 

Addition by Subtraction

Okay, there is a reason why we tend to all wish to live in Lake Woebegone.  Saying that people are “bad” is not nice.  

It’s important to note that when I say Green is a “bad” basketball player, I am not saying he is a “bad” person.  Just like many “good” basketball players don’t seem to be particularly “good” people, I am sure there are many “bad” players who are really nice people. For example, John Amaechi came across as a fairly nice person in promoting his book last year.  But for his career he produced (-18.9) wins, so he clearly qualifies as a “bad” NBA player.

So why am I picking on Green?  Well, I was going to write a post reviewing the 76ers in 2006-07.  And my angle was the impact of Green.  But it took me so long to flesh out this angle that I decided to focus the entire post on Green and other “bad” players, saving the Philadelphia post for another day.

So although this column sort of wandered off in a different direction, it does make an important point. When we look the Celtics in 2007-08 we note the importance of adding “good” players like Kevin Garnett, Ray Allen, and James Posey.  But a team can also see the same impact in the standings if it simply replaced a truly bad performer with someone who was just average.  In sum, addition by subtraction is a real phenomenon.  It simply requires that one recognizes which players need to be subtracted.

– DJ

Our research on the NBA was summarized HERE.

The equation connecting wins to offensive/defensive efficiency is given HERE

Wins Produced and Win Score are discussed in the following posts

Simple Models of Player Performance

Wins Produced vs. Win Score

What Wins Produced Says and What It Does Not Say