Three is the Magic Number

Posted on November 30, 2007 by


Henry Abbott at TrueHoop asked the following question:

Is Three the Magic Number?

I remember sitting with Kevin Pritchard before he was KP, the GM of the Trail Blazers, and he explained the Spurs’ mantra to me: Get three superstars and then fill the roster with guys willing to go through a wall to win.

For the Spurs, you can really see this philosophy in action. I mean look at their salaries. Tim Duncan, Tony Parker, and Manu Ginobili are the only ones who really get paid large amounts or for many years. The other pieces — sorry Bruce Bowen — are priced to move.

The team has been excellent pretty much throughout the Duncan era, but has always given long minutes to players with below average contracts. Today’s Francisco Elson, Ime Udoka, Michael Finley, and Darius Washington are yesterday’s Stephen Jackson, Devin Brown, Avery Johnson, and Mario Elie. The list is long.

And the message seems to kind of be that if you have three stars, anchoring everything, there are a lot of different guys — affordable guys, even — who might be capable of filling in around them. It is a basketball solution rolled into an all-important salary cap solution…..For whatever reason, the Spurs “Big Three” approach has been something that I have been thinking about a lot, ever since I heard it. 

I talked to ESPN’s David Thorpe about it, and he said most people think it takes three stars to win an NBA title, for whatever reason. He also says that he likes those three to be two guards and one big man.

Beyond that, he thinks it makes all the sense in the world to seek out not the most talented or biggest players available, but those most willing to contribute in a supporting role. They need not be expensive.

Return to the Pareto Principle

When I read this story I immediately thought of Vilfredo Pareto, an Italian economist who lived from 1848 to 1923.  Pareto made a number of important contributions to economics, but as I noted last August…

Pareto is perhaps best known for the Pareto Principle, a concept rarely discussed in economics (at least not in my classes). Pareto observed that 80% of the income in Italy came from 20% of the population. This observation led to a general rule of thumb: 80% of outcomes come from 20% of the people. So for businesses, 80% of sales come from 20% of clients, or 80% of your problems come from 20% of your workers, etc…

Although outside of economics the Pareto Principle seems fairly popular, I have always thought the 80-20 rule was far too simplistic. And yet, much to my surprise, it seems to apply to the NBA. In 2006-07 there were 1,230 regular season wins. When we look at Wins Produced, we see that 80% of these 1,230 victories were produced by 22.4% of the players.

Looking at a larger sample, since 1990-91 there have been 18,355 regular season wins in the NBA. Across these 16 seasons there have been on average 431 players per season, or 6,907 player observations across the entire time period. When we look at the data we see that 1,507 player observations, or 21.4% of all players, produced 80% of all victories. So it’s not quite 80-20, but it seems close enough to me.

Yes, when we look at the data we do see evidence that what Abbott is arguing is correct.  On a team of 15 players, the wins will primarily come from the top three players (or 20% of the roster).  Again, I return to what I said last August:

The wins for most teams are derived from just a handful of players. To see this, consider for each team in 2006-07 the productivity of the top three wins producers relative to the productivity of everyone else on the roster – which I call “The Rest”.

Table One: The Pareto Principle in the NBA in 2006-07

From Table One we see that on average, the top three players produce 73% of each team’s wins and these three players have an average WP48 of 0.206. “The Rest” of each team averages a WP48 of only 0.042, which again highlights the point that most wins for each team can be traced to its top players.

Updating the Story

I thought it would be good to update this story for what we have seen so far in 2007-08.  I don’t have the time (or the inclination) to look at every team in the league. But I did look at the top four teams in the Association.

Wait, let’s take a step back.  Who are the top four teams?

One could consider two criteria in ranking NBA teams. The first is the most obvious – winning percentage.  And from that perspective, the top four teams (after Wednesday night) are Boston (0.846), Orlando (0.824), San Antonio (0.813), and Phoenix (0.733).

In addition to winning percentage we can consider efficiency differential (offensive efficiency minus defensive efficiency). According to this statistic, the top four teams (again after Wednesday night) are Boston (12.0), San Antonio (9.1), Utah (8.0), and Orlando (7.8).  Phoenix (5.4) is actually ranked 6th in the league [behind Detroit (6.1)].  It’s important to note that it’s very early and one or two games can still have a huge impact on a team’s differential.

Okay, now that we have identified the top teams, let’s look at two questions:

1. Who are the top three players on each team in terms of Wins Produced?

2. What percentage of a team’s Wins Produced can be traced to these three players?

To answer this question, I have projected each team’s Wins Produced for the season, based entirely on what the team has done this season (as of Wednesday night).  I then evaluate the players on each team to see who should be credited with these wins.  With evaluation in hand, I can now go through each team and identify the top three players, project Wins Produced for these players {as well as Wins Produced per 48 minutes [WP48]}, and calculate the percentage of the team’s projected wins that are attributed to the top trio.  So without further fanfare, here are the top trios on the top teams in the league.

Boston Celtics

Kevin Garnett [28.8 Wins Produced, 0.440 WP48]

Paul Pierce [13.3 Wins Produced, 0.200 WP48]

Ray Allen [11.3 Wins Produced, 0.164 WP48]

Top Trio Wins Produced: 53.4

Team Wins Produced: 72.5

Percentage of Wins from Top Tri0: 74%

San Antonio Spurs

Manu Ginobili [19.6 Wins Produced, 0.398 WP48]

Tim Duncan [15.3 Wins Produced, 0.271 WP48]

Tony Parker [13.7 Wins Produced, 0.233 WP48]

Top Trio Wins Produced: 48.6

Team Wins Produced: 63.3

Percentage of Wins from Top Trip: 77%

Utah Jazz

Carlos Boozer [22.4 Wins Produced, 0.377 WP48]

Andrei Kirilenko [16.3 Wins Produced, 0.283 WP48]

Ronnie Brewer [13.2 Wins Produced, 0.256 WP48]

Top Trio Wins Produced: 51.8

Team Wins Produced: 61.8

Percentage of Wins from Top Tri0: 84%

Orlando Magic

Dwight Howard [29.9 Wins Produced, 0.463 WP48]

Jameer Nelson [12.1 Wins Produced, 0.248 WP48]

Hedo Turkoglu [8.4 Wins Produced, 0.135 WP48]

Top Trio Wins Produced: 50.4

Team Wins Produced: 61.3

Percentage of Wins from Top Tri0: 82%

Phoenix Suns

Shawn Marion [20.3 Wins Produced, 0.317 WP48]

Steve Nash [19.2 Wins Produced, 0.327 WP48]

Amare Stoudemire [8.1 Wins Produced, 0.215 WP48]

Top Trio Wins Produced: 47.5

Team Wins Produced: 55.4

Percentage of Wins from Top Tri0: 86%

Okay, I threw in the Suns – the team with the top trio from 2006-07 — so we have five teams.  Here is what we learned from this list.

1. Again, Abbott is essentially correct.  The wins on these teams primarily come from each team’s top trio.  I should note that the top trio does not always consist of the highest paid players on the team, although for the Celtics, Spurs, and Suns that is the case.

2. Thorpe argued that the top three should be two guards and a big man.  If Paul Pierce is a guard (he plays small forward this year, but has played guard in his career), the Celtics follow this pattern.  And the Spurs do as well.  But the other three teams listed employ a Top Trio consisting of two big men and a guard.   

3. Of this group, the Celtics are the least Pareto-like.  This tells us that the Celtics supporting cast is better than people think. Yes, the Big Three are the key to this team.  But the Celtics are getting above average contributions from Eddie House [0.167 WP48], James Posey [0.141 WP48], and Rajon Rondo [0.138 WP48].

4. So far, Kevin Garnett is producing far more than Tim Duncan.  If this continues (and it’s still early so it might not), will Bill Simmons change his perspective on the relative value of these two stars?

5.  Deron Williams is on pace to produce 11.6 wins with a 0.186 WP48.  This means that all of Utah’s wins can be traced to four players.  Paul Millsap is still above average this year, but Mehmet Okur and Jarron Collins are in the negative range so far.  Again, as I keep saying, it’s early.

6. Dwight Howard is off to a phenomenal start. To put his production in perspective, Shaq’s best season was 1999-00.  Shaq produced 28.2 wins that season with a 0.428 WP48.  It will be interesting to see if Howard can maintain his performance all season.  Although that might happen, we have to remember, though, that it’s still early.  

By the way, did I mention “it’s still early” enough times?

– DJ

Our research on the NBA was summarized HERE.

The Technical Notes at provides substantially more information on the published research behind Wins Produced and Win Score

Wins Produced, Win Score, and PAWSmin are also 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

Introducing PAWSmin — and a Defense of Box Score Statistics

Finally, A Guide to Evaluating Models contains useful hints on how to interpret and evaluate statistical models.