The Pareto Principle and the New Boston Celtics

Kevin Garnett has finally moved on to “greener” pastures. This is something I want to discuss in some detail (which means in multiple posts). Today I want to address an issue raised by Bob Ryan of the Boston Globe. Specifically, can Boston seriously expect to contend for a title simply because the Celtics will have a starting line-up featuring three legitimate All-Stars?

My answer begins with the work of a “famous” Italian economist, but eventually gets back to the topic at hand.

The work of Vilfredo Pareto

Perhaps my favorite course to teach (and I have taught quite a bit of what comprises the economics catalog at most universities) is the History of Economic Thought. This class consists of reviewing the work of various writers who have made a “contribution” to our understanding of economics.

Included in this class is a review of the work of Vilfredo Pareto (1848-1923), an Italian economist who is best known in economics for the concept of the “Pareto optimal position” or a distribution of resources where one person cannot be made better off without making another person worse off. This concept is much applied in the field of welfare economics, and by economists in day-to-day conversation (yes, economists are a fun bunch).

Pareto’s contribution to economics, as the History of Economic Thought website indicates, extends beyond the concept of Pareto Optimality. But despite all he did for economics, 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.

A First Glance at the Celtics

The 2007-08 Celtics are not a finished project. But if the Celtics employ a 15 man roster, then 20% of this team would be Paul Pierce, Ray Allen, and Kevin Garnett. The Wins Produced per 48 minutes [WP48] for each of these players last season was 0.202 for Pierce, 0.144 for Allen, and 0.330 for Garnett. For their careers these averages are 0.224, 0.170, and 0.335 respectively. In sum, each offered a bit less than their career averages last season, which may be a sign of injury or age. If it’s the latter, that’s bad news for the Celtics because you can’t recover from age. But if it’s the former, and the players can fully recover from these injuries, the news is a bit better.

Let’s start our analysis of these players with what they did last season. If we assume each player will average 35 minutes a contest in 2007-08, and their WP48 is unchanged from 2006-07, then these players will combine to produce 40.5 wins. If we assume each player is as productive as their career averages, then the combined wins production – again, assuming 35 minutes a night – is 43.6 wins.

Now if the wins total for these three players represents 80% of the team’s total victories, then the Celtics can expect to win between 50.6 and 54.5 games (depending upon whether we use last season’s performance or the career averages).

The Average Performance of the Top Three and “The Rest”

Again, the Pareto Rule seems far too simplistic to me. Its application to the NBA does teach a valuable lesson, though. 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.

If we were not so focused on the Celtics, we would note that the team with the most production after its three stars in 2006-07 was the Houston Rockets. And the team that received the least from “The Rest” was the New Jersey Nets.

A Second Glance at the Celtics

But our focus is the Celtics. Right now we are not entirely sure who the Celtics are going to play along side Pierce, Allen, and Garnett. If the Celtics surround this trio with a collection that is equal in productivity to what the average NBA team received from “The Rest” (i.e. a WP48 of 0.042), the Celtics can expect to win between 50 and 53 games in 2007-08. If the Celtics are able to find complementary players as productive as what we see in Houston, the wins for this team jumps into the 60 plus range. Of course, if “The Rest” for the Celtics is in the New Jersey Nets range, then we are looking at a team that is going to win less than 45 games.

In sum, this team does look like a playoff team regardless of who else it employs. Still, Bob Ryan is correct to note that the complementary players do matter. Although the Celtics only won 24 games last season, a 45 win season in 2007-08 will be considered a disappointment. For this team to truly contend for a title, “The Rest” is going to have to do something in Boston.

As noted, this is not my last comment on this trade. As Boston settles on its complementary players we will be able to say more about this team. I also want to comment on what this trade means for the Timberwolves. And perhaps another comment on what Pareto means for the NBA is in order.

Although I have not responded to comments much lately (I do read all of these), I am interested in what people have to say, especially with respect to the application of the ideas of a 19th century Italian economist to our understanding of the NBA in the 21 century.

– DJ

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