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
Wages of Wins Journal 
Jed
August 2, 2007
Hi DJ,
As a big KG fan and MN native, I’ve been eagerly awaiting this post ever since the trade. Thanks for coming through in a big way.
I wonder, concerning your application of the 80-20 rule, if there are any indications that a more “egalitarian” win distribution helps or hurts teams in general. Although my econ is a bit rusty, I know that there has been some research on the impact of the Gini coefficient (as I understand it, a measure of how stratified income distribution is in a society) on all sorts of indicators, such as corruption or total GDP.
Maybe it’s similar in the NBA. That is, a team with more smoothly distributed win scores (80% of wins from 80% of players) does better, all else being equal, than a team with a highly polarized distribution (80% from 20%).
I have no strong intuitions about whether or not this is the case, but it doesn’t seem obviously false. Off the top of my head, some reasons to expect this might be a) ability to overcome injuries to key players, b) ability to compensate for an off night”or key matchup, c) a tendency to keep all players interested, “on their game” and producing at their highest level instead of letting a superstar take over, etc.
I’m not sure what use this conclusion would be if it were true, though, since a team would always want to increase its total win score, even at the cost of increasing win-score inequality (“a rising tide lifts all players”). Even so, it would still be interesting, I think, just to see what patterns emerge retroactively.
BDG
August 2, 2007
I don’t think a successful egalitarian team would last long. For that to happen a lot of players would have to be above average. Wouldn’t those players want to be paid accordingly? That team would soon be in luxury tax hell. Plus there’d be the temptation to go somewhere else for more of the spotlight (and probably more cash).
A team of equally sucky players could last a while though.
Jacob Rosen
August 2, 2007
Detroit, 53 wins, 1st East – 55%
Cleveland, 50 wins, 2nd East – 65%
Chicago, 49 wins, 3rd East – 75%
Toronto, 47 wins, 4th East – 62%
Dallas, 67 wins, 1st West – 66%
Phoenix, 61 wins, 2nd West – 86%
San Antonio, 58 wins, 3rd West – 70%
Houston, 52 wins, 4th West – 50%
Utah, 51 wins, 5th West – 72%
Denver, 45 wins, 6th West – 65%
Top ten teams in the NBA – 67%
Other twenty teams – 76%
Playoff teams in the East – 69%
Non-playoff teams in the East – 78%
Playoff teams in the West – 69%
Non-playoff teams in the West – 77%
That is what jumped out at me first when I looked at the data. By my calculations, there is only a insignificant -0.347 correlation between top three percentage, and win summation, but it is still very interesting.
Mr. Parker
August 3, 2007
I suspect that the average will get much
closer to 80% of team wins coming from
top 3 players if their were a control for
games missed while injured.
Charlotte is a good example of this. If Sean May
played more games he would surpass Felton
in wins produced, his teams wins would increase,
and he would be solely responsible for the
increase thus the big 3 win percentage would
go up.
Steve Walters
August 3, 2007
Outstanding post, Dave. Brilliant, provocative, and well written.
Like Jed and Jacob, the thing that emerged from your discussion for me is that while a team’s win total does, indeed, tend to be concentrated a la Pareto, there seems to be a high correlation between a team’s overall success and the strength of its supporting cast. Kudos to Jacob for summarizing that data; I was thinking also of calculating a correlation coefficient between “the rest’s” output and a team’s overall quality from your Table 1.
So now I have 2 worries: Are PP, RA, and KG over the hill? And what else will Ainge do to help them out?
He could still screw this season up, IOW, even if the 3 Amigos are wonderful. Heaven knows, he’s screwed up before.
Todd
August 3, 2007
Great DJ. I love the analysis. I wonder how
the numbers change in the playoffs. As teams
shorten rotations and those ‘top 3’ guys are
given increased minutes would the percentage of
wins by top 3 players % increase, accordingly?
If so, then a team like the Celtic’s who are all
but assured a playoff spot, are then ‘built for
a playoff series’ and make a serious run even if
they only win 45-50 games???
wil
August 3, 2007
What no contract curve?
Tball
August 3, 2007
What jumped out at me was that twelve teams received less than 10 wins from ‘the rest’. Of those 12 teams, 2 went to the playoffs (Nets and Suns), which means 14 of the 18 teams that received more than 10 wins from ‘the rest’ went to the playoffs. All 7 teams that received more than 14.5 points from ‘the rest’ saw the postseason.
This sort of goes hand in hand with Jacob’s observation (where only 2 of the top ten teams and 3 of the 16 playoff teams received more than average (73%) contribution from their top 3 players), but it appears that getting a significant contribution from ‘the rest’ is a critical component to making the playoffs (significant being a .040+ WP48).
To Todd’s ‘built for the playoffs’ comment, three teams (Suns, Nets, Bulls) received more than 73%. Only one of the three (the Nets) outperformed their seeding (although no one with at least a 63% contribution from their big 3 underperformed their seeding). The small sample size would require far more research to develop any conclusions on the ‘built for the playoffs’ formula thought, but seeding intuitively seems to be a more reliable predictor than ‘big 3’ analysis. One factor that did stand out in the upsets in ’07 is go-to players stepping to the fore (Cle-Det) or failing to do so (GS-Dal).
Jason
August 3, 2007
This was very interesting indeed. If the vast majority of wins are the result of a very limited number of individual players, the chances of quantity trumping quality is minimal. It would also seem to support the notion that in trades, the team that winds up with the best player usually benefits the most, no?
MT
August 3, 2007
This is a super post, Dave!
B
August 3, 2007
I’d expect to see moe efficient scoring out of Allen and Pierce this year and better passing and rebounding numbers out of Garnett. Allen’s going to be getting some easy shots he never saw when he was on the Sonics because of the caliber of players around him. The same goes for Pierce, especially when you consider Garnett’s passing ability for a big man. All signs would point to shooting percentages going up all around. Using their numbers last year is conservative, though I do think there will be an injury at some point and 50-54 wins is about on cue, and Boston just has to hope this injury isn’t at the end of the year.
Jeff
August 3, 2007
Just to comment on Mr. Parker’s post. In the case of Charlotte, having May play more games and thus pushing Felton out of the top three would decrease the top three’s percentage. Felton would provide more wins for the ‘rest’.
OSA
August 3, 2007
Do 20 percent of the players in the NBA receive 80 percent of the salary?
Chippy
August 3, 2007
I love your blogs! I truly appreciate the mathematics and organization that go into making your arguments. I enjoy your articles the most out of all that read, because you back up everything you write with numbers. Keep it up!
steve t.
August 3, 2007
Great article. There area weird correlations all around us that make perfect sense, like advertising campaigns and newton’s law of cooling…but as far as the celtics go, the big 3 WILL go down to injuries. Its just a question of how many games, and what kind of free agents/trades Ainge can scrape together.
I think they will be lucky to get to 50 wins. Then again, if they get there with the starts injured, and they all come back for the playoffs, it could be a good run.
Okapi
August 3, 2007
Similar to this excellent post, Art De Vaney on using power law distributions to model home run totals– http://www.arthurdevany.com/webstuff/images/DeVanyHomeRunMS.pdf
Chirstopher
August 3, 2007
A few thoughts:
Paul Pierce, Ray Allen, and Kevin Garnett averaged 40, 37, 39 MPG last season, respectively. If you look at other prime time players (e.g., K Bryant, V Carter, D Wade) you’ll see that somewhere between 37-40 minutes is about right for an All-Star. That would likely be worth a few more wins in your calculations. Also, R Rondo was the 2nd best rookie last year in terms of WP48. Based on some recent work you’ve done that is more likely to hold. 4 starters with decent WP48’s: 0.202 for Pierce, 0.144 for Allen, 0.330 for Garnett, and 0.189 for Rondo. In the East that is enough to make the Finals, easily. Heck, the water boy could be 5th man :) Ainge needs to use what’s let of the MLE and the BAE to flesh out the bench a bit. Hustle guy, another PG. What I’m more interested in is Doc Rivers. You’ve mentioned doing some research on the link between coaches and players. I really think Doc is not a good coach. Do you have any numbers on that (e.g., if supposed better coaches allow teams to “overperform”) we could see?
kareem
August 3, 2007
Excellent article. I am glad you took a very academic approach to writting this article. You were careful not to overstate your point, but the numbers really drive home your general theory. Thank you so much, it was great pleasure to read you article. Can’t wait to read the rest of what you have to say about the trade
Idaho Jim
August 3, 2007
I love economics and I love Basketball, as a life time Celtics fan I would really like to see them sign a few more ‘Rockets’ and less ‘Nets’ type players. I’m looking at you Eddie House.
TG
August 3, 2007
Yeah, Ive got a comment : WHHAATTTT ?
TBall
August 3, 2007
Christopher’s post reminded me, why is Ray Allen in the big 3 instead of Rondo? If last year’s numbers hold, shouldn’t Allen be part of ‘the rest’?
bill
August 3, 2007
what did it look like say in the 1986 season compared to the 2007 season……… i would really really like to find that out. that is very intriguing. like say bird, mchale and parish and then the rest…… is it very similar??? wow, very intriguing, interesting…. GO CELTICS! rondo and perk will be great for the 1 and 5 in my opinion, rondo is great on defense and very good floor vision and quickness and passing running the offense but does need to improve his shot a bit. thats the 1 weakness but he is good. and perk is a banger at the 5, a big boy that isnt much on offense but is great on defense and rebounding and size……. go celtics!!!!!
bill
August 3, 2007
ray allen is NO WAY in the rest. get real. he is a franchise player.
bill
August 3, 2007
rondo was VERY low on minutes played and allen got hurt after 55 games……. just no way man haha. allen is a frn allstar comin off one of his best years (pre-injury…. and i think 2004-05 was his best personally)…. rondo hasnt even proven ANYTHING yet.
bill
August 3, 2007
allso about the 1986 compared to now i would really love to know how the 86 lakers with kareem magic and worthy compared to the rest would look like.
Zephyr
August 3, 2007
DJ, nice job on the Pareto Principle article. I grew up in Cambridge, recently lived in Seattle, and have an affinity for both Garnett and Heilbroner’s Worldly Philosophers. Great application of economics and sports – an excellent combination when each is well-detailed and rich in insight. Thanks for the contribution.
Kent
August 4, 2007
This post is awesome. Thank you very much for it.
Pete
August 4, 2007
Cheers to Dberri for a trenchant and cogent look at stars vs. role players on NBA teams! :-)
Michael Anstead
August 4, 2007
Hi DJ,
This is an interesting and important concept.
Looking back at Celtic history, the Celtics
won with 2-3 principal stars and several role
players. I really don’t think the ’81 celtics were any more talented than next years celtic roster. A little more talent might help, but establishing chemistry is even more important. Maladjusted talent added to the team would be more of a hindrance than a help. The 81 celts won with a rookie 6th man (Kevin Mchale, a fading star (Tiny Archibald), and journeyman guard (Chris Ford), and a recently acquired center who turned out to be abetter player than even Red could have hoped for (Robert Parish).
The fate of the 2007-2008 Celtics depends more than anything on establishing the right team chemisty and attitude to win a championship in camp than adding more talented players to the roster.
Michael
Jacob Rosen
August 4, 2007
I was thinking about how the Celtics will compare to other teams in the NBA in terms of egalitarianism. As proven by your wonderful analysis, only one team had an absolutely mind-boggling top three ratio, and that was the Phoenix Suns. The Suns had 86% of their wins by their top three players. Crunching some of the numbers, and I uncovered that the trio of Amare Stoudamire (25 years old,) Shawn Marion (29 years old,) and Steve Nash (33 years old,) were all top 18 players in terms of production last season. However, the Suns were fortunate in terms of avoiding major injuries, because their per 48 minute numbers indicate they should only be all top 25 players at best when healthy.
Now let’s return to the Celtics. They have a trio of compelling talent, none of whom are used to having such superstars with whom they can share the ball. Crunching some of my numbers, I found that the trio were all top 40 players in terms of total production (Garnett 2nd, Allen 26th and Pierce 39th,) but when injury free have the potential to be all top 25 players. The only thing that concerns me in comparison to the Suns is that Garnett (31 years old,) Allen (32 years old and played only 55 games last season,) and Pierce (turns 30 years old by the start of the season and played only 47 games last season) are a lot older, and more injury prone. Thus, they have a lot more of a downside because of the bigger potential to be injured or simply under-performing, or at least in comparison to the Suns.
Harald
August 4, 2007
Regarding your Pareto table (apart from obvious focus of the analysis on the Celtics):
– The Top 3 players from Denver are Marcus Camby, Reggie Evans, Nenê Hilario. What? I can understand why Iverson might not be on it yet, but where did Carmelo go?
– Same with Detroit. Where is Sheed?
– Chicago: Gordon?
– Golden State: J-Rich?
– Miami: Shaq anyone?
– Milwaukee: Michael Redd?
– Sacramento: Bibby?
– etc.
Are the guys I mentioned not among the Top 3 players that produce most wins? Did they miss too many games? If they are not the ones that produce most wins when on the floor they would be definitely overpaid.
George K.
August 4, 2007
Very, very interesting commentary. Thanks so much. Dave, does the negative correlation between top 3 % of wins and wins have something to do with diminishing returns?
Brian
August 5, 2007
I agree in principle with your points – however…
1)I would like to know how you determined the wins produced stat, or “WP48”. Any stat of this nature is subjective in terms of how you construct the formula.
2)I believe that the 80/20 rule would not be relevant – as their percentage in terms of minutes played will be closer to 45-55% – and minutes are certainly a better standard of contribution than roster space.
I look forward to some enumeration of your formula, to better explain such a vague and undefined statistical analysis.
mrparker
August 5, 2007
Brian,
Gotta read the book my good man. The stat
is not vague at all. Instead, Mr. Berri is
writing as if the reader automatically
understands the principles behind wp48.
P-Dawg
August 6, 2007
Fascinating as usual.
Before I read your piece, I posted on Celticsblog my prediction of 50-55 wins for this tema and a second round playoff exit.
What I’m interested in is the “Doc Rivers effect.” Last year, the Celtics should have won 30 games according to their win scores. They won only 24. Doc Rivers seems to have a talent for getting teams to underacheive. What will the impact of coaching be?
P.
mrparker
August 6, 2007
P-Dawg,
I would account it more to the tank effect.
Teams that dont play their best players major
minutes tend to underperform their projection.
Look at the Spurs. They were projected o win
63 games. Would you call Pop a bad coach?
He didnt play his stars as much and that
is why.
Doc played the young guys major minutes last
year and that is what created the large space
between actual and projected wins produced.
kozlodoev
August 6, 2007
An obvious comment: If the Pareto principle holds, then the optimizing strategy for teams is to invest in the best ‘top 3’ they can afford. The question is, why do teams tend to overpay for bench warmers and role players? Plenty of examples can be pointed out.
I am hard pressed to believe that 30 franchises consistently mismanage multimillion assets.
Another one is the distinction between “wins” and actual playoff success, which is allegedly more valuable. Does the principle hold when examining conference, division, and NBA titles?
erod
August 15, 2007
erod- nyc Only Yankees fan that is still a crazy Boston Celtics Fan. Yeah, that is right. I am dying to see the Pareto Numbers for KG, Ray-Al, and PPierce this year. Those numbers are going to be sick and out of this world to even imagine. Hope the rest of the team can put in their two cents. Hey, I do not want to knock King James(earned it) but he does not have two other guys to support him like PP will have in Ray-Al and KG
John
August 15, 2007
Forgive me if this has already been addressed as I’m new to this site. I am new to this but will become a regular reader. Is point differential factored into the equation? For example say if player x is coming from a team where the point differential -5 and player y is coming from a team where it’s -1. Does it hold the same value? Also where Can I find the formula on your site?