Per Diem: Greatest Big 3

[spectator]

http://sports.espn.go.com/nba/column...PERDiem-101224



When it comes to NBA star trios, it's all about branding.
The famous three-man pairings in NBA history have all benefited from a catchphrase, with the unoriginal but overwhelmingly obvious moniker of the "Big Three" in Boston being the most famous & so good they've used it twice, in fact. Similarly, before ever playing a game the Miami Heat's combo of LeBron James, Dwyane Wade and Chris Bosh conjured up a number of nicknames -- from complimentary ones like "Miami Thrice" and "Three Kings" to loaded names such as "The Three Mi-Egos" or "The Scheme Team."


Get past the slogans, however, and you might be surprised who the best big threes really are. In some cases, the third guy wasn't anybody we considered a big star at the time, but who was dramatically more effective than many more-famous third wheels. Jamaal Wilkes and Horace Grant, for instance, didn't move pulses the way some other famous players did, but each was part of one of the most effective championship trios in history.
The Heat aren't the first team to realize that when it comes to winning championships, it takes three to tango. It's long been viewed almost as a given that to win a championship a team needs three star-caliber players, especially in the salary-cap era in which the theoretical limit of max-contract players on a roster is three.

Analysis of recent champions shows that while this rule isn't ironclad, it's a fairly predictive rule of thumb.
I mention the Grants and Wilkeses of yore because they become important in relation to the current Miami group. Inevitably, we find ourselves asking questions, such as "Does Miami have the best star trio in history?" or "What star trio would they have to surpass to claim the honor?" But to know the Heat's place in history requires knowing everyone else's, too.


Which takes us to today's project: The "Trio Rating." Before the season, I created a formula to rate each season by a championship star trio since 1979-80, so that we can then compare the progress of the Miami trio (or any other) against some historic bars.

Trio Rating: How it works

As mentioned above, we only looked at championship teams, because it's difficult to dub a star trio the "best ever" when they were beaten.
As for the 1979-80 cutoff, that decision was made based on more practical reasons: The league didn't track individual turnovers until 1973-74, making comparison with previous seasons difficult. Since no trio from the later part of the '70s had any cachet whatsoever, the entry of Magic and Bird to the league seemed like a natural cutoff.

Trio Rating: The Formula

Trio Rating = (((EWA1 x EWA2 x EWA3)1/3 x (82/games) x (LDE/TDE) x (LDE/TDE) x 67 x 30)/2500) + 10.8
LDE= League Defensive Efficiency
TDE= Team Defensive Efficiency
EWA1=Estimated Wins Added of Player 1
EWA2=Estimated Wins Added of Player 2
EWA3=Estimated Wins Added of Player 3


My formula for rating the teams consists of three parts: player efficiency rating (PER), minutes played and the team's defensive performance. The CliffsNotes version is that we weighted the results of the top three players on each team and added or subtracted based on how the team defended relative to the league average. (The team defense adjustment is appropriate here given that, in nearly every case, we're looking at the team leaders in minutes and the club's three most important players.)
If that's all you want to know about the formula, scroll down two paragraphs. For the scientific types who want to replicate the study, read on. For each team, I took the estimated wins added (EWA) of their best three players (which is derived from PER and minutes played), multiplied the EWAs and took the cube root of the result. This has the effect of emphasizing having three strong performers rather than a single great one, so that we're more truly rating star trios rather than a team like, say, the 2001-02 Lakers, who had two awesome players and nobody else remotely close.


Having done that, I made the defensive adjustment by multiplying the score by (league defensive efficiency/team defensive efficiency), and then repeating the same operation. This gave a bonus of 18.1 percent to the best defensive team of the bunch (the 2007-08 Celtics) and a 3.5 percent penalty to the worst (the 2000-01 Lakers). Then I converted the score from an EWA measure back to a defense-adjusted PER for a 2,500-minute season by working backward from the EWA formula -- basically, we multiply by .804 and add 10.8 (the average replacement level PER across all five positions).

Having done all that, we ended up with a Trio Rating for every championship team for the past 32 years.


The surprise winner

As you can see from the chart below, the top individual season doesn't belong to either of the famous Celtics trios, nor a couple other ballyhooed triumvirates. Rather, it's the 1991-92 Bulls with Michael Jordan, Scottie Pippen and Horace Grant. How? Well, Jordan won the MVP award and was the league's best player, all three had PERs in the 20s and they played more than 9,000 minutes between them.


If you think this was just a case of Jordan's greatness lifting the overall average, you couldn't be more wrong. Actually, Jordan is the "weak" link here. As a great third banana, Grant brought up the average substantially -- his 1991-92 season had an EWA of 12.9, tying with Tony Parker in 2007 for the best mark of any third wheel. Pippen also had the best EWA of any No. 2 performer that season. The Bulls would have ranked even higher except that Jordan had something of an off year by his own ridiculously lofty standards.


Given that the Bulls won 67 games and a le with that group, even though no other player on the roster had a PER above the league average, their perch as the best single-season trio makes perfect sense. In fact, the Jordan-Pippen-Grant group can argue itself as the best "era" trio as well: They have three of the top 11 Trio Ratings for their three championship seasons.


Top-rated championship trios, 1980-2010

Season Team Trio Rating Player 1 Player 2 Player 3 1991-92 Bulls 26.4 Jordan Pippen Grant 1995-96 Bulls 25.0 Jordan Pippen Kukoc 2006-07 Spurs 25.0 Duncan Ginobili Parker 1999-00 Lakers 24.1 O'Neal Bryant Rice 1990-91 Bulls 24.1 Jordan Pippen Grant 1996-97 Bulls 23.5 Jordan Pippen Kukoc 1985-86 Celtics 23.4 Bird McHale Parish 1982-83 76ers 23.3 Malone Erving Cheeks 1979-80 Lakers 23.2 Kareem Magic Wilkes 1992-93 Bulls 23.1 Jordan Pippen Grant 2004-05 Spurs 22.8 Duncan Ginobili Parker 1983-84 Celtics 22.8 Bird Parish McHale 1981-82 Lakers 22.2 Magic Kareem Wilkes 2008-09 Lakers 22.0 Bryant Gasol Bynum 2007-08 Celtics 21.8 Garnett Pierce Allen

What about Boston?

These results no doubt will offend fans of basketball's most famous trinity, that of Larry Bird, Kevin McHale and Robert Parish. Unfortunately, I'm not ranking trios by how famous they were. Moreover, Boston's was more a case of long-term effectiveness than a single dominant season. While the 1986 champions produced the No. 8 season on the chart, their 1984 team was only 13th, and the 1981 champs didn't even include McHale in the trio. In terms of single-season dominance, they don't quite rank with the cream of the crop.


The same applies to the more recent Big Three of Kevin Garnett, Paul Pierce and Ray Allen, who ranked "only" 15th of the 32 champions. Garnett's 16.0 EWA was among the lowest of any leading man, hindered in part because he played only 2,328 minutes. Even the huge defensive adjustment couldn't entirely make up for their more modest offensive production and minutes played.


In fact, another big three that won a lone championship a year after trading for an all-time great proved far more potent in this ranking. The 1982-83 76ers united Moses Malone, Julius Erving and Maurice Cheeks and own the No. 9 spot on the board. If we had done a "big four" they may have ranked first -- Andrew Toney had virtually the same rating as Cheeks at a very solid 9.3 EWA.


L.A.'s top-ranked trios

Lakers fans may similarly be surprised by the chart, as the Magic Johnson-Kareem Abdul-Jabbar-James Worthy combo doesn't crack the top half of the list. The problem here is one of timing; by the time Worthy was ascendant, Kareem was deep into his 30s and no longer the dominant force he'd been at the start of the decade.
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As a result, L.A.'s top-rated one-season trio is the Shaquille O'Neal-Kobe Bryant-Glen Rice combo in 1999-2000. The still-young Kobe and fast-fading Rice were solid complements, but L.A.'s crew ranked fifth mostly because of Shaq's monstrous 31.5 EWA.

A more long-lived trio was the first great threesome of the modern Lakers era -- Magic, Kareem and Jamaal Wilkes. That was the trio leading the Lakers to the first two championships of the '80s, in 1980 and 1982, and to the Nos. 9 and 13 spots on the list. Wilkes has been largely forgotten but was a heck of a player and more effective than the No. 3 in several more-famous big threes. He made three All-Star teams and multiple All-Defense squads, and his 11.0 EWA in 1979-80 was the third-best of the No. 3's on the chart.


Toni Kukoc: Third Wheel Extraordinaire

Nonetheless, the two trios with the strongest claim to rival the Jordan-Pippen-Grant group are two that we don't often mention. The first is Chicago's second three-peat team that featured Jordan, Pippen and Toni Kukoc.

Yes, Kukoc. While Dennis Rodman was more famous and certainly more integral to defending Karl Malone in the Finals, Kukoc played more minutes in two of the three seasons and outperformed Rodman in PER by a vast margin. The fact that Rodman was unemployable after 1998 while Kukoc remained a second-tier star supplements the idea that The Waiter was more valuable -- at least in the regular season -- than his more-famous teammate.


Kukoc was good enough, in fact, for the 1995-96 and 1996-97 Bulls to hold the No. 2 and No. 6 spots on the list. (Pippen missed half the regular season in 1997-98, crushing that team's rating.) While Kukoc's minutes totals weren't high, his PERs in those seasons (20.4 and 20.2) were the best of any third wheel's except Grant's.


In 1995-96, Kukoc averaged a point every two minutes with a 58.9 true shooting percentage. And despite playing power forward, Kukoc had the best assist rate of any Bull except Pippen. A year later he missed 25 games with injuries, but posted the then-highest assist rate in history of any player 6-foot-10 or taller (Kevin Garnett later topped it).


However, one other star trio also warrants serious mention -- because it is still active. San Antonio's combo of Tim Duncan Manu Ginobili and Tony Parker owns the No. 3 spot on the list with their 2006-07 season, as well as the No. 11 position in 2004-05. The three are getting long in the tooth but still have put up big numbers over the past two seasons. Should the Spurs eke out another le, they would likely join the Jordan-Pippen-Grant group as the only one with three finishes in the top dozen.


What about 2010-11 Heat and Lakers?

And now, the biggest question of all: Where might Miami's trio end up on this list? And, where will this season's Lakers threesome land if they manage a threepeat?
I approached the situation in two different ways. First, to take the long view, I looked at some statistical projections I did for the Heat's stats in an article I wrote last summer. The results were a PER of 29.0 and 3,100 minutes for James, a PER of 25.6 and 2,850 minutes for Wade, and a PER of 22.9 and 2,600 minutes for Bosh.


2010-11 Trio Ratings

Team Top Three Players Rating
MIA James, Wade, Bosh 26.7
LAL Bryant, Gasol, Odom 24.8
SA Ginobili, Duncan, Parker 23.2
OKC Westbrook, Durant, Ibaka 21.5
BOS Garnett, Rondo, Pierce 21.5
BOS Garnett, Pierce, Allen 21.2

Using those numbers, Miami would have come out on top by a mile. Wade and Bosh had the best projected EWA of any No. 2s or No. 3s, by far -- Wade and Bosh, in fact, would have rated fairly strongly as a 1-2 combo on their own. With no team defense adjustment rating whatsoever, Miami's projected rating of 27.5 would haved still comfortably surpassed Chicago's in 1991-92. But these were only projected numbers.


Alas, as we now know, putting this trio together has been a bit stickier. All three players have fallen well short of their former offensive numbers, at least thus far, and as a result their EWA's don't quite match those of the Chicago trios. Still, at the moment they would rank No. 1 by a hair, with a 26.7 Trio Rating, thanks in part to their often spectacular defense, which has them No. 2 in the league in defensive efficiency.


And how about the two-time defending champion Lakers? Their last two teams didn't rate on the same level as those Bulls, but this season's edition may land in better company. Through 29 games the trio of Bryant, Pau Gasol and Lamar Odom have a 24.8 Trio Rating, which would put them near the top of our list if they manage the threepeat. And if those three put up the same numbers and the defense improves over the final 53 games, L.A. could even rival the Bulls' mark.


Of course, that threepeat talk takes us to the one giant asterisk when discussing either team. In the all-time rankings, we are rating only championship trios, and the 2010-11 Heat and Lakers haven't won yet. Until they do, Jordan, Pippen and Grant are safe in their perch.

[spectator]

Top-rated championship trios, 1980-2010

Season Team Trio Rating Player 1 Player 2 Player 3
1991-92 Bulls 26.4 Jordan Pippen Grant
1995-96 Bulls 25.0 Jordan Pippen Kukoc
2006-07 Spurs 25.0 Duncan Ginobili Parker
1999-00 Lakers 24.1 O'Neal Bryant Rice
1990-91 Bulls 24.1 Jordan Pippen Grant
1996-97 Bulls 23.5 Jordan Pippen Kukoc
1985-86 Celtics 23.4 Bird McHale Parish
1982-83 76ers 23.3 Malone Erving Cheeks
1979-80 Lakers 23.2 Kareem Magic Wilkes
1992-93 Bulls 23.1 Jordan Pippen Grant
2004-05 Spurs 22.8 Duncan Ginobili Parker
1983-84 Celtics 22.8 Bird Parish McHale
1981-82 Lakers 22.2 Magic Kareem Wilkes
2008-09 Lakers 22.0 Bryant Gasol Bynum
2007-08 Celtics 21.8 Garnett Pierce Allen

[DieHardSpursFan1537]

Top-rated championship trios, 1980-2010

Season Team Trio Rating Player 1 Player 2 Player 3
1991-92 Bulls 26.4 Jordan Pippen Grant
1995-96 Bulls 25.0 Jordan Pippen Kukoc
2006-07 Spurs 25.0 Duncan Ginobili Parker
1999-00 Lakers 24.1 O'Neal Bryant Rice
1990-91 Bulls 24.1 Jordan Pippen Grant
1996-97 Bulls 23.5 Jordan Pippen Kukoc
1985-86 Celtics 23.4 Bird McHale Parish
1982-83 76ers 23.3 Malone Erving Cheeks
1979-80 Lakers 23.2 Kareem Magic Wilkes
1992-93 Bulls 23.1 Jordan Pippen Grant
2004-05 Spurs 22.8 Duncan Ginobili Parker
1983-84 Celtics 22.8 Bird Parish McHale
1981-82 Lakers 22.2 Magic Kareem Wilkes
2008-09 Lakers 22.0 Bryant Gasol Bynum
2007-08 Celtics 21.8 Garnett Pierce Allen

[spectator]

in my opinion, this shows how much we depended on duncan from 99 to 04. he was the main guy on a team with really poor supporting cast (ok, it was not a bad supporting cast, but in the context of great championship teams, those players were either too green or too old; i still remember the 04 playoffs when no one other than timmy could average more than 16 pts/game vs la). for those who have seen those games, i would point out many play-off games that the spurs finished/played for significant stretches without parker and/or without manu.

in addition to that, duncan is the only player to have led (this part is huge - as the best player on the team) a team to 4 championships, without having another top 15 player on his team that year. for this, i would direct you to the wikipedia page for all-nba teams (99, 03, 05 and 07 spurs had no one other than timmy in top 15). the disgrace of giving the finals mvp to parker can only be appeased by the fact that the same thing happened to other greats of the past (e.g. cedric maxwell instead of bird for the 81 celtics).

for those who are fans of advanced statistics, i would point out that the player with the highest play-off win shares ever recorded is the 03 tim duncan: http://www.basketball-reference.com/..._season_p.html

he is so far above everyone else that his HOF induction plaque should hold the number for future generations to remember.

the bottom line is that duncan carried the 99-04 spurs and he made the 05 to 08 trios become legendary because he was - similar to jordan - out of this world.

[SpursDynasty85]

[DMC]

ESPN in the mouth. They have the Bulls and Lakers alongside Miami in their pic, yet the Spurs are above the Lakers on that list.

ESPN articles should be banned here.

[kaji157]

How are we tied with the Bull for the second place but came up 3rd and the Lakers are tied up with the bull for the 4th and came up 4th?

[DMC]

Bigger question: What about all the teams throughout the years who had great trios (or great duos, throw in a third wheel to qualify) who maybe had better stats but didn't win a ring? Since the Heat are being compared to actual winners, why not compare the other teams who are actually not winners?

More ESPN Heat bull .

[Manudona]

So, Tim Manu Tony are only behind the 1991-92 Bulls 26.4 Jordan Pippen Grant? And people are still arguing which is the best active trio???

[DMC]

It's all stats. Durant is the season's scoring leader, but he's not the best player in the game. There's a lot more to a player than the stats Hollinger used.

[chazley]

Bigger question: What about all the teams throughout the years who had great trios (or great duos, throw in a third wheel to qualify) who maybe had better stats but didn't win a ring? Since the Heat are being compared to actual winners, why not compare the other teams who are actually not winners?

More ESPN Heat bull .

I'd venture to say it wouldn't make a huge difference, but this Heat sample size is too small to compare to anything previous champions have done anyways, it was pretty much a useless article in that sense, but it was a cool article overall.

[DMC]

I'd venture to say it wouldn't make a huge difference, but this Heat sample size is too small to compare to anything previous champions have done anyways, it was pretty much a useless article in that sense, but it was a cool article overall.

Is that your way of telling Hollinger "cool story bro"?

[Josh810]

"Miami Thrice" is the gayest thing I've ever heard

[Phenomanul]

I was a bit irked by the "Big Three" in-game-caption during the 1st Quarter of the Lakers/Heat game.... Of 8 possible slots to give mention to Duncan/Ginobili/Parker trio they weren't even an afterthought...

I really, really abhor the ABC/ESPN agenda machine... always the first to cry if and when the Spurs "kill" their ratings but it's their own fault for not giving them enough credit... when they do; it always comes off as "forced"...