NBA Championship Title Leaders Adjusted for Era

Introduction


NBA titles leaders are usually trotted out in discussions of the best players in the history of the league. Bill Russell regularly comes up in this respect because the media love to mention that he won 11 out of 13 titles when he was in the league. He's often called the best player or one of the top three best in the history of basketball for that fact alone. However, there were less than ten teams in the league during most of his playoff run. Even conferences today are much larger. In order to contextualize title leaders from different eras, you need to make some simple adjusments.


Methodology


In order to adjust championship titles, first I found the number of teams every year of the league. This was pretty easy, and there are some surprising numbers. There were only eight teams throughout much of the 60's, but after the NBA and ?BL merged in 1950 there were 17 teams. The league soon dropped some teams, but for most of its history new organizations were steadily added until the mid-90's as the Charlotte Bobcats are the only new one.

Next I put together a list of every player for a championship winner since the first title in 1947 when the league was known as Basketball Association of America (BAA). I included everyone who tallied playing time in the playoffs. Unfortunately, that does not include bench guys who didn't receive any minutes, but I don't think it actually matters in the greater context of this study. Teams can give rings to pretty much whoever they want -- even guys who operate the shot clocks have gotten them -- yet I think when looking at who's collected the most titles I think it's more proper to only include the guys who actually played in the playoffs. There are extenuating circumstances like Caron Butler with the Mavericks last year as he got injured before the title run, but ultimately it doesn't affect much of the top standings.

The first method of adjusting titles is to simply rate a title based on how many teams there are in the league. Winning an eight-team league is much easier; there's no debate there. I adjusted each title win to present standards meaning a win in a ten-team league is worth 10/30 or 0.33 titles. I know some will argue that winning a title before the league was "diluted" is more impressive, but you also have an influx of international players and a much larger US population. Basketball also wasn't very popular until the 80's. Another consideration: expansion teams typically take guys from each team, so the level of parity isn't heavily distorted in the years with new teams as one might think. Then a player's adjusted title for each year is added together.

The second method attempts to reward guys who contribute to winning teams as opposed to role players who ride the coattails of better ones to a title. For production, I used Win Shares as it helps guys who play large minutes and those that lead their teams. It's not perfect, obviously, but it separates Hakeem Olajuwon from, say, Rick Fox well. That year's entire playoff Win Shares were used instead of only the finals because it's a larger sample set and producing for the entire playoff run is more important. Then you take the percentage of that player's Win Shares out of his team's for the playoffs and multiply it with that season's adjusted title (teams/30) for the WS title score. Last step is to add a player's WS title scores for each championship year.

Results


In the table below, you can see how the total adjusted titles compare to the traditional total titles leaders. Instead of hall of fame center Bill Russell it's ... Robert Horry. It's surprising, but in some ways it isn't. In a previous study I found that he's the greatest playoff performer in terms of increasing his PER score from the regular season. He's been compared to the NBA's Forrest Gump, always in the right place at the right time, winning championships with Olajuwon, Shaq, Kobe, and Duncan, providing big shots in big moments. A critic of the adjusted titles method would say Horry at the top is enough evidence to sink the list, but he has the most titles out of any non-60's and 70's era Celtic, and the only player who's won multiple titles on three different teams.

More appropriately, Michael Jordan is second on the list with his teammate Scottie Pippen. I think there are many people who consider winning 11 titles in Russell's era than 6 in Jordan's, but there's enough reason to overturn that reasoning. One is that, obviously, it's easier to win when there are less teams in the league, which is what the adjusted titles does, but it's also an era with more rules to spread talent among teams evenly and one with heavier scouting and advanced defense. The Bulls weren't exactly stacked either; Jordan deservedly receives a lot of credit.

The leaders for the adjusted total titles are mostly Lakers and Bulls players at the top, while for the total titles it's Celtics and a few Lakers. One could argue that adjusting for the number of teams in that season is unfair to winners, but again I'd argue that looking at total titles it's unfair to those in the present.

Rank	Player	Adjusted total titles	Last title year	Rank	Player	Total titles	Last title year
1	Robert Horry	6.70	2007	1	Bill Russell	11	1969
2	Michael Jordan	5.60	1998	2	Sam Jones	10	1969
2	Scottie Pippen	5.60	1998	3	Tom Heinsohn	8	1965
4	Derek Fisher	4.90	2010	3	K. C. Jones	8	1966
4	Kobe Bryant	4.90	2010	3	Satch Sanders	8	1969
6	Ron Harper	4.83	2001	3	John Havlicek	8	1976
6	Steve Kerr	4.83	2003	7	Jim Loscutoff	7	1964
8	Dennis Rodman	4.63	1998	7	Frank Ramsey	7	1964
9	Kareem Abdul-Jabbar	4.37	1988	7	Robert Horry	7	2007
10	Tim Duncan	3.93	2007	10	Bob Cousy	6	1963
11	Shaquille O'Neal	3.90	2006	10	Kareem Abdul-Jabbar	6	1988
12	Magic Johnson	3.80	1988	10	Michael Jordan	6	1998
12	Michael Cooper	3.80	1988	10	Scottie Pippen	6	1998
14	Horace Grant	3.67	2001	14	George Mikan	5	1954
14	John Salley	3.67	2000	14	Jim Pollard	5	1954
14	Will Perdue	3.67	1999	14	Slater Martin	5	1958
17	Bill Russell	3.43	1969	14	Larry Siegfried	5	1969
18	Robert Parish	3.27	1997	14	Don Nelson	5	1976
19	John Havlicek	3.23	1976	14	Michael Cooper	5	1988
20	Sam Jones	3.17	1969	14	Magic Johnson	5	1988
21	Kurt Rambis	3.07	1988	14	Dennis Rodman	5	1998
22	Bruce Bowen	2.97	2007	14	Ron Harper	5	2001
22	Manu Ginobili	2.97	2007	14	Steve Kerr	5	2003
22	Tony Parker	2.97	2007	14	Kobe Bryant	5	2010
25	Brian Shaw	2.90	2002	14	Derek Fisher	5	2010
25	Devean George	2.90	2002	26	Vern Mikkelsen	4	1954
25	Jud Buechler	2.90	1998	26	Frank Saul	4	1954
25	Luc Longley	2.90	1998	26	Bill Sharman	4	1961
25	Randy Brown	2.90	1998	26	Jamaal Wilkes	4	1985
25	Rick Fox	2.90	2002	26	Robert Parish	4	1997
25	Toni Kukoc	2.90	1998	26	Kurt Rambis	4	1988
32	Sam Cassell	2.80	2008	26	John Salley	4	2000
33	Mario Elie	2.77	1999	26	Horace Grant	4	2001
34	B.J. Armstrong	2.70	1993	26	Will Perdue	4	1999
34	Bill Cartwright	2.70	1993	26	Tim Duncan^	4	2007
34	James Edwards	2.70	1996	26	Shaquille O’Neal	4	2006
34	John Paxson	2.70	1993
34	Scott Williams	2.70	1993
34	Stacey King	2.70	1993

One problem with the above approach is that role players can rack up titles playing with all-time greats (Robert Horry, Steve Kerr, Horace Grant, etc.) Perhaps a better one is to look at who contributes to the total, and award credit based on total production during the playoffs. The simplest method would be using points, and then more advanced versions add rebounds, assists, blocks, steals, etc. The logical conclusion is to use a method something that takes into account as much information as is possible. Thus, you give championship title credit based on how many wins shares a popular produces compared to the rest of the team. 

The winner by this method is none other than Michael Jordan, and he wins in a landslide. He has 42 more percent than the second ranked player, Kobe Bryant. His lead is enormous, and it's apparent why -- he was the overwhelming force on six championships in the modern era. What Jordan did in the regular season was enough for him to be legendary, but in the post-season he made his name transcendent. Moving down the list the right names are near the top than in the other lists. Robert Horry is still ranked high, but he was a pretty good player, especially for the Rockets. I'm amazed Fisher is ranked so high, however. I tried to season with that by realizing there is one whole Win Share to go around, and a starter can easily take 0.1 of those Win Shares if he gets major minutes even without taking a ton of shots. Fisher won five titles, and on average  he was decent so he totaled over half a title Win Share. 

Rank	Player	Total adjusted Win Shares titles	Last title year
1	Michael Jordan	1.650	1998
2	Kobe Bryant	1.164	2010
3	Tim Duncan	1.139	2007
4	Scottie Pippen	1.035	1998
5	Shaquille O'Neal	1.026	2006
6	Kareem Abdul-Jabbar	0.847	1988
7	Robert Horry	0.763	2007
8	George Mikan	0.684	1954
9	Larry Bird	0.684	1986
10	John Havlicek	0.645	1976
11	Magic Johnson	0.633	1988
12	Sam Jones	0.618	1969
13	Derek Fisher	0.552	2010
14	Bill Russell	0.549	1969
15	James Worthy	0.539	1988
16	Horace Grant	0.508	2001
17	Pau Gasol	0.498	2010
18	Tony Parker	0.497	2007
19	Hakeem Olajuwon	0.481	1995
20	Tom Heinsohn	0.478	1965
21	Manu Ginobili	0.442	2007
22	Dennis Johnson	0.412	1986
23	Jamaal Wilkes	0.395	1982
24	Toni Kukoc	0.394	1998
25	Ron Harper	0.367	2001
26	Kevin McHale	0.333	1986
27	Jim Pollard	0.332	1954
28	Michael Cooper	0.326	1988
29	Isiah Thomas	0.326	1990
30	Dwyane Wade	0.324	2006
31	Norm Nixon	0.323	1982
32	Dennis Rodman	0.318	1998
33	Byron Scott	0.309	1988
34	David Robinson	0.294	2003
35	Joe Dumars	0.276	1990
36	Rick Fox	0.263	2002
37	Robert Parish	0.253	1997

As a tangent, the "record" for highest proportion of Win Shares during a title playoff run is George Mikan in 1949 with an astounding 53.2 percent. Cliff Hagan in 1958 is next with 45.7 percent. Shaq has the modern record at 35.6 percent in 2000 with Tim Duncan close behind in 2003. On another tangent, the way Wins Shares are calculated a player can a negative number, which means he didn't even contribute to nothing; he's worse than that. Teammates Jim Cleamons and John Trapp hold the dubious distinction of lowest Win Shares for the playoffs while still winning a title with -0.018 in 1972 for the Lakers. Darko Milicic, by the way, wasn't far away at -0.011. Take that LeBron.

Awarding titles based on how many competitors you have also brings about the possibility to see adjusted title leaders by team. The Celtics are obviously hurt the most in this because they won most of theirs in the first couple decades of the league. The table below shows the adjusted leaders, and the Lakers take the top spot in this method. Even if you discount the Minneapolis Lakers years they still have the edge over the Celtics. Once again basketball fans are reminded that the titles are nearly all held by a few teams at the top. The NBA has been about dynasties, not parity and competitive balance. 

Team	Total title shares
Lakers	11.20
Los Angeles Lakers	9.27
Celtics	7.90
Bulls	5.60
Spurs	3.93
Pistons	2.70
Minneapolis Lakers	1.93
Rockets	1.80
76ers/Nationals	1.37
Warriors	1.20
76ers	1.10
Knicks	1.03
Heat	1.00
Mavericks	1.00
Blazers	0.73
SuperSonics	0.73
Washington Bullets/Wizards	0.73
Bucks	0.57
Royals/Kings	0.37
Baltimore Bullets*	0.27
Hawks	0.27
Nationals	0.27

Italicized: Championships separated from franchise by city

*: Defunct team (those Bullets aren't the same organization as the Washington one)

Conclusion


People saying Bill Russell is the greatest of all-time because of his titles need take his era into context. This is all without judging 60's era basketball based on its unathletic play, the lack of defense -- there were only eight teams for many of the years he won a championship, and there's no arguing that doesn't make it easier to win a title. They were definitely a great team and historically important, but be wary of making grand assessments about players and teams from that time. Russell's eleven titles when properly valued are less impressive than Jordan's six with the Bulls, Duncan's four with the Spurs, Kobe's five with the Lakers, and Shaq's four. Arguing otherwise is based on the false assumption that all championships are created equal.


Update: Bonus! Picture form. Click to enlarge and share with your friends at school. They're be so envious.

How to Fix Lottery Tanking

The NBA draft lottery is set up to help less talented teams gain more talent through new players. Over the years it's been tweaked and adjusted so that strong teams don't have much of a chance to win the lottery as it's seen as unfair and to minimize the power of intentionally losing games to gain the first overall pick. Before 1985, for a number of years the worst teams in each division would literally flip a coin for the rights for the first pick, meaning you were guaranteed a great pick if you were the worst in your division. The year before people accused Houston of tanking their games in order to draft Olajuwon, who later won them two titles. It was also such a deep draft with the Bulls taking Jordan third and Stockton and Barkley later that it was reasonable to assume there was a high enough incentive to lose games that teams would do it intentionally. And the year before that Houston also won the first overall pick and took 7' 4" center Ralph Sampson, whose career was ended short by injuries. There is no guarantee the first pick will be a great player, but you have a much better chance than picking 12th.

A Brief History

The modern lottery system was started in '85 when the league gave every non-playoff team an equal chance to win the top pick. This led to the Knicks landing Patrick Ewing (third worst record in the league), which created a conspiracy theory that commissioner Stern and company planted the top pick for the Knicks since it would put a big star in their biggest market. Obviously, the problem with giving teams who just missed the playoffs and cellar dwellers the same probability is one of unfairness. The worst teams need more help than the ones with near 0.500 records. Also, starting in 1987 the lottery determined the first three picks, rather than every lottery pick. After the third pick, your record decides your place in the draft. The consequence is that the team with the worst record in the league can do no worse than fourth in the lottery.

In 1990, the league decided to give the worst teams more odds to win the lottery. This was done in a way that the worse your record was, the better your odds. However, in 1993 the Orlando Magic won the rights to the first pick despite having the best record out of any lottery team and odds of winning at 1.5%. This was a year after they drafted Shaq first overall, mirroring the back to back Houston picks in the 80's. The league responded by lowering the odds for the best teams and increasing them for the worst. Since 1994, the worst team had only a 0.5% chance, while the worst 25% instead of 16.7% the year before. Each probability is shown in the table below. Interestingly, the team with the worst record has never had the first overall pick, but don't mistake that fact with any decreased probability of winning the first pick. Odds are odds.

Lottery seed	1	2	3	4	5	6	7	8	9	10	11	12	13	14
Odds (out of 1000)	250	199	156	119	88	63	43	28	17	11	8	7	6	5

The top prizes in the draft over the years since 1994 have included Tim Duncan, LeBron James, Kevin Durant, Carmelo Anthony, Dwight Howard, Jason Kidd, Elton Brand, Derrick Rose, and Blake Griffin. This year it's Anthony Davis, a long-armed defensive star shooting 66% from the field who can handle the ball surprisingly well for a player for his size and is averaging a staggering 4.8 blocks a game with only 1.9 fouls. With how much a single player can transform a team from the bottom of the league to a perennial contender there is a very high incentive to land these players, many of whom are seen as franchise players while still in high school or college. There is also no question that some teams have performed in tanking, intentionally skirting the team's chances for the rest of the season after it becomes apparent the playoffs can't be reached with some maneuvers like placing a healthy player on the injury list (I doubt Eric Gordon would have missed as many games on the Bulls) or trading away all their talent (the Bobcats have started looking for a starting small forward on Craigslist.) The problem is that the organization is throwing away the season for the fans too. You don't just hit "simulate the rest of the season" and hope for a better season next year; people have to watch your terrible games.

Looking back at the history of the draft and why it's developed into the current version, there are two contrasting problems -- tanking to get better draft odds or good teams unfairly winning the top pick. An ideal solution thus balances between the two mechanisms.

The Solution

Here's mine: the bottom seven teams all have the same odds of winning the lottery, and the top seven have odds that decrease with their win total. It would nearly eliminate tanking because if you're bad, there's no incentive to be any worse, and the teams that have lower odds are close enough to the playoffs that they would be much more unlikely to punt the season. The odds linearly decrease after the worse seven teams. If the odds were to plummet at a nonlinear rate with, for example, exponential decay, whose curve sharply drops off then levels, then there would be too much of a difference between the odds for the seventh worse team and the ninth worst, inducing tanking once again. The other flavor is a curve that only gradually declines until the very end, but that arguably gives too many odds to the "best" lottery teams.

Only a little math is needed to distribute the odds. With the current lottery system, the odds are out of 1000, so a team with a 25% chance of winning has 250 hypothetical ping pong balls. Know this, it's a simple algebra equation to create your own system. My proposal calls for even odds for seven teams and linearly decreasing for the rest. Call the highest odds "x" and base everything on that variable.

The straight line that connects the odds for the 14th place team and the seventh has eight different "steps" to reach the top, hence the team with the lowest chance has x/8 odds, the second lowest 2*x/8, etc. It's eight rather than seven because one of the seven teams with the highest odds is included in this imaginary line. Then set it up into a tidy equation and solve:

1000 = 7*x + x/8 + 2*x/8 + 3*x/8 + 4*x/8 + 5*x/8 + 6*x/8 + 7*x/8

1000 = 7*x + x(1/8 + 2/8 + 3/8 + 4/8 + 5/8 + 6/8 + 7/8)

1000 = 7*x + x/8(1 + 2 + 3 + 4 + 5 + 6 + 7) = 7*x + x/8(28)

1000 = 7*x + 28*x/8 = x(7 + 28/8)

x = 1000/(7 + 28/8) = 95.24

The next step is to distribute the odds to each place and round appropriately to ensure the total odds equal 1000. Seen in the table below, the odds are calculated for each lottery team based on how poor their win-loss record was. To convert to percentage, simply move a decimal point in between the numbers (95 to 9.5%, 83 to 8.3%, etc.) Even the worst team only has roughly a ten percent chance of snaring the top. The odds increase by 11 or 12 as you move up in the lottery seeding, but the great thing about that system is that increasing by 11 is more important when you're a 14th seed than an eighth or ninth. You're double you're odds at 14th, but only increasing them by around 14% from eighth to seventh, meaning there is higher motivation to tank to increase your odds the closer you are to the playoffs, which cancels out the effect.

Lottery seed	Odds out of 1000
1-7	95
8	83
9	72
10	60
11	48
12	36
13	24
14	12

With the draft lottery, it's not just the top pick that's decided by the odds; it's the top four. Higher odds means you also have a higher chance of getting the second, third, or fourth pick, and the rest of the draft is ordered by team record (i.e. lottery seed.) I would argue that it would be better to expand that to the first eighth or so picks decided by the odds to similarly discourage tanking. If the league can't figure out how to manage that, how can they run a multi-billion dollar sports business?

Final Thoughts


Rewarding the worst teams with substantially higher chances of landing the top pick creates a league complacent with bad management and unfairly sticks the best players on dreadful teams. Additionally, organizations have an incentive for throwing away entire seasons in the hope of landing a franchise-changing force of nature like a LeBron James or Dwight Howard. By skewing the odds, you can eliminate most of tanking, which punishes fans who pay for the games. A successful lottery system knows how to balance motivation to encourage better played games and the advantages of  better draft lottery chances.

As a last note, in comparing the proposed lottery odds with the current one, the new method spreads the odds more evenly throughout the worst teams. The cumulative odds mean that at lottery seed two it's the sum of the first and second lottery seed, at number three it's the sum of first, second, and third, etc. The five worst teams in the league have over an 80% chance at receiving the top pick, while in the propose system it's  only 47.5%. This is not a tragedy for small-market teams because even if you have little money to pay and attract players with good management you can at least be sixth or seventh from the bottom, which from the lottery standpoint is the same as last place.