Stats and the Best Players in NBA History

The week before last, I wrote about Total Statistical Production (TSP), a stat-based rating system for basketball players. If you haven't read that piece yet, go check it out now, or this one won't make any sense.

Okay, ready?

Let's talk about ranking players historically. TSP rewards floor time, and this is intentional. Per-minute ratings sometimes say a sixth man who plays 25 minutes a game, or a starter who misses the last month of the season, is just as valuable as a 40-minute man who plays every game, which — if their per-minute numbers are even close — obviously isn't true. At the same time, however, we don't want players to rate high just because they were on the court a lot. This is particularly important if we want to rate multiple seasons or full careers. Surely there's a way to balance excellence and efficiency with consistency and production? Actually, there are two ways. One involves replacement level, but this week we'll look at my preferred method, TSP2. Let me show you results, and then I'll explain how we got there. By raw TSP, these are the top 10 regular-season players of the '90s:

1. Karl Malone, 86.3
2. David Robinson, 80.5
3. John Stockton, 76.6
4. Hakeem Olajuwon, 69.4
5. Scottie Pippen, 66.8
6. Charles Barkley, 65.9
7. Gary Payton, 65.1
8. Shaquille O'Neal, 61.9
9. Reggie Miller, 61.1
10. Michael Jordan, 59.5

Keep in mind that Jordan retired twice during the '90s and only played about 60% of the decade. Still, even 60% of M.J. probably should rate higher than 10th. The TSP2 list is:

1. David Robinson, 79.4
2. Karl Malone, 75.9
3. John Stockton, 68.4
4. Michael Jordan, 65.8
5. Shaquille O'Neal, 64.7
6. Hakeem Olajuwon, 64.4
7. Charles Barkley, 61.0
8. Scottie Pippen, 54.8
9. Gary Payton, 52.5
10. Dikembe Mutombo, 47.5

I think that's a fair evaluation of Jordan, given that he played 503 games and Stockton played 770. The new list is designed to reward longevity, consistency, and peak performance. To arrive at these ranks, we start with individual seasons (rather than looking at the decade as a whole). Let's use Karl Malone as an example. Season by season, his TSP ratings are:

1990: 9.6
1991: 9.1
1992: 10.0
1993: 8.7
1994: 9.1
1995: 9.0
1996: 9.5
1997: 8.8
1998: 4.4
1999: 8.0
sum: 86.3

To arrive at our new values, take each of those numbers, then square and divide by 10: TSP²/10. Our new results are:

1990: 9.3
1991: 8.2
1992: 9.9
1993: 7.6
1994: 8.3
1995: 8.1
1996: 9.1
1997: 7.8
1998: 5.1*
1999: 6.5
sum: 79.8

* Adjusted for strike-shortened season

By this method, the difference between good and great seasons grows larger. A 10-TSP season is still worth 10 (100/10), but a 5-TSP season is worth only 2.5 (25/10). When we talk about the best ever, we don't just mean someone who played a lot of games — we mean someone who lit the world on fire, who dominated the game, did things that had never been done. Squaring before finding the sum emphasizes peak performance and rewards the players who dazzled us.

There's one more step — two, really. Multiply the player's TSP per minute played (TSP/MP) by 25,000. This usually yields a number similar to his career TSP. Malone's TSP/MP in the '90s was 0.0029, which comes to 72.3. For the final result, find the harmonic mean of the squared sum (79.8) and MP25K (72.3); for Malone, that number is 75.9. The formula for harmonic mean is 2xy/(x+y): 2 * 79.8 * 72.3 / (79.8 + 72.3). This method, TSP2, has limitations, but for full-time players with substantial careers, it is usually effective and provides an accurate representation of their performances.

This method is not effective for individual seasons. In fact, it's ridiculous. To adapt it for individual seasons, multiply TSP/MP by 3,000 instead of 25,000. You can also use TSP Over Replacement (explained next week), or just use raw TSP, which generally gives an accurate picture on its own and shouldn't require much adjustment.

For rating careers, however, I prefer TSP2. I'll show why now, listing the top players at each position. These lists are exclusively statistical, and do not reflect my subjective opinion. They were generated by finding the harmonic mean of (1) the squared sums of a player's individual seasons and (2) his career TSP/MP multiplied by 25,000. By TSP2, here are the top centers in NBA/ABA history:

1. Wilt Chamberlain, 133.2
2. Kareem Abdul-Jabbar, 111.4
3. Bill Russell, 92.1
4. Hakeem Olajuwon, 87.1
5. David Robinson, 85.7
6. Walt Bellamy, 82.6
7. Artis Gilmore, 80.7
8. Moses Malone, 79.8
9. Shaquille O'Neal, 79.7
10. Bob Lanier, 68.0

Two groups of players are notably underrated on this list: great defenders and elite postseason performers. Traditional statistics usually fail to capture defensive value, and the ratings you see are based solely on regular-season numbers. Russell, who was one of the finest defenders in history, and the most successful postseason player of all time, is probably a lot closer to Chamberlain and Abdul-Jabbar than he appears. Olajuwon probably deserves a boost for the same reasons. Shaquille O'Neal, a three-time Finals MVP, surely deserves to rank higher than ninth. Subjectively, I rank them this way: Wilt, Kareem, Russell, Olajuwon, Shaq, George Mikan, Malone, Robinson, Gilmore, Bellamy.

Rounding out TSP2's top 15: Wes Unseld, Robert Parish, Patrick Ewing, Bob McAdoo, Nate Thurmond. Nowhere near the top 15, Alonzo Mourning (42.7) rates as a very good center, but not nearly as good as his reputation. He ranks behind contemporaries Dikembe Mutombo, Vlade Divac, and Ben Wallace. On the other side, Bellamy, Gilmore, and Lanier are among the more underrated centers. With all due respect to, say, Patrick Ewing, it's absurd to suggest that he was a better center than Bellamy or Gilmore. George Mikan, whom I believe was easily one of the 10 best centers of all time, doesn't make the stat-based list because his career was so short.

Players are listed at the position that I judged to fit them most closely, but some guys spent time at (for instance) center and power forward, or shooting guard and small forward. In this system, fortunately, a player's listed position only affects which list he appears on, not his score. The top 10 power forwards:

1. Charles Barkley, 90.3
2. Karl Malone, 86.5
3. Bob Pettit, 83.5
4. Jerry Lucas, 79.8
5. Kevin Garnett, 78.5
6. Elgin Baylor, 73.5
7. Dan Issel, 70.2
8. Tim Duncan, 69.0
9. Dirk Nowitzki, 67.0
10. Dolph Schayes, 64.1

For anyone doing the math at home, you might notice that a few guys rate a little higher than they're supposed to. Any season shorter than 79 games is pro-rated to 80 games, so players like Pettit aren't punished for playing when the season was only 72 games long. This adjustment is particularly important when we square the single-season TSP, and a shorter schedule represents a significant handicap. This is especially meaningful for the 1998-99 strike season.

The rest of the top 15: Elvin Hayes, Bailey Howell, Shawn Marion, Billy Cunningham, Kevin McHale. TSP2 probably underrates Tim Duncan as much as any player. He's a terrific defender and a successful postseason player, plus he played in the 2000s, when slow game pace limited team possessions, and thus individual opportunities. Garnett and Nowitzki are undervalued for the same reason, as are contemporary players at other positions. This formula rates Duncan as the eighth-best power forward in history, but that's a shortcoming of the system. Duncan is not overrated.

Singling out someone as underrated, I might look at Issel, who played six seasons in the ABA, but was also a terrific player after the merger. I counted ABA seasons as having 90% of the value of NBA seasons. I don't believe Issel is really the seventh-best power forward in history, but I do think he's top-10.

You may note that the scores in the next group are a little lower. Modern small forwards rate about the same as power forwards, but before the introduction of the three-point line, post players who could rebound and score inside were usually far more productive. More on this later.

1. Larry Bird, 81.4
2. Julius Erving, 80.4
3. LeBron James, 63.1
4. Larry Nance, 60.8
5. Alex English, 60.2
6. Adrian Dantley, 58.4
7. Scottie Pippen, 58.1
8. Rick Barry, 57.7
9. Dominique Wilkins, 55.5
10. Chris Mullin, 50.8

Filling out the top 15: Paul Pierce, Terry Cummings, Dennis Rodman, Marques Johnson, Tracy McGrady. Notably absent from the list is Hall of Famer James Worthy (43.3). He was a good player on three championship teams, but the championship aura rubbed off on him in a way that enhanced his reputation beyond reality. Compare Worthy to Nance, who played mostly the same years and about the same number of career minutes:

Worthy scored 633 more points, but he missed 1,032 more shots. Worthy had 398 more assists, but 2,644 fewer rebounds. He had 169 more steals, but 1,403 fewer blocks. He committed 148 more turnovers. Statistically, there is no comparison between them. Yet Worthy's reputation far exceeds Nance's, because he had the good fortune to play with Magic Johnson and Kareem Abdul-Jabbar, on a team coached by Pat Riley.

Two-guards:

1. Michael Jordan, 95.5
2. Clyde Drexler, 69.7
3. Kobe Bryant, 62.0
4. John Havlicek, 56.5
5. Reggie Miller, 56.2
6. George Gervin, 53.8
7. Ray Allen, 50.9
8. Jeff Hornacek, 50.0
9. Fat Lever, 49.5
10. Vince Carter, 47.7

The rest of the top 15: Hal Greer, Alvin Robertson, Dwyane Wade, Dave Bing, Allen Iverson. Two players who deserve special attention are 13th-ranked Dwyane Wade and 15th-ranked Allen Iverson. Wade has only played 547 regular-season games; no one in the top 10 has fewer than 900. When Wade gets more experience, he's a lock for the top 10.

I've listed Iverson as a shooting guard partly just to get him onto a list at all (he'd be 21st among point guards). According to TSP2, Iverson (41.6) is among the most overrated players in history. What TSP sees in The Answer is a guy who played a lot of minutes and took a lot of shots. Iverson was a 42.5% shooter who committed over 3,000 turnovers. You can get away with that if you're Jason Kidd and you have 12,000 assists and 8,000 rebounds, but Iverson only had half that many (5,624 and 3,394).

Also notable by his absence from the top 15 is Joe Dumars (29.7), who benefitted from the same kind of championship halo as Worthy. Playing 35 minutes a game, Dumars averaged just 16 points, 4.5 assists, and 2.2 rebounds, with twice as many turnovers as his blocks and steals put together. That makes Iverson (26.7 ppg, 6.2 apg, 3.7 rpg) look like Michael Jordan.

Few of the shooting guards are terribly underrated. Several of them are a little underrated, but most have reputations more or less in line with what TSP2 shows. The exception is Lafayette Lever. He played only eight full seasons, but his career TSP/MP (.0025) is the third-best of any two guard in history, behind only Jordan and Drexler. Compared to replacement level, he ranks even higher than this. Lever had the misfortune to be a contemporary of Jordan and Drexler, and his skills were subtle. He wasn't a great scorer (shot 44.7% and averaged 13.9 ppg), but he grabbed 6 rebounds and 6 assists per game — sensational numbers for his position — plus he was a very good defensive player.

How many players have at least three seasons averaging 7 points, 7 rebounds, and 7 assists per game? Six: Oscar Robertson, Magic Johnson, Jason Kidd, LeBron James, Larry Bird, and Fat Lever. That's select company. Lever spent most of his career on mediocre Nuggets teams, but in his best seasons (1986-90), he had Magic Johnson numbers: 19 ppg, 9 rpg, and 7.5 apg, with more steals than turnovers every year. He was easily one of the top ten players ever at his position, maybe top five. Point guards below:

1. Oscar Robertson, 101.8
2. John Stockton, 87.8
3. Magic Johnson, 86.2
4. Jerry West, 73.6
5. Jason Kidd, 61.8
6. Gary Payton, 60.2
7. Walt Frazier, 55.3
8. Steve Nash, 53.7
9. Lenny Wilkens, 51.5
10. Maurice Cheeks, 49.7

Okay. Stockton is ahead of Magic. I know. Stockton played 1,500 games, Magic played 900 games. Magic was more effective per minute (0.0032 to 0.0029), but 600 games, almost 15,000 minutes ... If you had a pretty average team, 30-30 or so heading into the end of the regular season, trying to make a playoff push, and you could add Magic Johnson to your roster for 9 games, or John Stockton for 15 games, which would you take?

The issue, when you're rating careers, is that you're not asking about Magic for 900 games and Stockton for 900 games. You're looking at Magic for 900 games and Stockton for 1,500. TSP agrees that Johnson was better when he was on the court, but it sees Stock as more valuable because he played so much longer. Here are some career totals:

Are Magic's 2,500 rebounds worth Stockton's 5,500 assists? Are his 750 fewer turnovers worth Stock's 1,500 steals? Are his 50 blocks worth Stockton's 2,000 points? These are huge advantages for Stockton. I believe Magic should rate ahead anyway, because this data does not include postseason performance. Magic starred in the playoffs and Finals in a way that Stockton did not, and that should move him ahead. That said, I don't believe there's anything wrong with the formula that "mistakenly" caused John Stockton to rate too high, or Magic too low. As an assessment of their regular-season careers, I believe these ratings — which are almost equal, actually — are fair to both players.

The difference between the top three or four point guards and the rest of the bunch is monumental — no one is close. The TSP2 gap between Stockton and Kidd is about the same as the difference between Kidd and Mike Bibby (35.4, about 30th). The Wages of Wins network has been making some noise recently to the effect that Kidd might reasonably be compared to Stockton. Both are all-time greats, but I do not believe their careers are truly comparable.

The biggest differences are rebounds, assists, and especially scoring and shooting percentage. The rebound difference (4,153 in Kidd's favor) and the assist difference (+4,228 for Stockton) roughly cancel out (unless you use a rebound-oriented rating system like the Wages of Wins people do). But the shooting categories represent an enormous advantage for Stockton. Stockton made 1,071 more field goals than Kidd, in 1,207 fewer attempts. TSP recognizes that as a difference of about 30: 2,000 points and 1,000 possessions.

Kidd was such a poor shooter that his offense is basically just ball-handling — his shooting rates only slightly above "worthless" — but the Wages of Wins systems place a huge premium on rebounding, and underrate assists and steals (two areas where Stockton excelled). Win Score, the more basic of the Wages of Wins stats, evaluates boards being just as valuable as steals and twice as valuable as assists. You can judge for yourself whether or not that makes sense.

Kidd rates nearly equal to Stockton in that system ... because he rebounded like a forward. Let me quote from Arturo Galletti: "Big Men (F/C) are on average more productive than everyone else. They in fact account for 50% of all productivity ... a lot of the exceptional players in league history were tall for their position or played and produced like big men (Magic, Charles Barkley, Dennis Rodman, Jordan, Kevin Garnett, and LeBron James are six examples that come quickly to mind)."

Okay, one point at a time:

1. Big men dominate the Wages of Wins stats because the Wages of Wins place enormous emphasis on rebounding. TSP doesn't overrate rebounds, so centers rate the same as everybody else. Their TSP2 totals are higher than other positions because they have longer careers, not because their TSP scores were any higher. A 40-year-old guard who has lost his speed probably can't play in the NBA. A 40-year-old center is still 7' tall and probably still very strong in the paint. But season-by-season, big guys don't rate any higher than guards.

2. Of course players who are an unusual height for their position excel. If you want to be a 6'9" point guard, you had damn well better be Magic Johnson. I remember being 10 years old at basketball camp, trying to explain to my coach that I was a point guard, not a center. I wasn't very assertive when I was 10, so that didn't work, but on the last day of camp, when we had shooting competitions, I finally proved I was the best outside shooter on the team. Someone who is effectively allowed to play out of position relative to his height has to be an exceptional player, or they'll move him back "where he belongs."

3. My favorite part: "a lot of the exceptional players in league history were tall for their position or played and produced like big men." So you either have to be tall ... or else do the same things, even though you're not tall. That's some fascinating analysis: being tall is really important ... except when it's not. If you rate rebounds being twice as valuable as assists, of course you'll say all the best players are big men (or small men who rebound). You might even reach the conclusion that Jason Kidd was just as good as Stockton.

Is Kidd one of the greatest point guards in history? Of course. Was he in Stockton's class? Absolutely not. You compare Stockton to Magic and West; you compare Kidd to Payton and Nash and Frazier.

Anyway, rounding out the top 15 point guards, we have: Chris Paul (rising quickly), Terry Porter, Kevin Johnson, Isiah Thomas, and Tim Hardaway. There are three point guards so badly overrated as to merit discussion. One is Isiah Thomas, a low-percentage shooter who committed a turnover once every 10 minutes. His TSP/MP is about the same as Mookie Blaylock or Sam Cassell — fine players, but hardly all-time greats.

Pete Maravich (33.6 TSP2) played just 658 games, and was active for only 10 seasons. He scored often (24.1 ppg), but he didn't have a high percentage (44.1%) and wasn't a great assist man. Most overrated players have at least three of the following points in common:

1. Famous before they got to the NBA, or made headlines off the court.
2. Played with good teammates and won multiple championships.
3. Scored a lot, didn't get many rebounds or assists.
4. Low shooting percentages.
5. Poor defense.
6. Lots of turnovers.
7. Short careers, so people remember them at their best.

A player who meets one or two of these criteria is seldom significantly overrated. Those who meet 3-4 of the conditions above are usually regarded as being much better players than they actually are. Those who fit five or more of these standards are always significantly overrated. Maravich probably qualifies for four of those points (1, 3, 4, and 7). I'm not trying to pick on Pistol Pete, or Isiah Thomas, or Iverson or Mourning or any of the players I identified as overrated. The tricky thing about calling someone overrated is that it usually leaves nobody happy. Many fans mistakenly read "overrated" as a synonym for "bad", which it isn't. All of the guys I named were good players, some of them very good. But when you label people like that, the fanboys (and fangirls, presumably) come out to defend their heroes, sometimes forgetting their manners. Just to save everybody some trouble, I'm not biased against your team, my mental health is quite sound, and I could beat you in one-on-one.

The other side's problem is that it's very, very hard to refute an "overrated" accusation. If I say James Worthy is overrated, and you say I'm biased/crazy/stupid, it kind of proves the point. I'm saying lots of people think he's great, even though he's not. You say he is so. I mean, have you no sense of irony? Incidentally, though, it's math that thinks Worthy is overrated, not me. Well, actually, I agree — he is overrated — but I'm just passing along the numbers here.

Anyway, the third point guard I wanted to comment on is Bob Cousy (42.7). Last week, I noted, "The equality among positions in TSP goes back more than 30 years. It is true, though, that in the game's early years, centers and power forwards dominated." Oscar Robertson and Jerry West were superstars right away, and TSP recognizes that. But before them (and Lenny Wilkens, who debuted the same year), small forwards and guards — even Hall of Famers like Cousy — don't rate well statistically. Cousy's best season, according to TSP, was 1955-56, when his rating was 6.1 (6.8 if you adjust for the 72-game season). That 6.8 would have ranked 14th in 2010-11, between Al Horford and Amare Stoudemire. Hey, that's a good season. But it's nothing special, and that's Cousy's very best year.

It's not that Cousy is overrated, precisely. He probably was the best guard of his era. But do we really need an adjustment to bring Cousy's scores into line with those of Bill Russell and Bob Pettit, or Robertson and West? I would liken it to what Bill James calls the "Gavy Cravath argument":

"If Gavy Cravath is the best home run hitter of 1915 and Babe Ruth is the best home run hitter of 1925, is Gavy Cravath equal to Babe Ruth? No, he isn't, because 20 homers are not the same as 50, no matter how many home runs anybody else in the league may have hit."

Cousy was a 37.5% shooter, actually never shot as high as 40% in any season. That's on two-pointers. He averaged 7.5 assists per game. Steve Nash averages 8.5, Robertson averaged 9.5, Stockton averaged 10.5, Magic averaged 11.2. Cousy was a good guard, but he was not a dominant player. Dave Heeren, in his seminal Basketball Abstract, wrote that Cousy "was the outstanding NBA guard for the decade of the 1950s. But by standards of any of the succeeding decades neither he nor any other guard of the 1950s was much better than average. Cousy's frilly, but not essentially excellent, style of play became antiquated the minute Oscar Robertson and Jerry West entered the league in 1960."

If Cousy was the best point guard of the '50s, does that make him the equal of Robertson or Magic, the best point guards of their respective eras? No, for the same reason Gavy Cravath wasn't Babe Ruth. The dominant players of the '50s and '60s, apart from Robertson and West, were all big men, and TSP recognizes that. In my mind, a stat adjustment to bring the numbers for Cousy or Sam Jones into line with those of Pettit and Russell distorts what actually happened. When Cousy played, you could win without a good point guard; you couldn't win without a dominant big man.

Similarly, to suggest that Cousy was as dominant in his league as Big O or Magic or Stockton is ludicrous. It's simply not true. I'm not trying to pick on Cousy, because this is true for every guard of his era, but when modern analysts equate Cousy being the best guard of the '50s to Stockton or Kidd being the best of their respective eras, and assume that Cousy was as valuable a player — that's just not the case. For six seasons (1950-56), the Celtics had two Hall of Fame guards, Bill Sharman and Cousy. The team never finished better than second in the East and never reached the NBA Finals, not even once. Guards of the 1950s generally were not very effective players, and TSP reflects that.

A good statistic has to shake things up a little — but only a little. If you're interested in stats, you've probably read something along these lines before: a statistic that tells you nothing you already know is flawed, and a statistic that tells you only what you already know is useless. If TSP showed that Muggsy Bogues was the best player of all time, and Rodman more valuable to the Bulls than Jordan, it wouldn't be useful; you couldn't trust the stat. But if all it did was confirm conventional wisdom, it would be pointless. I believe TSP and TSP2 find the middle ground. They mostly synch up with common sense — the stuff we already know — but there are also some knocks at players who are widely celebrated, like Derrick Rose or Isiah Thomas.

To wrap up this column, I'll present the TSP2 All-Time Team. Next week, I'll tackle replacement value.

First-Team All-TSP2

G: Oscar Robertson
G: Michael Jordan
F: Larry Bird
F: Charles Barkley
C: Wilt Chamberlain

Second-Team All-TSP2

G: Magic Johnson
G: Clyde Drexler
F: Dr. J
F: Karl Malone
C: Kareem Abdul-Jabbar

Third-Team All-TSP2

G: John Stockton
G: Kobe Bryant
F: LeBron James
F: Bob Pettit
C: Bill Russell