Posts Tagged ‘Michael Jordan’

In the last post, I looked at nine of the most explosive wing scorers of the past 25 years. In a 40-point game, the ball has to go in the hole frequently, thus, TS% is quite good on average in such games. But what about removing scoring from the equation and simply looking at shooting volume?

High-Volume Shooting

Let’s use field goal attempts to examine what happens when these players shoot a lot, setting the cutoff at 30 or more FGA’s in a game. These are high-volume attempt games, in which efficiency counts more than lower volume games.

Returning to variance, here are the standard deviations for the same nine players in 30+ FGA games. “Stdev” is the standard deviation for the statistic to its left:

Again, LeBron James is a beacon of consistency, although he only shoots 30+ shots about once in every 20 games. LeBron also shoots the ball much, much, much better than anyone else when he shoots it this much. Note the ridiculous TS%.

So does that translate to team success? Actually, no. The ONLY player of these nine perimeter scoring-machines to see his team’s win% increase when he shoots the ball so much is…you guessed it, Allen Iverson. (Kudos if you actually guessed it.) Below are the results, along with frequency of 30-shot games and relative true shooting percentage (Rel TS%):*

This, despite Iverson having a break-even relative TS% (only Wilkins was worse relative to the league environment in such games). Which hits at the volume-efficiency tradeoff argument, because Iverson seems to be a player who can increase his volume — here, 95 of 561 games (16%) with over 30 attempts — and maintain similar efficiency to his normal standard. That’s not a ringing endorsement for Iverson as a team cog, but it certainly helps to justify his role and value in a system like Philadelphia’s.

On the opposite end of the spectrum is Kobe Bryant, whose teams suffer mightily when he shoots the ball a lot. And, unfortunately, he’s done this about every eight games in his career. Bryant’s relative TS% in such games is almost 3% off his normal average in the same time period, and his scoring varies greatly. (How many players have a 40-point difference between their two highest FGA games?)

This is further evidence that good players can shoot too much. All of these stars, except for Allen Iverson, see a drop in their team win% in high-volume attempt games. Some might cry chicken-and-egg; Are the star players suddenly shooting this much because the team is losing, or are they losing because of so much shooting? There is ample evidence that one player going rogue, or worse, forcing shots doesn’t help an offense in the first place. Being behind is no excuse to abandon ship and undertake a flawed strategy.

Coming full circle, as far as I know, there isn’t a single advanced metric that considers variance. Nor is there an advanced metric that takes into account team strength in matters like variance and volume. Means are beneficial, but wins are tallied after 48 minutes. It’s not like overall point differential — while a great predictor — determines playoff seedings. Perhaps we should look beyond averages and weigh consistency and team strength against those averages in individual player analysis.

*Relative TS% and win% difference are weighted by year. For eg, if half of one’s 40-point games were in a single season, that one season’s TS% and win% differential accounted for half the weight in both categories.


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In the last post, I examined different measures of variance in this generation’s Mt. Rushmore of wing players, LeBron, Kobe, Wade and Michael Jordan, all the while keeping in mind that it’s possible for inconsistent play to result in a few more wins on weak teams and fewer wins on good teams.

Of those four superstars, Kobe Bryant had the most games with “inefficient shooting” (under 50% True Shooting) and the fewest games with “efficient” shooting (over 60% True Shooting). However, we ignored the amount of shots he attempted when he was shooting poorly or shooting well. Turns out, all four players shoot more when they’re shooting poorly. And of the group, Dwyane Wade has the biggest increase in FGA’s per 36 minutes in his inefficient shooting games. In order of change in FGA’s per 36 from good games to bad:

  1. Wade +1.2 (17.6  in good shooting games to 18.8 in bad ones)
  2. Kobe +0.9 (19.1 to 20.1)
  3. Jordan +0.4 (21.7 to 22.1)
  4. LeBron +0.2 (18.7 to 18.9)

Before we focus on attempts any further, let’s first look at what happens when elite wings score a lot.

High Volume Scoring

There have been just nine wing players with at least 25 40-point games since 1987 (the beginning of Basketball-Reference’s game logs):

  • Michael Jordan
  • Dominique Wilkins
  • Allen Iverson
  • Vince Carter
  • Kobe Bryant
  • Tracy McGrady
  • Gilbert Arenas
  • LeBron James
  • Dwyane Wade

We have our four usual suspects and five more players who collectively amassed 35 All-Star game appearances and 26 All-NBA nods. Not too shabby. Here is the volume and frequency of 40-point games from this group during their prime scoring years:

Not surprisingly, the greatest scorer in NBA history, Michael Jordan, dropped 40 in nearly one in every five games during his prime years. Yikes. Although Jordan isn’t the most efficient of the bunch in such games. That would be Gilbert Arenas, who boasts nearly 70% True Shooting in his 40-pointers:*

As expected, all these players increase their efficiency in 40-point games. Although Kobe’s shooting numbers are surprisingly low, residing next to someone labeled as an inefficient “chucker,” Allen Iverson. So Iverson and Kobe must not be helping their teams win those big games as much as their contemporaries. Right?


It turns out that Iverson’s teams actually improved the most when he scored 40 or more!*

In Iverson’s 72 40-point games, Philadelphia’s win% improved by nearly 20%. That’s a startling contrast – about 16 extra wins over the course of a season. But why would Iverson’s teams improve so much when he has the lowest relative TS% of the lot?

If we buy the argument that AI’s 76er teams lacked a scorer who could create his own offense — certainly a reasonable stance — then Iverson’s scoring explosions shored up that offensive deficiency and buoyed them to victory more often than his run-of-the-mill 25 or 30-point nights, regardless of the drop in efficiency relative to his peers. (This somewhat echoes Paine’s Monte Carlo run.) Besides, AI’s shooting efficiency in such games is still significantly better than both the league average and his own career average.

There’s also further evidence here supporting the idea that weaker teams are helped more by big performances: Jordan played on the best teams in this time period (win% with MJ in the lineup of .713) and saw the smallest change in team W-L when going for 40. From 1990-1998, once Chicago ascended to elite team status, the Bulls were 68-20 when Michael went for 40 or more, for a .772 win%. Slightly worse than his team’s .779 win% (387-110) when he didn’t go for 40.

Tracy McGrady played on the second worst teams of these nine players (Arenas the worst). When McGrady was in Orlando (01-04) the Magic went 19-11 (.633) in his 40-pointers. 121-144 (.457) in his other games. Then he went to a better Houston Rocket team, and went 7-4 (.636) in 40-point games and 119-66 (.643) in other games.

The same reasoning explains why LA has faired so well despite Kobe’s lower efficiency numbers; Many of Bryant’s games were in 03, and 05-07 when his team needed volume scoring. LA was 50-24 (.676 win%) in his 40-point games in those years, while going 112-119 (.485) in Kobe’s non-40 games. (In the other seasons, a .724 win% in his 29 40-point games and a .715 win% in all other games.)

So these players are helping bad teams with big scoring nights and not doing much for good teams with the same outbursts. Balance, it seems, is indeed better.

Yet we haven’t completely addressed the issue of what happens when players shoot a lot. That is the topic of Part III

*Relative TS% and win% difference are weighted by year. For eg, if half of one’s 40-point games were in a single season, that one season’s TS% and win% differential accounted for half the weight in both categories.

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Last June, Neil Paine over at Basketball-Reference examined consistent vs. inconsistent performances by Kobe Bryant and LeBron James vs. the Boston Celtics. Using one catch-all metric (statistical plus-minus), James and Bryant had similar average performances over the course of their series. But their game-to-game performances varied greatly; James was high-variance — some great games and some awful ones — while Bryant was steadier throughout. If we buy Neil’s simple Monte Carlo simulation, his findings were:

  • Good teams are helped more by a consistent player
  • Average teams are helped more by a consistent player
  • Bad teams are helped more by a high-variance player

This makes sense to a certain degree; Big performances by stars can boost bad teams to wins they otherwise wouldn’t have had, and the bad performances still result in losses they probably would have incurred anyway. In theory, the inverse would hold true for good teams and really bad performances by stars.

Last year’s NBA Finals aside,  Bryant is actually more high-variance than James using measures like points, FG% and GameScore. (GameScore is a rough measure of productivity for a single game.) Below is a comparison of variance between the best wings of my lifetime, Kobe (2001-2010), LeBron (2006-2010), Dwyane Wade (2006-2010) and Michael Jordan (1987-1998):

“Stdev” is the standard deviation of the statistic to its left. If we use a summary statistic like GameScore, LeBron wins the consistency battle handily. Jordan would place second by virtue of his ridiculous 25.3 average GameScore, then Wade and Kobe by the same logic.

If we focus on consistency of shooting and scoring, LeBron wins again. (LeBron outpacing the field is becoming a theme on this blog.) Of course, one could argue LeBron played with a weaker team from 2006-2010, so higher variance would be better when compared to Kobe and Jordan. But unlike Neil’s Monte Carlo run, LeBron’s averages are significantly higher than Kobe’s and Wade’s to begin with.

Kobe, not surprisingly, is higher variance with his FG% — easily the lowest of the lot — and in particular with his scoring performances. But only looking at standard deviations overlooks the importance of the averages. A lower average means more poor shooting games.

EDIT: Bryant’s GameScore standard deviation is 9.5 (mean 22.0) from 2005-2007 on his “weak” teams.

Another way to view consistency is by frequency of games, delineated in a specific range. For instance, we can call games over 60% True Shooting (TS) “efficient” shooting games and games under 50% TS “inefficient” shooting games.

Player Efficient Games (> 60% TS) Inefficient Games (< 50% TS)
Michael Jordan 41.4% 20.5%
LeBron James 40.1% 21.6%
Dwyane Wade 37.8% 26.7%
Kobe Bryant 35.3% 29.3%

Now Bryant’s shooting inconsistency can be seen more clearly. While James and Jordan have an efficient game twice as often as an inefficient one, Kobe shoots well a little more than 1/3 of the time, and shoots poorly a little less than 1/3 of the time. And, if we come full circle to the original claim about consistency helping good teams, that doesn’t bode well for Kobe Bryant’s impact on wins relative to his averages.

For those visually curious, and for the sake of consistency, here is the distribution of TS% for all games played in the respective time frames:

The frequency of games based on TS% for elite wings. Frequency (y-axis) is the percentage of games a player shot a given TS% (x-axis) for the following years: Jordan (87-98) Kobe (01-10) LeBron (06-10) and Wade (06-10).

Of course, none of this accounts for volume — in theory, players should shoot more when they shoot well, and shoot less when they shoot poorly. And that is the topic of the next post: high-volume scoring games.

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Unfortunately, Basketball-Reference doesn’t have a pace-adjusted scoring metric. I normalize most of my stats to an estimated 75 possessions played, which for points produces a “scoring rate,” per se. For instance, Wilt Chamberlain averaged over 50 points per game in 1962. But he played more than 130 possessions a game using the simple method of pace estimation. That comes out to about 28.1 pts/75, not enough to make the cut here.

Up to that point in NBA history, Chamberlain’s number was the highest scoring rate. Individual players just didn’t score as much — teams were more balanced before expansion and the advent of the 3-point line. So Wilt’s season did stand out in its time. For comparison, some other notable pre-1980 players and their highest career mark:

  • Bob McAdoo 26.7 in 1975.
  • Kareem Abdul-Jabbar 25.4 in 1972.
  • Rick Barry 25.3 in 1975.
  • Tiny Archibald 25.0 in 1973.
  • Elgin Baylor, 24.7 in 1962.
  • Jerry West 23.4 in 1965.
  • Oscar Robertson 21.5 in 1968.

Listed below are the top scoring rate seasons in NBA history, measured in points scored per 75 possessions. “Rel TS%” is True Shooting% (TS%) relative to the league average. For example, if league average is 50% TS, and a player boasted a TS% of 53%, he would have a Rel TS% of 3%.

Regular Season

Yes, Michael Jordan owns seven of the eight best normalized scoring seasons ever. Not too shabby. Two other names that might surprise people are LeBron James and Karl Malone. Malone has three top-30 seasons, all at ridiculous shooting efficiency. James was a scoring machine before winning his first MVP, and holds four top-30 seasons.

What about playoff rates? Let’s only consider players who have played in at least two postseason series in a given playoff. If we do that, we get the following select club over 30 pts/75:

Playoffs (minimum 2 series played)

Again, MJ occupies more than half of the list, with LeBron’s 2009 epic playoff run topping the list. Some notable single-series performances that did not qualify: Jordan vs. Boston in 1986 (35.7 pts/75), Hakeem Olajuwon vs. Dallas in 1988 (34.9) and Dwyane Wade in 2009 (vs. Atlanta) and 2010 (vs. Boston) posted 31.2 pts/75 in both series.

The big Chicken and Egg question here: Are top-end scorers better than they were in the past, or have changes in the game simply facilitated more individual dominance?

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Thanks to the recent statistical movement in major sports, basketball now has its share of “advanced” metrics to dazzle the eye and confuse the mind. All the new acronyms can be a little overwhelming at times: PER. WS. APM. TNT. OK, so the last one’s a TV network, but there are enough formulae that we need genius George Costanza to explain things:

Player Efficiency Rating (PER)

PER is a decent all-encompassing stat for summarizing basic box score data. But it has issues. The major failures of PER can be read about here, with the big flaw explained nicely:

Given these values, with a bit of math we can show that a player will break even on his two point field goal attempts if he hits on 30.4% of these shots. On three pointers the break-even point is 21.4%. If a player exceeds these thresholds, and virtually every NBA played does so with respect to two-point shots, the more he shoots the higher his value in PERs. So a player can be an inefficient scorer and simply inflate his value by taking a large number of shots.

Which means that volume shooting is rewarded by that metric as opposed to volume scoring. 11-30 shooting (37%) scores better than 5-12 shooting (42%). Yet at low percentages, the more attempts there are the worse the outcome is for overall offensive efficiency. Sorry, but I don’t find too much “advanced” information in a stat like that.

Wins Produced (WP)

The other advanced stat that I rarely ever use. There is a good detailed discussion of Wins Produced here.

The biggest issue with the stat is how it treats scoring and rebounding, which is how it was possible to predict 57-wins for the Warriors this year after summer transactions, while simultaneously identifying shooting guard as their weakest position. Monta Ellis, the team’s leading scorer and ostensibly its best player, happens to play SG.

With WP, a player who shoots under 50% from 2-point range hurts his score, regardless of how much he scores. Rebounding is given tremendous importance and there is no way to generate a negative rebounding score. Compare the following results based on the marginal values:

  • Player A: 17-30, 5 rebounds
  • Player B: 3-3, 15 rebounds

Player A earns 0.288 WP’s. Player B 0.576. Which means Ben Wallace is way better than Kobe Bryant. In other words, Wins Produced just assumes that scoring at a reasonably high baseline-rate will happen automatically. So the flaw with both WP and PER is the way they treat scoring, which happens to be the most important element of the game. Kind of a major flaw in a metric.

Plus-Minus Statistics

There is an entire family of +/- numbers that have been tracked this decade stemming from raw plus-minus.

  • Raw +/- is borrowed from hockey, and measures the team’s net result with a player on the court. When player A is in the game, if his team is 10 points better than the opponent, Player A’s +/- is +10.
  • On/Off looks at what happens when Player A leaves the game as well. If Player is +10 for the half of the game he plays, and in the other half his team is +10 without him, his on/off is 0. In theory, he didn’t affect team play much.
  • Adjusted Plus-Minus (APM) attempts to correct for teammate and opponent quality when a player is on the court.

Raw +/- has its obvious issues, some fleshed out in this New York Times article. Namely, team quality is the primary force behind the stat. Derek Fisher has an enormous +/- figure, but that probably has something to do with being on the floor with Kobe Bryant and Pau Gasol. It’s hard to find too much value in raw PM, particularly over short periods.

On/Off corrects much of that issue by looking at how a player performs relative to his own team. It’s an incredibly good stat for measuring situational value, assuming adequate sample sizes APM models also have some theoretical value, although not without issues.

There are three important things to be mindful of when comparing on/off and APM:

  1. The worse a team is, the easier it is to have a large number
  2. Noise
  3. The problem of Multicollinearity

First, when Kevin Garnett used to leave the game for the Minnesota Timberwolves, they’d fall apart. In a nutshell, Garnett’s impact measured in on/off and APM was enormous in Minnesota because it’s a lot easier to improve a 20-win team than a 60-win team. When Michael Jordan subbed off the court for the Dream Team, they probably didn’t miss a beat.

Second, there is an incredible amount of noise in plus-minus figures. A 10-0 run here, an injury there, some garbage time, whatever. In a small sample — something that plagues the plus-minus family — these make a big difference. Ken Pomeroy ran an interesting simulation to show how profound this effect can be in small samples.

Third, multicollinearity is a statistical phenomenon that, in this context, means the same players are constantly playing together. For example, Odom and Bryant in LA or Varejao and LeBron in Cleveland. It becomes difficult for any plus-minus model to differentiate between two players if they always play together.

For further issues facing APM models, I suggest Joe Sill’s paper on Regularized APM (RAPM). I will not delve into RAPM models because even Genius Costanza would be bored by machine learning techniques.

Win Shares

The good news about Win Shares (WS) is that they require no Ph.D. and yet they aren’t bland (the full explanation is here). WS are the resident stat over at Basketball-Reference and based largely on Dean Oliver’s great work with the box score. Win Shares are an extension of the individual ORtg and DRtg stats based on Oliver’s work.

Win Shares use box scores values, compares them to league averages (like points per possession) and finally adjusts for possessions played. The number of win shares is not based on actual team win-loss record, but the formula is designed to estimate contributions to a win based on these numbers, and the resulting shares approximates win-loss record quite well.

So, how in the world do we interpret Win Shares? First, similar to PER, they are limited by using only traditional box score metrics. However, unlike PER, I’ve yet to find a glaring flaw in WS. PER will break down if there aren’t enough shots to go around, which happens on a balanced team like the 2008 Celtics. Which result passes the sniff test?

Player PER Rank WS per48 Rank
K. Garnett 25.6 5th .265 2nd
P. Pierce 19.6 30th .207 10th
R. Allen 16.4 81st .177 21st

It’s fairly obvious that Win Shares is doing a pretty decent job ball-parking a player’s value using just the box. As such, I think it’s a really good summary/quick glance stat and much prefer it over PER. Of course, it will sometimes incorrectly assign credit based on certain roles because of failures in the box score. For instance, distributors like Steve Nash are thought to be slightly undervalued by Win Shares. Defensive players who don’t bode well in rebounding, blocks or steals will be undervalued by WS.

The other factor to be wary of when looking at the per 48 minute rate is just how much that player plays. Manu Ginobili is a great example of being able to do more well because he’s logging shorter periods on the court.

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In 1966 Wilt Chamberlain attempted 25.2 field goals per game. He led the 76ers in True Shooting% by a comfortable margin. In other words, Wilt was the team’s most efficient scorer and he shot it the most. But did he shoot too much? This idea might seem counterintuitive; Wouldn’t a team want its most efficient player to shoot more, not less?

Surprisingly, less can be better.

Based largely on Braess’s Paradox, there is an excellent paper by Brian Skinner called “The Price of Anarchy in Basketball” that explains how this is possible.  (Here’s an intersting blog post which might be easier to ingest.) In Chamberlain’s case, his scoring attempts represented one possible “path” for his team to score. In 1966, he converted those attempts at 54.7 TS%.

But there are other “paths” the team followed to score. Sometimes Chamberlain twisted, turned and passed. Sometimes, he didn’t even touch the ball before a teammate shot. For all the “paths” that didn’t end with a Wilt attempt, the 76ers team scored at a rate of 47.1 TS%.

Instinctively, one might ask why doesn’t Chamberlain shoot more since he converts so much more frequently than his teammates? Perhaps he should shoot every time and his team’s TS% would gravitate toward 54.7%? I hope it’s intuitively obvious why that’s not a good idea and why we’ve never seen something like that work at basketball levels above Lisa Leslie’s high school games. (Efficiently declines as usage increases, and practically speaking, the other team might adjust by double or triple-teaming if it were working.)

Indeed, it’s possible for Chamberlain to actually shoot less and have his team’s overall efficiency improve. If he looks to pass the ball more and aid his teammates in scoring (or even be used as a distraction off the ball), he can shoot a lot less — even shooting at the same or lower (!) efficiency — allowing his teammates to be more efficient, leading to an overall increase in team efficiency.

After all, the goal is to optimize team performance, not an individual’s, and it turns out at high levels of basketball this can rarely be done with an individual shooting too much. In the case of Wilt’s 76ers, the optimal offensive balance was one in which Wilt shot less. Significantly less.

In 1967,* Chamberlain shot the ball eleven fewer times per game. This, after several record-setting seasons in which he shot at least 25 times per game in each season. The result? The league’s best offense by a landslide — using the simple method of pace estimation, 6.7 points better than average — and the highest rated offense to that point in league history.

*The 66 to 67 Phily team is a great example of this phenomenon due to little team turnover and retaining the same core group of players, one through six.

His teammates scored at 50.7% efficiency. Wilt’s TS% went up as well. But, here’s the most interesting wrinkle: Even if Chamberlain’s TS% had remained the same, the overall team efficiency would have gone from 49.0% to 51.4%, and at well over 100 “attempts” per game, that results in a colossal shift in scoring efficiency. (As it were, the team’s TS% increased to 52.8% because Chamberlain’s TS% also increased.)

In 30 NBA player seasons has someone attempted more than 25 FGA’s per game. Only one of them, point guard Tiny Archibald in 1973 (who also led the league in assists), played on a league-best offense. That doesn’t mean offensive machines like McAdoo, Gervin, Jordan, Bryant and even the oft-maligned Allen Iverson don’t significantly help a team’s offense in high-volume roles. It just means the best offenses in NBA history are never too focused on an individual shooting the bulk of the attempts. And sometimes, as in the case with Wilt’s Sixers, a team’s optimal approach can be to increase everyone else’s role and decrease the superstar’s.

Most of those players carried offenses with a good deal of success.  Some were even elite. But as impressive as 25 points per 75 possessions on positive TS% is, it can also be less optimal for the team if it would perform better with that player taking fewer shots. The more evenly distributed pathway is often the better one.

Practically speaking, it’s easier to defend an individual than a balanced attack of five players.

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Only a handful of MVP-level players have ever switched teams in the middle of their careers. Before this year, the biggest void left had been Moses Malone’s departure from Houston in 1982. That team completely fell apart in 1983 as Moses sauntered to fo fo fo. But then LeBron took his talents to South Beach. And it turns out, that might have been a pretty good decision. No pun intended.

Here are the largest drops in team SRS after the departure of a superstar:

  1. LeBron (Cavs) – 14.9
  2. Moses (Rockets) -10.7
  3. Shaq (Lakers) -6.7
  4. Shaq (Magic) -6.4
  5. Barkley (76ers) -4.0

That list only includes players changing teams mid-career. Look at the list if we include superstars who retired and simply left basketball, like Magic and Jordan. (OK, technically they both un-retired and are likely planning comebacks for 2012.)

  1. Jordan (Bulls) -15.8
  2. LeBron (Cavs) – 14.9
  3. Moses (Rockets) -10.7
  4. Magic (Lakers) -7.7
  5. Wilt (Lakers)  – 7.3*

*Jerry West also missed 51 games in 1974

Only the Bulls also lost Scottie Pippen. And Dennis Rodman. And Luc Longley. And Phil Jackson. After 35 games this year, Cleveland’s top-8 players in minutes are Parker, Varejao, Jamison, Gibson, Williams, Sessions, Hickson, Moon.

Last year, outside of James, the leaders in minutes were Williams, Parker, Varejao, Hickson, West, Z, Shaq, Gibson, Moon, Jamison,** with only the three players in red departing.

**Aqcuired via trade and has averaged 2 fewer minutes per game this year

That’s fairly strong roster continuity outside of James. And yet the decline in the Cavs is essentially unparalleled in NBA history. It’s even comparable to the deconstructed Bulls of 1999.

It’s not news that LeBron James has been really good for the last few years. What might surprise people is just how god-awful the team around him was.

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