OT: LeBron James Fouls 50% Less Than the Average Player

Shapecity · Jan 29, 2010

LeBron James’ statistics are amazing. He’s putting up 30 points, 7 boards, and 8 assists per for essentially the sixth season in a row, and there are exactly zero players who can get close to that trio of numbers for even one season. But he’s doing something else, just as consistently, that no one else of consequence is able to do: not get called for fouls.

Look at the personal fouls column for the top-10 scorers in the league. Nine of them collectively average 2.7 fouls per, falling within the range of 2.3 – 3.4. These nine include some of the NBA’s biggest names who obviously have “earned some calls,” guys who can easily score 10 from the charity stripe in a night while getting the refs’ attention for only their two most obvious hacks.

And the tenth player? That would be James, who averages 1.8–and that’s rounded up. Many people suspect the league helps protect the Wades, Kobes, Anthonys, and other marquee players who keep those turnstiles turning, but how in God’s green earth does LeBron absolutely smoke them all in not getting whistled for defensive misdeeds?

And this isn’t the first time he’s been in the referee’s good graces to this degree. Last year, James averaged 1.7 fouls per. Going backwards from there, you have 2.2, then 2.2, then 2.3, then 1.8, then 1.9… then he was at his high-school prom. Not only is 2.3 fouls per the worst of LeBron’s career, it actually marks the best in the careers of both Wade and Bryant.

Is James, who happens to be the most marketable guy in the league, just that much superior to everyone at not fouling players? We’ve all seen him play, and he’s obviously a very good defender, but he’s no Shane Battier, Ron Artest, Gary Payton, Dennis Rodman, or Bill Russell. James, however, has done a much, much better job than any of them at not being whistled.

Breaking down in great detail LeBron James’ “amazing” fouls rate after the break…

Basic Statistical Comparisons
For starters, we should know how often fouls are being called around the league so we can see if there really is a big difference with LeBron. Through January 22, James played 1702 minutes and committed 77 fouls, good for one foul every 22.1 minutes of court time.

Everyone else in the NBA logged 298,868 minutes and committed 26,473 fouls, good for one every 11.3 minutes. Comparatively, James is half as likely to be called for a foul than the other 300-odd players as a whole. Without even picking up a calculator, it looks like most NBAers who would play 38.7 minutes a game, like James does, would accrue about 3.5 fouls per (remember that his 1.8 is rounded up).

But The Chosen One is no regular professional baller. He just happens to be supremely talented, score a bunch of points, and play on one of the best teams in the league. On top of that, James is the biggest marketing tool the NBA has as it expands its revenue base all over the world in China.

(Eastern Europe and South America have produced far more NBA players, but don’t vote for the All-Star team, aren’t having arenas built in their countries by the league, and don’t host preseason games.)

But the league has had other uber-marketable superstars over the past 30 years. Didn’t they get all the calls as well? Here are three players whose fame and status were similar to LeBron’s, and how their foul counts looked in their first seven seasons:

- As a Laker teamed up with Shaq, Kobe Bryant was a big deal from early on. He guards roughly the same players that LeBron does, and his defensive reputation has been better for most of his career. In Bryant’s first seven full seasons (following two as a reserve), his fouls per game ranged from 2.6 to 3.3, with an average of 2.9.

- Magic Johnson’s smile, collegiate exploits, and style of play made him an instant hit, which the NBA rode up to and beyond his untimely retirement. Magic’s foul counts in his first seven seasons ranged from 1.8 to 2.9, with an average of 2.5 fouls per.

- Michael Jordan was already well known when he entered the league in 1984. He was the NCAA’s consensus Player of the Year, and he had won a national championship at North Carolina. Not only that, I think it’s safe to say that Jordan’s defensive abilities and reputation far trump those of James (Jordan won the Defensive Player of the Year award in 1987-88). His first seven seasons (not counting 1985-86, when he was injured) ranged from 2.5 to 3.5, with an average of 3 fouls per.

Although these three had better foul counts than an average player, LeBron still registers far fewer. On top of that, Jordan and Bryant carried better defensive reputations during their careers, and James often guards big men inside, which almost always results in higher-than-usual foul counts.

Less Than One In a Million
Okay, maybe the Cavs star really is just that much better than the league, other current stars, and three of the most marketable superstars of the David Stern Era at not fouling the man he’s guarding. I’d say that’s highly unlikely, and thankfully math gives us a vehicle to measure how unlikely.

Using a chi-square test (it’s a pain in the ass to explain, so Google away if you’re so inclined) with LeBron’s foul data and the league’s foul data, one derives a chi-square value of 35.9, which translates into a P-value of 0.00000. The P-value is what’s of most use to us here because it tells us how likely something is to happen due simply to chance (e.g. 0.4 means it has a 40% chance of happening). This all means that the likelihood of LeBron’s foul counts occurring with his minutes is less than one in a million.

(A big thank you goes out to Dr. Bradford Crain, a statistics professor at Portland State University, who helped with the calculations and their interpretations.)

That astronomically low number has to be taken with a grain of salt since there are actually a few players in the league who fall into this category, but it’s usually pretty obvious why. For example, Steve Nash is committing a career-low 1.2 fouls per, but he’s such a bad defender, everyone he’s guarding simply dribbles past him and then he’s out of the play. It’s not so obvious with LeBron, considering he’s regularly guarding extremely dynamic players who routinely go to the line, and he’s often banging with the big boys underneath, where a majority of fouls are called.

A more meaningful way to look at the rarity of his foul counts is by comparing him to players who play similar minutes. There are 12 non-centers (centers’ foul counts are always high) who are playing between 38 and 40 minutes per. I decided not to look at their fouls per, since I already know how James stacks up here, but to look at how often these players get into foul trouble compared to James. If a player is in foul trouble, it affects how aggressively he can play in crunch time and if a coach needs to make substitutions, two things that can alter the outcomes of games.

These 12 players (not a slouch in the bunch – Bryant, Gay, Durant, Roy, etc.) combine for 469 games, during which they got called for 4 fouls 53 times, 5 fouls 31 times, and 6 fouls (fouled out) only 4 times. James has logged 44 games, 3 with 4 fouls, and 0 with more. In fact, 4 fouls is the most he’s been called for over the past two seasons.

Using a chi-square test on this data gives us P-values of 0.047 and 0.060 for games with 4-plus and 5-plus fouls, respectively (the calculations for 6 fouls are meaningless since they’re so rare for the entire group). That means that LeBron had a 4.7% and 6% chance of having so few games in those types of foul trouble due simply to randomness. Therefore, something else is at work here (most mathematicians consider anything under 5% to be “significant”).

Checking last year’s data, it’s even worse. There were 10 players who logged between 37.5 and 38.5 minutes per (James, 37.7), and collectively they played 777 games, 109 with 4 fouls, 48 with 5 fouls, and 13 with 6 fouls. James had 9 games with 4 fouls during his 81-game season. This data yields P-values of 0.023 and 0.0089, so he had a 2.3% chance of having so few 4+ fouls games and a 0.89% (less than 1%) chance of having no 5+ fouls games.

Yes, there is definitely something “significant” happening here.

Regular Superstar Treatment?
Maybe the face-of-the-NBA stars ranked similarly low during their top seasons. It turns out Magic was close, but none of them could match what LeBron has been doing for most of his career.

It makes sense to assume Michael Jordan stayed out of foul trouble during his 1992-93 MVP season. In 78 games, he had 4 fouls 10 times, 5 fouls 7 times, and he never fouled out. The nine non-centers who played between 38 and 40.5 minutes totaled 681 games, 124 with 4 fouls, 56 with 5, and 7 with 6. This data yields a P-value of 0.285 for games with 4+ fouls, and 0.936 in games with 5+ fouls. Thus, Jordan had a 28.5% and 93.6% chance of getting into foul trouble at the same rate as these other guys, and he was second to Hakeem Olajuwon in Defensive Player of the Year voting.

Kobe Bryant was similar in his 2007-08 MVP season. In 82 games, he had 18 games with 4 fouls, 6 with 5 fouls, and 1 foul out. The 12 players who played between 37.7 and 39.9 minutes registered 908 games, 162 with 4 fouls, 68 with 5, and 17 with 6. This data produces P-values indicating Kobe’s numbers fit right into this group; he had a 52.3% chance of having that many 4+ fouls games and a 80.5% chance of that many 5+ fouls games.

Magic Johnson did better in his 1986-87 MVP season, playing in 80 games, getting 4 fouls 10 times, 5 fouls 5 times, and never fouling out. The 10 non-centers with 37.1 to 38.6 minutes per totaled 799 games, 128 with 4 fouls, 82 with 5 fouls, and 19 foul outs. The P-values indicate Magic had a 5.9% chance of producing the amount of 4+ fouls games he did with that many games, and a 9.4% chance for games with 5+ fouls. I should mention that these percentages are actually skewed low by the inclusion of four players who had more foul trouble than anyone in LeBron’s years.

None of these players had a percentage fall into the “significant” range, and these three seasons represent some of the best case scenarios of likely “star treatment.”

Conclusions
There is no question that LeBron James is a freakish talent that can do it all, including turning a 17-65 squad into a perennial contender. Not only does he get a lot of points, rebounds, and assists, but he producers these numbers at very good rates (55% eFG%, 11.1 Reb%, 2.2 A/TO).

Where I have some concern is how seldom he’s in foul trouble. This gives an unfair advantage to the Cavaliers, since he never has to watch how he plays or sit for any reason other than to rest. The P-values show how extraordinarily unlikely it is for James to end up with these low foul counts, and his style of play and comparison to more-defensive-minded superstars makes his counts even more unbelievable.

The numbers all come out so ridiculous, it’s undeniable that either a) we’re witnessing a defensive talent more capable than Bill Russell, or b) the NBA/referees are blatantly protecting him. That first one was meant to be a joke, by the way.

Considering there are multiple studies indicating various referee biases, there are several examples of really obvious butcher jobs from the officials that always just happen to help the big-name teams and players, and at least one guy—who the FBI confirms was able to win 80-90% of his bets simply by knowing who was reffing—alleges the NBA has its hands in the outcome of games, I feel comfortable assuming the league is protecting its biggest star to a degree we’ve never seen before… and might never see again.
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Source: EmptytheBench

rocketeer · Jan 29, 2010

The numbers all come out so ridiculous, it’s undeniable that either a) we’re witnessing a defensive talent more capable than Bill Russell, or b) the NBA/referees are blatantly protecting him. That first one was meant to be a joke, by the way.
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or maybe lebron just doesn't commit a lot of fouls. it's not like he's the only guy who doesn't get called for fouls often. steve nash, derrick rose, and andre igoudala all foul less than lebron. are the refs blatantly protecting them as well?

Shapecity · Jan 29, 2010

rocketeer said: ↑

or maybe lebron just doesn't commit a lot of fouls. it's not like he's the only guy who doesn't get called for fouls often. steve nash, derrick rose, and andre igoudala all foul less than lebron. are the refs blatantly protecting them as well?
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Here's one counter argument from the article in regards to Nash..

For example, Steve Nash is committing a career-low 1.2 fouls per, but he’s such a bad defender, everyone he’s guarding simply dribbles past him and then he’s out of the play. It’s not so obvious with LeBron, considering he’s regularly guarding extremely dynamic players who routinely go to the line, and he’s often banging with the big boys underneath, where a majority of fouls are called.
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rocketeer · Jan 29, 2010

Shapecity said: ↑

Here's one counter argument from the article in regards to Nash..
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andre igoudala would be the one i would be most interested in.

Shapecity · Jan 29, 2010

rocketeer said: ↑

andre igoudala would be the one i would be most interested in.
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He must be part of this group...

These 12 players (not a slouch in the bunch – Bryant, Gay, Durant, Roy, etc.) combine for 469 games, during which they got called for 4 fouls 53 times, 5 fouls 31 times, and 6 fouls (fouled out) only 4 times. James has logged 44 games, 3 with 4 fouls, and 0 with more. In fact, 4 fouls is the most he’s been called for over the past two seasons.

Using a chi-square test on this data gives us P-values of 0.047 and 0.060 for games with 4-plus and 5-plus fouls, respectively (the calculations for 6 fouls are meaningless since they’re so rare for the entire group). That means that LeBron had a 4.7% and 6% chance of having so few games in those types of foul trouble due simply to randomness. Therefore, something else is at work here (most mathematicians consider anything under 5% to be “significant”).

Checking last year’s data, it’s even worse. There were 10 players who logged between 37.5 and 38.5 minutes per (James, 37.7), and collectively they played 777 games, 109 with 4 fouls, 48 with 5 fouls, and 13 with 6 fouls. James had 9 games with 4 fouls during his 81-game season. This data yields P-values of 0.023 and 0.0089, so he had a 2.3% chance of having so few 4+ fouls games and a 0.89% (less than 1%) chance of having no 5+ fouls games.

Yes, there is definitely something “significant” happening here.
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rocketeer · Jan 29, 2010

Shapecity said: ↑

He must be part of this group...
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so they lumped him together with guys who foul more often to pretend that he doesn't foul even less often than lebron? that seems like something they'd do to hide the actual facts on the matter to make it appear like lebron is getting preferential treatment when really there are other guys other there that foul less often than him.

my guess is that the guy who wrote the article could have written the conclusions section before he ever started. he wanted to "prove" something, so he "did".

the guy can talk about how ridiculous and unbelievable the numbers are but when guys like igoudala and deng put up similarly low foul numbers playing against the exact same guys as lebron, his point entirely disappears.

NJNetz · Jan 29, 2010

Jason Kidd doesn't foul often.

durvasa · Jan 29, 2010

Least fouls committed per 36 minutes in last 3 seasons (at least 3000 minutes played):

Code:

[B]Rk       Player              G         MP        PF  [/B]
1        Tracy McGrady       107       3667      1.3
2        Tayshaun Prince     176       6131      1.3
3        Michael Finley      180       4851      1.4
4        Allen Iverson       162       6235      1.4
5        Derrick Rose        125       4596      1.4
6        Antonio Daniels     145       3182      1.5
7        Steve Nash          203       6873      1.5
8        Michael Redd        123       4397      1.5
9        Jamal Crawford      189       7013      1.6
10       Tony Parker         181       6055      1.6
11       Chris Duhon         190       5904      1.7
12       Kevin Durant        199       7449      1.7
13       Peja Stojakovic     181       6059      1.7
14       Ronnie Brewer       202       6151      1.8
15       Luol Deng           156       5476      1.8
16       Andre Iguodala      209       8314      1.8
17       LeBron James        203       7895      1.8
18       Brandon Roy         192       7227      1.8
19       DeShawn Stevenson   150       4028      1.8
20       Joe Johnson         205       8119      1.9

Shapecity · Feb 1, 2010

Here's the rebuttal
Four days ago Zachariah Blott posted a fairly sensational article over at Empty the Bench that you probably saw; it certainly made its way around the internet. The gist was that LeBron James gets called for so few fouls, he simply must be getting preferential superstar treatment from the referees.

Zachariah Blott uses some fancy statistics to back up his assertion, and that’s what reeled me in. As someone interested in advanced statistics, I took a look at what Blott had put together and was disappointed to find that not only are the statistics misused, but they actually back up exactly the opposite of Blott’s assertion: meaning, that there is actually no superstar treatment for LeBron.

Mr. Blott, consider this to be a rebuttal.

I’ll be completely transparent about being an LBJ fanboy. We all know, though, that he gets some no-calls; there very likely is some superstar treatment floating around among the refs, and there’s neither much we can do about it, or good ways to measure it. Instead, I’ll limit my comments to specifically why the aforementioned Mr. Blott’s statistics do not show, and instead show heavily against, superstar treatment for LeBron James.

Here goes.

Mr. Blott starts by pointing out that LeBron averages the fewest fouls out of the top-10 scorers in the league. I like the idea of comparing him to other stars, but there’s no direct correlation between scoring and fouls that we can really rely on—especially with a few bigs (who tend to get called for more fouls because of the physical nature of defensive post play) like Dirk Nowitzki, Chris Bosh, and Antawn Jamison on that list.

Instead let’s expand our sample out to the whole league. Filtered for players that have played at least a thousand minutes so far this season (there are 157), I put together a list based on number of fouls per 48 minutes. That’s my preferred statistical measure—it negates the difference in playing time that plagues per-game numbers, and per-48 is easier to look at than per-minute.

It turns out that LeBron actually gets called for the seventh-fewest fouls in the league, so far this season (data as of 1/29/10):
Code:
Player	Min	Fouls	Fouls Per 48 Min
Derrick Rose	1595	57	1.72
Steve Nash	1609	62	1.85
Jason Williams	1052	43	1.96
Chris Duhon	1511	64	2.03
Andre Iguodala	1802	77	2.05
Eric Gordon	1168	50	2.05
LeBron James	1815	83	2.20
Peja Stojakovic	1258	58	2.21
Luol Deng	1685	78	2.22
Jonny Flynn	1393	67	2.31
What Blott has exactly right is that Kobe Bryant isn’t on this list (he’s 46th); neither is Dwyane Wade (he’s 30th).
Without going any farther, we can draw a few conclusions:

If there is superstar treatment, it means there is either collusion or sub-conscious agreement among all or most of the officials in the league (Covers.com indicates that there are 75 referees) to make it happen. With that many referees, bias averages out unless the bias is very widespread.
Assuming there is superstar treatment, then the refs have collectively misidentified Chris Duhon, Jason Williams and others (everyone above LeBron as that list) as superstars along with The King.
Assuming the above, they have also failed to identify Kobe Bryant or Dwyane Wade as superstars.
Those conclusions are ridiculous, obviously, so make this the takeaway point so far: The fact that six players commit fewer players than LeBron, and that some of them aren’t real stars, is actually a nice tidy argument that LeBron quite simply commits fewer fouls than most players.

You’ll notice that I’m talking about a generalized “superstar treatment”, which should logically apply to all superstars, instead of LeBron-specific treatment. The fact that Kobe and D-Wade get called for more fouls than LeBron does not indicate different treatment; rather, all we know from that is that they’ve been called for more fouls, for any variety of reasons. The idea that a strong majority of the league’s refs would give special treatment to LeBron because he’s a star and not Kobe is absurd. Unless LeBron has paid them off, or some outstanding variable that also seems absurd.

Let’s move on.

The most provocative part of Blott’s article is his use of a chi-square test, with some wild numbers as the result. I’ll quote:

“Using a chi-square test (it’s a pain in the ass to explain, so Google away if you’re so inclined) with LeBron’s foul data and the league’s foul data, one derives a chi-square value of 35.9, which translates into a P-value of 0.00000. The P-value is what’s of most use to us here because it tells us how likely something is to happen due simply to chance (e.g. 0.4 means it has a 40% chance of happening).”

Since he’s interpreted this wrong, I’ll take on the “pain in the ass” task of explaining it. Don’t worry, it’s not really that complex.

Chi-square is used to test “fit”, as in, how well something fits. You started with how you expect something to turn out (often the results of a survey, for example; it will be the expected value based on chance or probability, like in an election with two candidates you’d start with 50-50), then you use that as a yardstick for comparing the actual results. The higher the P value, which Blott uses, the better it fits. An exact 50-50 election would generate a P value of 1. (Additionally, here’s a fairly technical description at Wikipedia. Their phrase “goodness of fit of an observed distribution to a theoretical one” is much more precise, if a bit wordy.)

Let’s apply. For our purposes you’d use the league mean (for players over 1000 minutes) as the expected value; it’s about 3.8 fouls per 48 minutes. You then use that as a yardstick to compare how well LeBron’s foul rate fits with the league average. Lo and behold—we find that it doesn’t fit well at all. We find that LeBron’s foul rate is quite different from the league’s average.

All that Blott’s chi-square results mean, then, even with the help of a statistics professor, is that LeBron gets called for fewer fouls than most players. Which we already knew.

The fallacious part comes in at the very end of that paragraph by Blott:

“This all means that the likelihood of LeBron’s foul counts occurring with his minutes is less than one in a million.”

This is wrong. To make the assertion work, we’d have to adjust it to say that the likelihood of an average player, who is fully statistically average and who we would otherwise expect to average 3.8 fouls per 48, having a season where he averages 2.2 fouls per 48 is less than one in a million.

So, don’t be swayed by the extreme number. The P-value of 0.00000 that Blott cites is true also for Rose, Nash, Williams, Duhon, Iguodala, and Gordon.

Here’s how we can put it in perspective. If you ran a chi-square comparing LeBron’s scoring to the league average, you’d get a P value similar to that 0.0000. Same if you compared Dwight Howard’s rebound average to the league average, or Chris Paul’s assist average to the league average. All the chi-square tells you is that there is a difference between them and the league average, and we already know that.

You could determine how many standard deviations away from the mean LeBron is, in terms of fouls, but again that only tells you that he gets called for fewer fouls than most players.

Instead, I’d probably just chart them like this:

The trendline gives you a nice parabolic curve centered around the mean, showing that most players average around that 3.8 per 48. Plotting LeBron, Kobe, and Wade shows that all three of them are below the league average, but that none of them (including LeBron) can be considered an outlier. The fact that LeBron doesn’t get called for the fewest fouls—only the seventh fewest, in a sample of only 157—makes it seem downright reasonable.

One in a million? More like 7 in 157, or 1 in 22.

None of this ought to be considered a personal attack on Mr. Blott, who is well-experienced both in basketball and in journalism. I frequently get carried away in my writing (remember when I called for Mike Brown’s head, two games into the season? Sheesh), but in this case I felt that I could responsibly rectify these particular errors.

The real problem here, which we all make in the wonderful world of sports statistics, is trying to discern causation with numbers. The only way we could actually prove bias toward LeBron James would be to remove every single other variable, which is impossible. Mr. Blott can’t prove that there is or isn’t bias, and neither can I.

Is it possible that LeBron James gets called for relatively few fouls because of bias, and that the players who get called for fewer fouls legitimately commit fewer fouls? Yep. Is it possible that all the refs in the league hate Kobe and D-Wade, and so call them for more fouls? It’s possible. Is it possible that LeBron James is either good at not fouling, or even just good at disguising it? All of these things are possible, but the conclusions are well outside the realm of statistics.

What we have discovered is something that is remarkable about a few players. I’m not sure that anyone is surprised the Steve Nash is second for the fewest fouls in the league (an aging perimeter player with a reputation for full-of-holes defense? make sense), but how about Derrick Rose? Perhaps we should make it the real story that the young, rising Rose is committing the fewest fouls in the league.

And amongst all that, it definitely is impressive that someone with the high intensity of LeBron James manages to get called for so few fouls. Who knows how he does it?

I don’t.
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Source: HowToWatchSports

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