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):
| 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.
Feel free to contact me with questions about my numbers or methodology, or if you’d like to further the discussion. Moreso, if there’s an error in my assertions, please let me know. I can be reached at roger@howtowatchsports.com.
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Oh, snap!
Yeah, you are ignoring all the OFFENSIVE FOULS he gets away with on a daily basis.
i dont see a rebuttal.
i see the exact same stuff, but with a “but this only proves something we already know, that he commits few fouls” attached to it.
i see the same stat corrected to 48 mins, which is the wrongest way you could ponder fouls, as people who commit less can actually play more.
the issue blott had in the other article was that other important players have to sit out if they pick up 2 fouls in the quarter, you negate that by considering 48 mins.
also, you have to take account how some of these guys actually play.
wade is aggressive on both ends, yet he gets away with some no-calls, but he doesn’t have to guard forwards like lebron has to.
kobe is even less athletic than wade, yet he gets more fouls than both.
lebron is clearly favored by the refs, both on defense and on offense, getting an obscene amount of ‘and 1’s with defenders doing so much as breathing near the guy.
if you deny this, You, sir, are biased.
It’s not a rebuttal in the sense that I’m arguing the other side, I’ll agree with that. I’m just disagreeing that the statistics prove the original assumption.
I’d argue, though, that per-minute (or per-48-minutes) stats are a better way to gauge fouls, because they do take into account how much time a player spends on the floor. Per game stats are silly in that a game with 5 minutes’ playing time counts equally against a game with 40 minutes’ playing time. I say let’s count 5 minutes as 5 minutes, and 40 as 40.
And believe me, I’ve seen these guys play. I certainly won’t deny that LeBron gets no-calls… I said that in the article. And-1’s, or more exactly drawn fouls, should be included in a discussion of referee bias but fall outside the scope of this article where we’re just talking about committed fouls.
I’d be really interested if there was a good way to prove that there was (or wasn’t) more (or less) referee bias for different players, but I just don’t think it’s going to happen statistically. Stats would have to be just a supporting argument… and perhaps the only conclusive evidence would be a Donaghy-esque admission of collusion.
I’d note that correlation is not causation. For causation you probably need regression. And from where I sit, that’s no easy task considering the subject and the number of variables you’d like to control for (and the potential non-linearity).
And whether you use regression or some other statistical tool, specifying the model is the key. And finding a model people can agree on may be just as hard as doing the analysis. (Though I would start by separating out players by position, then maybe using a combined/interaction variable for quarters played and minutes played.)
ERR has obviously not watched all that many Cavs games, especially not lately. In the five game stretch leading up to the release of Mr. Blott’s “statistical revelation”, there wer two games in which James was assessed with two quick fouls-one offensive and one defensive in each case. When he returned to the court after sitting out for X number of minutes, he was noticeably more conscious of his style of play…IN OTHER WORDS, he had adapted to these particular referee’s style and went on to post numbers Cavs fans are used to seeing without fouling out…ERR fails to take into account that LeBron James might just be able to ADAPT to most any given situation within a basketball game…The only bias I’m seeing in this blog and comments is ERR’s unswerving faith in HIS ability to analyze without considering ALL of the facts or possibilities
Adjusting for pace would be better than just doing per 48 minutes. Since the Cavs play at a relatively slow pace compared to the Suns. Fouls per 48 minutes adjust for time on the floor, but pace would also adjust for fouls per possession. This would probably go better towards proving your point.
And Derrick Rose is also a liability defensively, thats why he has so few fouls.
That’s a good call… that would probably account for Duhon too.
Wait, that’s reversed. Adjusting for the fast pace of the Suns and Knicks will imply even fewer fouls for Nash and Duhon. Wow.
This is 100% retarded. The superstar treatment is referring to the obvious fact that LeBron draws fouls that dont happen. To gauge this with statistics(which ultimately can be interpreted any way you want) you would look at how many more (or less; probably more) fouls the players GUARDING LeBron pick up. Offense is what makes superstars, so focus on the fouls against him on that end of the floor, not on fouls he commits defensively.
Have you thought that the biggest factor is that he isn’t the defensive player that everyone thinks he is? He doesn’t guard the players Wade and Bryant do. They hide him on defense and let him play the passing lanes. It’s fairly obvious that’s the reason he is never in foul trouble. And yeah, like someone else said, he doesn’t get called for all those offensive fouls he commits.
Actually, I think the issue when Sam Smith brought it up last season was really about how LeBron could be considered one of the best defensive players in the league and still not draw any fouls, not just committing fouls in general. Rose and Nash, for instance, are on that list of fewest fouls committed because they’re both terrible defenders and aren’t close enough to their man when they blow by to pick up the whistle (someone else on the team usually gets it). But LeBron was lauded as one of the best defenders in the league, and yet he somehow was committing less than 2 fouls a game. If he’s really manning up on D, it seems implausible that every other 3 in the league cannot draw a foul on LeBron with any regularity, so the assumption is either that he’s getting some extra help, or he’s not actually getting all that close to who he’s guarding.
I tend to believe that LeBron is not the defensive beast that people think he is. If you saw him last year in the playoffs vs the magic, he was “guarding” Rafer Alston. (Standing five feet away and not contesting shots isn’t really guarding). Not until the last few minutes of a close game will he even guard the other team’s best scorer.
The reason for this is obvious, and fits with the theme of this post. LeBron does not guard aggressive or “superstar” players until late in games to protect him from foul trouble. I think it is accepted that LeBron is the most important player the Cavaliers have on their roster. If LeBron gets into foul trouble early in games and has to sit on the bench, the Cavaliers are much more likely to lose those games. Therefore, it has been the Cavaliers’ long standing strategy to put LeBron on a lesser perimeter player and have him play “free safety”, limiting passing lanes and picking up loose balls until the fourth quarter when he is allowed to become more aggressive defensively on the other team’s better players. This keeps him on the floor for entire games by limiting his fouls, and makes the Cavaliers a formidable fourth quarter defensive team as LeBron is generally able to neutralize other star players very effectively. If LeBron were in that defensive mindset for the entire 48 minutes of the game, he would effectively shut down opposing star players, but also commit many more fouls doing so. The Cavaliers would not win many games this way.
I dont see how anyone can deny the special treatment, Kobe gets it at times, Shaq got it quite a bit, and now Lebron is the leagues princess. It is not Lebron paying the refs, it is the league, and the league needs to make money. So of course they are going to allow their superstars a little room for error. James’ style of play, lower your shoulder and go, is a foul prone style.
For the aggressive play style Lebron has he gets called for very few fouls. The other players with fewer fouls per minute all have very different play styles. Most of them are point guards the others are players who arent consistently the #1 scoring option when it comes down to the end. None of them also have the presence offensively and defensively that Lebron has.
I think rather than just looking at fouls per minute it would be better to break them down into two categories. Offensive fouls per attempt and defensive fouls per combined block/steal/defensive rebound. the latter is far from perfect but I think could be an indicator of a players overall contributions to defense.
I’m pretty sure those numbers would show that Lebron (and some others) are definitely getting preferential treatment (actively or subconsciously).
LMAO, some of you clearly have your hate-colored glasses on.
Watch LeBron’s last second defense of Durant and Wade in consecutive games, then tell me he isn’t a physical, outstanding defense.
Also, he gets called for more offensive fouls than Wade and Bryant.
Thank you.
1) The “statistical analysis” used in Blott’s article was so painfully misguided. I’m surprised so many reputable outlets linked to it. I love the mainstream proliferation of stats-to-explain-sports, but feel the complete opposite when they’re used in such poor form.
2) Talk about more than just one variable– Corey Maggette averages 1.5 trips to the line more than Kobe. If this is any sort of superstar-treatment-gauge, then, umm…
3) The biggest conclusion I draw from all this has nothing to do about superstar treatment. Mainly, why the hell isn’t Lebron more aggressive on defense? Him having lower foul totals than Kobe or Jordan or Wade doesn’t tell me that he gets better ref treatment; it tells me that unlike those other guys (who, coincidentally or not, are Champions), he’s leaving opportunities on the floor. If he has 2 fouls late in the 3rd quarter, and a guy has him beat, why isn’t he reaching? If the opposing team isn’t in the bonus, there’s literally no opportunity cost.
In other words, is Lebron not doing as much as he can to help his team win?
Quoting: From the first three conclusions, drawn on this article, it is apparent that the writer has failed his deductive reasoning class time and again.
Numbers can be spinned any way we want them to, reasoning cannot.
Your assessment of the f/48 stat is, to be polite, wrongheaded. We all have allegorical evidence of LeBron’s “defensive renaissance” last season being the referees simply allowing him to bowl people over on defense and then take the ball, but this year he has cooled off on that a bit. He is not, however, considered a defensive liability. In fact, it’s generally accepted that he is, at worst, a competent defensive player.
Now, look at the rest of that list. Nearly every one of those players is regarded as a defensive liability. The exception is Iguodala, who seems to trend similarly to LeBron in fouling. However, of the top 10 that you listed, eight are very poor defenders. Others have pointed this out, but only individual players, like Rose and Nash.
It’s just a fact that in the NBA you will pick up fouls if you’re D-ing up aggressively. When in doubt, the benefit will always go to the offensive player. So, as others have noted, either LeBron’s defensive reputation is out of whack, or refs simply don’t call fouls on him.
Last year, I thought that the refs were giving him a break because he was a star busting his ass on defense, and because the way that he insisted on playing would mean he would be on the court for 15 minutes a game if they called everything he did. Obviously, they couldn’t do that. This year, I see him kind of coasting for a lot of defensive possessions, and occasionally unleashing a massive block or steal. Largely, though, he is allowed to play that “free safety” position, as the announcers like to call it. Well, when you play pickup football, do you know who is usually left to play free safety? The offensively-talented guy conserving energy for when his team gets the ball back… or the lazy kid.
I was under the impression there would be no math.
Well-reasoned rebuttal. One angle to take is that perhaps Lebron should be playing more aggressive defense and drawing a couple more fouls a game.
Also, as you point out, its hard to identify bias wrt referees. But there is a longstanding tendency in the NBA for rookies not to get calls and I think that’s a really bad way to do things. Assuming this is a real phenomenon and not a myth, it creates the belief that refs have a tendency towards bias and thus routinely effect the outcomes. Former-player announcers only worsen the problem when they make comments like “the rookie won’t get that call”.
Another, similar issue is the tendency, at least the perceived tendency, to call the game differently at “crunch-time”, i.e. “he’s not going to make that call at this point in the game”. Again, this just fosters the impression that refs alter their officiating for the situation and for the player.
Can you imagine a major league umpire calling strikes differently because its the ninth? Or an NFL ref not making a call on a rookie? But these biases are taken for granted in the NBA.
Interesting work, though I think your analysis of the top players with regards to the fewest fouls per game is a bit iffy at best.
Showing the top ten players with the fewest fouls per 48 minutes, then using the fact that James isn’t the number one, and that Kobe and Wade aren’t there shows nothing. Did you look at the rest of that list?
Who else on that list is a stand out, physical defender? All things are not equal here, and to assume that they are is simply an attempt to misrepresent what the data is telling you.
Derrick Rose, Steve Nash, and Jason Williams being the top three says nothing about “star treatment”. It says EVERYTHING about their defense. They have none. They aren’t down in the paint mixing it up and getting physical either.
If you want to chart something to show “star” treatment honestly,and remove the bias, remove impact from position, from defensive assignments etc. You would need to chart fouls called versus fouls committed. For every player in the league. Then do a comparison. After that, chart phantom calls as well. Again, for every player, then compare.
Until someone does that, none of this “statistical analysis” is valid. Let me rephrase that. None of the conclusions offered from this analysis mean anything. Conclusions offered here are simply a misrepresentation of the numbers. Nothing more.
I read both articles about LeBron’s foul rate a few days ago and I am lazy to go reference them again, but I believe that the whole point of the article was to prove that LeBron foul’s at a rate far less than all the superperstars, which makes inclusion of the entire league mute. That’s why his statistics, including the chi-square test has completely different values than yours. Another point of the article was that LeBron is one of the top defensive stoppers because he plays so aggressive, as does Kobe and DWADE, but he gets called for so few compared to the two. The discrepancy between lebron and the rest of the leagues stars is what is reported to be one in a million, not him out of the entire league.
This article isn’t about LBJ, it’s about irresponsible journalism. It was mislabeled as a rebutal which it isn’t, it never attacks Blott’s conclusion. What this article actally is, is a criteque on the piss poor methodology and misinterpretation of data by Blott.
I majored in math in college, have taken multiple statistics classes, and can tell you that Blott’s analysis is attrocious.
It seems like 2/3 of the people that posted responses either didn’t read the entire article, or weren’t able to follow the errors in Blott’s mathematical reasoning, or both.
Statements like “This all means that the likelihood of LeBron’s foul counts occurring with his minutes is less than one in a million.†are 100% mathematically false. You cannot make that statement or conclusion from this data or this type of analysis.
You don’t have to like or dislike LBJ or even basketball to understand that Blott’s article was poorly conceived and terribly executed.
Blott’s article is a joke and had it been in something more reputable than an internet blog he’d be printing a retraction.
GTown FTW.
Player seasons who played at least 1500 minutes, starting in 2001.
Pts48: Fouls48
0…10: 4.95
10…15: 4.49
15…20: 4.09
20…25: 3.84
25…99: 3.52
There’s an obvious relationship. Causality is up for debate.
Do you know if this relationship holds true if you look at each position (i.e., guards, forwards, centers) separately? Or are we just seeing that “bigs” score less and foul more compared to “smalls”? (Not saying that this assumption is true since I haven’t seen any numbers on this point, but it seems like one potential confounding piece of information)
LBJ makes the bulk of his fouls on offense = at least 2-3 a game.
The refs protect James more than Kobe! DWade gets about the same assistance as LBJ for the most part when relating to calls in his favor whether its mysterious call or no call. The refs refuse to call the offesive charge on LBJ thats the most damning thing.
The refs choose to call more fouls on Kobe or Dwade because they are making some regular calls and some bad calls vs them = It occurs in flow of the game so its understanable that these type players make 3 fouls per game when you factor in thy players they are guarding and their aggressive defenive ways. When it comes to LBJ, its seems like the refs just dont want to call fouls on him whether offensive or defensive unless its just to plain obvious.
This is the worst refute article I have read. There is no evidence to counter the original article. This guy doesnt use the same players nor factor in that no otehr players in the NBA matter when calculating this except Kobe, Wade, Mello, LBJ, Pierce, KG, Duncan = (Only Superstar can achieve this type of help to where it influences the outcomes of games. All other role players or the newbies = new stars cant be used because they dont affect their teams Win outcome as the Superstars mentioned above.
yeah LeBron is this important to America…YOU’RE TALKIN ABOUT FOULS? I’M MEAN COME ON? FOULS. I’m from Cleveland and give us the rings already…we’ve already whooped everyone!
LeBron is the best player, and he plays for my favorite team.
nyah nyah nyah nyah nyah!
[...] The Fu Manchu: Roger Pimental makes a rebuttal against Zachariah Blott’s article claiming that the statistics show Lebron is receiving preferential treatment from the officials. Very solid stat work here. [How To Watch Sports] [...]
This is why I can’t watch NBA games anymore, it is just too frustrating to watch the best players so blatantly being rewarded by refs on every single possession. And yes, any idiot with eyes can tell that LBJ gets more than any other star out there and on top of it he still complains nonstop. I just don’t get today’s players, I mean what more do you want, maybe we just let the refs vote for the NBA champion, that way LBJ could finally get one. I honestly thought the Tim Donaghey thing might straighten out the calls this year, but once again the NBA continues to disappoint. Maybe they can figure out how to do something about this before hockey surpasses them in popularity.
(Disclaimer: I didn’t proofread every single post for a similar comment because most people are too long winded) The only possible way to determine if someone is getting calls is to go through all the video from all the games. There are just too many variables that dispute statistics like this. Here’s how it works: LeBron haters find examples of LeBron getting calls, others find examples of everyone else. Period, end of discussion. I watched John Wall travel blatantly last night, but as a Georgia fan I am not going to make any generalizations about him unless I watched all his film.