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.
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|
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?
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 firstname.lastname@example.org.