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February 3, 2010
No Foul Play
LeBron James' Low Foul Rate

by Kevin Pelton

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Cleveland Cavaliers superstar LeBron James has been a topic of conversation the last couple of weeks, but not for the usual reasons. Instead, focus has turned to James' low foul totals--just 1.8 per game this season. Last week, Zachariah Blott argued at Empty the Bench that James' foul rate is so low he has to be benefiting from the largesse of the NBA's referees. After Blott's initial post was cited on TrueHoop, Roger Pimentel rebutted it at How to Watch Sports, noting that James' foul rates were not extraordinary among the NBA as a whole.

Now, this topic isn't entirely new. It was briefly something of a cause célèbre after Sam Smith mentioned it on Bulls.com last April. Then, for whatever reason, James' foul rate didn't draw headlines like "Donaghy Reprised? Lebron Has 50 pct Less Fouls!" which appeared on SportsByBrooks.com and surely started some sort of red light flashing at NBA HQ, given the league's preference to never hear about the disgraced ex-referee again. As a result of the attention, I think it's worth taking a deeper look.

Let's start by getting a sense of James' actual foul rate. When adjusted both for his playing time and Cleveland's ultra-slow pace, we find that James has fouled on 2.1 percent of the Cavaliers' possessions this season. That is low, but as Pimentel pointed out, hardly the lowest in the NBA this season.

Player             PF%
----------------------
Derrick Rose       1.6
Steve Nash         1.7
Chris Duhon        1.9
Andre Iguodala     1.9
Jason Williams     1.9
Eric Gordon        2.0
Earl Boykins       2.1
Luol Deng          2.1
LeBron James       2.1
Jonny Flynn        2.2

At the same time, as unfair as it is to compare James to a league average that includes 7-foot stiffs fouling every five minutes, James might not belong with this group either. After all, as Blott noted, James is a 6'8" active defender who racks up steals and blocks and occasionally plays power forward. Is that really equivalent to the 5'5" Earl Boykins' role on defense?

My answer was to use James' other stats to predict his expected foul rate based on regression analysis. This process is complicated to some extent because the overwhelming factor in predicting foul rate is simply height or position. As a result, seemingly unrelated things like assist rate are correlated individually with foul rate. It is therefore important to use logic when creating this kind of regression. We also want to ensure a causal relationship to the extent that we can, which is why I did not use minutes. There's a definite relationship between minutes played and fouls, but it's unclear whether players who play heavy minutes compensate by fouling less (or earn more respect for referees) or simply that they are allowed to play more minutes because they are not in foul trouble.

I first used the three individual defensive stats we have to predict foul rate--defensive rebound percentage, block percentage and steal percentage. The regression analysis showed that defensive rebounding adds little to this equation, so it was omitted. The surprising result is that steals are still negatively correlated with fouls when blocks (which effectively proxy height) are in the regression. Apparently, players that go for steals don't put themselves in position to pick up fouls or the same ability that allows players to rack up steals (quick hands, for example) limits their fouls. This should surprise anyone who watches Venoy Overton play in the Pac-10.

What I then did for players with at least 500 minutes this season (the same group used in the regression) was see how much their projected foul rate based on their frequency of blocks and steals deviated from their actual foul rate. Here are the players who fouled much less often than we would expect.

Player              Tm   pPF%   aPF%   Diff
-------------------------------------------
Pau Gasol          LAL    5.0    2.6   -2.4
Derrick Rose       CHI    3.9    1.6   -2.3
Tim Duncan         SAS    5.2    2.9   -2.3
Luol Deng          CHI    4.3    2.1   -2.2
Steve Nash         PHO    3.9    1.7   -2.2
Rasual Butler      LAC    4.3    2.2   -2.1
Marcus Camby       LAC    5.0    3.0   -2.1
LeBron James       CLE    4.1    2.1   -1.9
Andrei Kirilenko   UTA    4.5    2.7   -1.8
Brandon Rush       IND    4.3    2.6   -1.7

James is on the list, but ranks just eighth in the league. More notable is the fact that post players like Pau Gasol and Tim Duncan foul relatively infrequently while racking up blocked shots (and getting relatively few steals).

Another combination of stats actually did a better job of predicting foul rate than blocks and steals--blocks and offensive rebounds (when part of this regression, steals were no longer significant). Why specifically offensive rebounding correlates better to foul rate than defensive rebounding I'm not certain, but these two stats have a combined correlation of .584 with fouls as opposed to .490 for blocks and steals.

Here's the list of players who foul much less than we would expect based on this regression.

Player              Tm   pPF%   aPF%   Diff
-------------------------------------------
Ben Wallace        DET    5.7    3.0   -2.7
Marcus Camby       LAC    5.5    3.0   -2.5
Tim Duncan         SAS    5.4    2.9   -2.5
Pau Gasol          LAL    5.1    2.6   -2.5
Kevin Love         MIN    5.7    3.9   -2.4
Zach Randolph      MEM    5.4    3.1   -2.3
Luol Deng          CHI    4.2    2.1   -2.1
Derrick Rose       CHI    3.5    1.6   -1.9
Chris Bosh         TOR    4.9    3.0   -1.9
Shawn Marion       DAL    4.6    2.7   -1.9

This list is now dominated by big men who foul less frequently than their hack-happy peers. When I think of big men who defend without fouling, Ben Wallace and Duncan are probably the first two players who come to mind, and Marcus Camby is also part of the discussion. James, who is not a particularly good offensive rebounder, ranks 14th on this list, fouling on 1.6 percent fewer possessions than expected.

Looking at these players offers a natural digression to the other aspect of the discussion of James and his non-fouling: Is this a good thing or a bad thing? My general perspective has long been that fouls are like turnovers: Some of them are necessary in order to do other good things, but the more those can be accomplished without the miscues, the better. (You could call this the "omelette theory," based on the old cliché about cracking some eggs.) The ability to offer help defense without fouling is part of what makes Wallace and Duncan so great as defenders, and what separates players with prodigious block and foul percentages in limited action from the true impact defenders. WARP's defensive ratings operate largely on this principle, heavily penalizing players for fouls.

At the team level, the numbers bear this out. Avoiding putting opponents on the foul line is an important part of a quality defense. However, a different regression analysis makes the opposite argument at the individual level. Statistical plus-minus is a way to weight box-score stats by regressing them against the results generated by adjusted plus-minus. When analysts have run this regression, most recently Basketball-Reference.com's Neil Paine, they have found a positive value associated with fouls. Even when holding blocks, offensive rebounds and other beneficial statistics seemingly related to fouls constant, players who foul more have better adjusted plus-minus ratings, indicating the benefit of playing aggressively could outweigh the cost of giving up a few extra free throws.

In the specific case of James, I think his low foul rate is more good than bad. It reflects his ability to use his immense physical gifts to be disruptive defensively without taking unnecessary risks. Before doing this research, I was willing to believe that some preferential treatment from the referees was a factor as well--not so much in the conspiracy-theory sense as what others have pointed out in James' defense, that he's such a freak athlete that the refs may give him the benefit of the doubt when they would believe a lesser player fouled.

I think the numbers suggest that to the extent that James is called for fewer fouls than we would expect, the magnitude of the effect is not extraordinary. As much as the overall numbers, the example that sold me was Luol Deng. Like James, Deng is an athletic small forward who occasionally plays at the four. Their block rates are identical and their rebound percentages are similar, and Deng is called for fouls as infrequently as James. So if you're going to argue that referees have decided not to call fouls on James, you have to be prepared to make a similar argument about Deng, who is a solid player but has never been an All-Star. Any takers?

Follow Kevin on Twitter at @kpelton.

Kevin Pelton is an author of Basketball Prospectus. You can contact Kevin by clicking here or click here to see Kevin's other articles.

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