NBA Home Court Advantage: Really Just The Refs?

March 4, 2011 - by David Hess

Today at the 2011 Sloan Sports Analytics Conference, Scorecasting author Tobias Moskowitz gave a great talk on home field advantage across various sports, and how he believes it can largely be explained by referee bias. We’ll go over his main points, then present some interesting numbers that we feel aren’t entirely explained by his claim.

Some of the evidence he presented demonstrated that home and away teams perform the same in situations where there is little referee interference, and that the home advantage is not travel related:

NBA FT shooting — no difference between home and away FT% (actually, according to our numbers below, there is a small difference, but it amounts to only a 0.05 point per game advantage)
Shootouts in NHL — no difference between home and away success rate
Pitchers/batters in MLB — for things like the percent of pitches in strike zone, mean velocity, horizontal movement, swing probability, and contact rate, there are no differences between home and away
Travel fatigue — there is no real difference in winning percentage based on distance traveled

He also presented evidence that referee bias in favor of the home team is widespread and significant:

In soccer, there is around twice as much injury time when home team is down by one, versus when the home team is up by one.
In baseball, there is no advantage for the home team in non-crucial situations, but a 0.5% difference in ball-strike calls in “very crucial” situations.
Over a season, visitors get 516 more strikeouts and 195 fewer walks than they “should.”
In the NFL, more penalties are called on visitors, and instant replay decisions tend to favor of the home team.
In the NBA, fouls and other violations are called more often on the road team, and the home team gets the benefit of the doubt in situations where there could be either an offensive or defensive infraction called.
The crowd seems to affect the referees. The larger and more vocal the crowd, the bigger the influence on the measured statistics. In other words, home advantage grows with attendance.

Overall, he painted a fairly complete picture: clearly referees are a part of home court advantage. But, are they truly responsible for the majority of the advantage?

We dug into our NBA statistics archives (going back to the 2003-2004 season) and pulled out a variety of home versus away stat splits. There should be no need to adjust for quality of play, as every team plays an equal number of home and road games. Below the table, we’ll highlight a couple of things that make us wonder if referee bias really tells the whole story:

Stat	Away	Home	Diff	%Diff
Steals	7.27	7.39	0.12	1.6%
Turnovers	14.02	13.59	-0.43	-3.1%
Off Rebounds	11.07	11.52	0.45	4.0%
Def Rebounds	29.70	30.75	1.05	3.5%
Total Rebounds	40.77	42.27	1.50	3.6%
Off Reb%	26.5%	28.0%	1.5%	5.4%
Points	96.41	99.72	3.32	3.4%
Fastbreak Points	10.47	11.89	1.43	12.7%
2PFG%	47.2%	48.7%	1.4%	3.0%
3PFG%	35.5%	36.0%	0.5%	1.5%
FT%	75.5%	75.7%	0.2%	0.2%
Fouls	22.15	21.13	-1.02	-4.7%

First, check out the steals and rebounds. The home team registers more of each, and their advantage is larger than the fouls advantage: +0.12 in steals, +0.45 in offensive rebounds, and +1.05 in defensive rebounds, compared to -1.02 in fouls. Even if every single extra visitor foul is called on what would have been a legitimate rebound, home teams still have an advantage in steals and rebounding. Beyond that, the foul disparity also needs to account for the shooting percentage difference, which it can’t do if we assume all the extra fouls occur in rebounding situations. There is just not enough of a foul difference to account for the disparities in the other stats.

Second, examine the fast break points. The home team has a 1.43 edge, despite only 0.12 extra steals. This seems like it must be due to some kind of qualitative difference in the way the two teams are playing, because the extra opportunities themselves don’t seem to be enough to account for it. Unless, perhaps, that extra foul occurs on a fast break. But, again, that leaves us with nothing to explain the other home/away differences.

Third, look at the shooting percentages: the home team is +0.2% in FT%, +0.5% in 3pFG%, and +1.4% in 2PFG%. As above, let’s assume that the extra foul on the visitors always occurs on what would have otherwise been a legitimate field goal defensed. So, add 1.02 misses to the home team’s line. If we add all those misses to the 2PFG% calculation, the home team still ends up at 47.9%, or +0.7% over the away team. Again, the fouls themselves aren’t enough to account for the disparity. Surely we’ve all had the experience of playing for the first time on an unfamiliar court, and feeling that we can’t quite judge our shots correctly. It’s hard to imagine this doesn’t happen to some small extent in higher levels of sport, even if on a much smaller scale.

Moskowitz clearly showed that referee bias plays a large role in home court advantage. All we’re asking is: are we sure it’s the entire story? After all, if referee performance is affected drastically by the home crowd, why wouldn’t player performance be as well?