A Quick Look at Home Court Advantage

by Jeff Fogle 11. March 2011 01:32

The other night, NBA Network analyst Chris Webber said something along the lines of "Miami doesn't have a home court advantage" because of a home crowd that's been criticized for arriving late and expecting victories. I hadn't seen the numbers for this year and decided to dig them up...

Using the "team splits" option over at Basketball-Reference that appears on the Navigation pull-down for each team, I logged the average home score and road score for all 30 franchises. Those of you familiar with NBA stats know that home court is generally worth something in the neighborhood of three points. For any non-statheads out there, imagine for the sake of example that it's worth 4 points. For an average team, that would create a breakdown like:

Winning 102-98 at home
Losing 98-102 on the road
Playing 100-100 ties on a neutral court

A difference of +4 at home to -4 on the road for a differential of 8 points. I think it's generally been worth less than four points for many years now. Try writing up an easy example with 3 points where you don't have to explain what a 99.5 all tie looks like! Back in the 1980's it was worth more than four points when tempos were much faster and travel less friendly. If you just pencil in 3 points as a general rule in the modern game, you're going to be in the ballpark.

Individual years for individual teams have such a small sample size that you can't really trust the numbers in a confident way. Atlanta for example has a NEGATIVE home court advantage this year because of a couple of blowout losses where they fell behind early and let the margin blow up. Atlanta is likely to regress to its mean in the future and post a more standard differential.

Still, it's interesting to see how the differences shape up. And, Webber was right in reporting that Miami has one of the smallest home court advantages in the league this season.

Biggest Spreads from Road Margin to Home Margin:
Denver: +11.4 (equating to a home court advantage of 5.7)
Washington: +10.8
LA Clippers: +8.8
Indiana: +8.8
Orlando: +7.9
Cleveland: +7.6
Minnesota: +7.5
New Jersey: +7.4
Oklahoma City: +7.3
Philadelphia: +7.3
Charlotte: +7.3
Chicago: +7.1
San Antonio: +7.0

Cut each in half to determine what an "advantage" would be over a neutral site game. San Antonio's equating to a home court advantage of 3.5 points to this point in the season (all stats in this article are through the games of Wednesday night). The Clippers would be at 4.4. Denver, which historically has a big split because of its home altitude advantage, is almost off the charts.

Of course, it wouldn't be out of line to equate some of this to what might be termed "road court disadvantage" for bad teams who stink up the joint away from home. We can save that discussion for another time. I just wanted to get the numbers up when I had them handy.

Standard Splits
Golden State: +6.3
Memphis: +6.2
Toronto: +6.2
Portland: +6.1
LA Lakers: +5.4
Detroit: +5.3
Sacramento: +5.3
Utah: +5.2
Houston: +5.1

Note that Memphis and Toronto at 6.2 are the medians for the 30 team league. That gives you 3.1 for the median home court advantage.

Smallest Splits
New Orleans: +4.7
Milwaukee: +4.4
Miami: +4.0
Phoenix: +3.9
New York: +2.2
Boston: +1.9
Dallas: +1.9
Atlanta: -1.4

We have some good teams down at the bottom here. Many top contenders are playing very well on the road this season. Again, it's easy to start spinning around in circles when defining terms. This group is seeing less of a lift at home than you normally get in the NBA. That doesn't mean Boston is an easy place to play. Miami is showing the 6th lowest differential out of 30 teams between home margins and road margins.

With the playoffs coming up soon, talk of home court advantage will become a lot more prominent. It will be good to have some numbers to frame the discussion.

This will be it for Thursday night. Looks like the late games were blowouts anyway. The NY and Dallas defenses seemed to play tired with both in their fourth game in five nights. New look Denver still seems to have a chip on its shoulder based on their win in Phoenix. Friday's marquee matchups are Boston-Philadelphia and Atlanta-Chicago. Notes on those games and a few others a bit before midnight...

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Comments

3/11/2011 11:49:19 AM #

Jimmy

You can use the Chi-Square test to tell whether home court is significant for a given team based on win/loss vs. home/away.  So far this year, if using a 95% confidence interval, we can only say the following teams have had a significant home court advantage (or "away-court disadvantage"):

CHI
DEN
DET
GSW
LAC
MEM
NJN
NOH
PHI
SAS
WAS

Washington is the obvious case of an "away-court disadvantage".  Even though they're only 15-18 at home, they're 1-29 on the road!

Jimmy United States

3/11/2011 12:20:10 PM #

Crow

A 95% confidence interval is too demanding.
If you look multi-season I am confident that home court advantage (or "away-court disadvantage") is real for most to nearly all teams.

Crow United States

3/11/2011 12:30:25 PM #

Jimmy

95% confidence is not "too demanding", it's a law of statistical significance.  There's not really any room for play (at least not in the realm of statistics -- maybe there is among sports fans).  

That said, you are right.  If you look across the last 3 seasons, only 3 teams do not have a statistically significant home/away spread:  Boston, Minnesota, and Philadelphia.  However, I'm sure if you look even further back, those teams do as well.

Jimmy United States

3/11/2011 2:25:59 PM #

Crow

I was going to follow-up earlier with a revision  saying a 95% confidence interval is too demanding "for one season" but decided not to.  In part because I wasn't sure how quickly it would change by adding a few seasons and I was torn whether to make further statement.

The choice when you don't have 95+% confidence is either, as some would have you, believe that you can't "know" the theory to be  correct to the standard and therefore do not believe or act that it is, which may be quite appropriate for many issues; or, if say the confidence level is only 85% or 70% you can select to accept the degree of uncertainty and some risk but act in accord with the theory as it is still more likely that the next observation or set of observations will be in line with the theory.  I think a sports fan or sports executive can take 85% or 70% confidence on many things and would often be more wise to do so than not.  High certainty is great if you can achieve it but often you can't. For a game, if the choice is admitted ignorance (and then what do you actually do?) or a bet with the odds in your favor, which would you select?

Crow United States

3/11/2011 2:57:03 PM #

Crow

The home court advantage for just this season for almost all 19 teams not meeting the 95% standard  didn't disappear altogether, it just moved outside the standard using a 1 year test. Fortunately a longer, better test was available, if you are willing to believe past and current teams behave similarly. I wouldn't stop believing and acting as if the home court advantage was true or worth treating as true though it couldn't be proved to the 95% confidence standard on the 1 yest test.


Better to know the confidence level than assume it and better really high than not,  but if it is still "strong" I'd tend to go with it more often than not in basketball. If everything had to be proven to 95% confidence before you used it at all you wouldn't have much as much to work with and you'd probably do worse than if you accepted a bit lower confidence standard and a bit more risk of being wrong.

Crow United States

3/11/2011 3:08:49 PM #

Crow

I forgot to say: thanks for the data and follow-up data Jimmy.

Crow United States

3/11/2011 5:11:21 PM #

Jimmy

No problem, Crow.  It's not that there aren't circumstances under which <95% confidence is significant, it's that statisticians can't arbitrarily lower the confidence threshold "post hoc" to confirm the hypothesis we were trying to test in the first place.  But in this case, it's all for show, anyway.  We sort of already "know" that there is a home-court advantage.

If interested, here is the data for the past three years (tab-separated).


Team  H/W  H/L  A/W  A/L  CHI-SQ CONF.
ATL  83  29  54  62  99.9%
BOS  86  29  72  39  50.0%
CHA  70  44  35  79  99.9%
CHI  79  34  48  66  99.9%
CLE  82  32  57  57  99.9%
DAL  84  31  68  46  95.0%
DEN  93  22  52  62  99.9%
DET  54  61  35  79  98.0%
GSW  58  56  25  89  99.9%
HOU  73  39  55  63  99.0%
IND  65  49  30  84  99.9%
LAC  50  65  23  91  99.9%
LAL  92  20  76  42  99.0%
MEM  61  53  39  77  99.0%
MIA  75  39  59  56  95.0%
MIL  66  48  39  74  99.9%
MIN  32  84  23  91  50.0%
NJN  43  71  23  90  99.0%
NOH  74  39  50  68  99.9%
NYK  56  57  39  76  98.0%
OKC  64  49  49  65  95.0%
ORL  90  27  69  43  98.0%
PHI  57  57  44  70  90.0%
PHO  78  36  55  58  99.0%
POR  81  32  60  55  99.0%
SAC  37  78  20  91  98.0%
SAS  87  28  69  44  98.0%
TOR  55  60  35  78  99.0%
UTA  83  32  52  62  99.9%
WAS  43  72  18  94  99.9%

Jimmy United States

3/11/2011 6:18:55 PM #

Crow

Thanks for showing how strong confidence is with 3 years of data.

  "statisticians can't arbitrarily lower the confidence threshold "post hoc" to confirm the hypothesis we were trying to test in the first place."

I agree with that for statisticians and formal hypothesis testing.

But, though I am being repetitive,  managers looking to go beyond  not knowing between an either / or choice for lack of 95+% confidence, could decide to  go with the stronger choice if the confidence is well above 50%. Before the test or after it.

Crow United States

3/12/2011 1:50:56 AM #

Jeff Fogle

Great stuff Jimmy and Crow. Can you come up with a confidence interval at the league level? Say, there's a 95% chance or better that home court advantage is worth 2.7 to 3.3 points or something similar? I think we agree that the math proves home court advantage exists (particularly if you're using more than one year). What can be pinned down about it?

Back in the mid 1980's a place called Computer Sports World (which I think still exists) used to have a feature called 32A that would show you home and road totals for every team, then have a league composite at the bottom. Since the composite was "the league against itself" the home court advantage math on that scale was always right there. You could see if it was 4.2 of 4.7 or whatever (higher back then). Amazing how much you learned about teams and the league from that one chart, which they used to update daily. Things have come unimaginably far since then obviously. Amazing everything Joe has here at hoopdata.

Jeff Fogle United States

3/12/2011 3:31:11 AM #

Crow

I think there has been a recent academic paper or two on HCA for league in general. A confidence interval  may have been included or could be constructed.

And there maybe other league estimates at APBRmetrics or elsewhere.

And, though it is a different product,  I think someone in the blogosphere produced team level HCA point estimates. I recall they varied by maybe up to 1 point.

But I don't have the energy to search for them right now.

My comments were more about being willing to go outside a 95% confidence interval in basketball decision-making than about HCA.

Crow United States

3/12/2011 8:45:47 PM #

Crow

Found this article on HCA this season from a few weeks ago.

www.covers.com/.../articles.aspx?theArt=223346

Crow United States

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