Saturday, February 26, 2011

Why is there no home-court advantage in foul shooting?

There's a home-site advantage in every sport.

Why is that? Nobody knows. One hypothesis is that it's officials favoring the home team. One piece of data that appears to support that hypothesis is that when you look at situations that don't involve referee decisions, the home field advantage (HFA) tends to disappear. In "Scorecasting," for instance, the authors report that, in the NBA, the overall home and road free-throw percentages are an identical .759. Also, in the NHL, shootout results seem to be the same for home and road teams, and likewise for penalty kick results in soccer.

However, there's a good reason for the results to look close to identical even if HFA is caused by something completely unrelated to refereeing.

The reason is that free-throw shooting involves only one player. At the simplest level, you could argue that foul shooting is offense. All other points scored in basketball are a combination of offense and defense. Not only is the offense playing at home, but the defense is playing on the road, which, in a sense, "doubles" the advantage. Therefore, if the home free-throw shooting advantage is X, the home field-goal shooting advantage should be at least 2X.

That's an oversimplification. A better way to think about it is that a foul shot attempt is the work of one player. A field goal attempt, on the other hand, is the end result of the efforts of *ten* players. Not every player is directly involved in the eventual shot attempt, but every player has the potential to be. A missed defensive assignment could lead to an easy two points, and the offense will take advantage regardless of which of the five defensive players is at fault. The same for offense: if a player beats his man and gets open, he's much more likely to be the one who gets the shot away. The weakest or strongest link could be any one of the ten players on the court.

So it might be better to guess that the HFA for a possession is 10X, rather than just X. We can't say that for sure -- it could be that the things a player has to do on a normal possession are so much more complex than a free throw, that the correct number is 20X. Or it could be that a normal possession is less complex than a free throw, so perhaps 5X is better. I don't know the answer to this, but 10X seems like a reasonable first approximation.


What would the actual numbers look like?

The home court advantage in basketball is about three points. That means that instead of (say) 100-100, the average game winds up 101.5 to 98.5.

Three points per game, divided by 10 players, is 0.3 points per game per player. Over (say) 200 possessions, that's 0.0015 points per possession per player.

If home-court advantage were made up only of serious mistakes, mistakes that turn a normal 50 percent possession into a 100 percent or zero percent possession, then that works out to exactly one point per mistake. In that case, the average player would make one such extra mistake every 667 possessions. That's a little less than one every three games. If you assume that a mistake is worth only half a point, then it's one mistake per player for every 333 team possessions.

In reality, of course, it's probably not nearly as granular as "mistakes" or "good plays". It's probably something like this: a player plays his role with an overall average of 50 effectiveness units, random between possessions, plus or minus some variation. But that's an average of home, where he plays with an average of 51 effectiveness units, and road, with an average 49 effectiveness units.

Still, that doesn't matter to the argument: the important thing is HFA is one point per player for every 667 total team possessions, regardless of how it manifests itself.


Now, let's go back to free throws. I'm going to assume that a player's HFA on a single possession should be about the same as a player's HFA on a single free throw. Is that OK? It's a big assumption. I don't have any formal justification for it, but it doesn't seem unreasonable. I'd have to admit, though, that there are a lot of alternative assumptions that also wouldn't seem unreasonable.

But the point of this post is that it is NOT reasonable to assume that a player's HFA on a free throw should be the same as the overall HFA for an entire game. That wouldn't make any sense at all. That would be like seeing that the average team wins 50 percent of games, and therefore expecting that the average team should win 50 percent of championships. It would be like seeing that the Cavaliers are winning 17 percent of their games, and expecting that they score 17 percent of the total points.

In any case, the overall argument stays the same even if you argue that the HFA on a single possession should be twice that of a single free throw, or half, or three times. But I'll proceed anyway with the assumption that it's one time.

If the HFA on a free-throw is the same 0.0015 points per player as on a possession, then you'd expect the difference between home and road free throw percentages to be 0.15%. Instead of the observed .759 home and road, it should be something like .75975 home, and .75825 road.

Why don't we see this? Well, here's one possible explanation. Visiting teams are behind more often, so will commit more deliberate fouls late in the game. They will try to foul home players who are worse foul shooters. Therefore, the pool of home foul shooters is worse than the pool of road foul shooters, which is why it looks like there's no home field advantage in foul shooting.

Since we're talking about such a very small HFA in the first place, this doesn't seem like an unreasonable explanation. It would be interesting to run the numbers, but controlling for who the shooter is. I suspect if you have enough data, you'd spot a very small home-court advantage in foul shooting.

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At Saturday, February 26, 2011 8:48:00 AM, Blogger King Yao said...

Here's the data I have from 2006/2007 season to the 2009/2010 season on Free Throws:

Overall game:
Home 75.95% (132,889 attempts)
Away 75.72% (126,128 attempts)

1st Quarter:
Home 76.02% (25,922 attempts)
Away 75.72% (24,241 attempts

2nd Quarter:
Home 75.41% (33,090 attempts)
Away 75.24% (31,633 attempts)

3rd Quarter:
Home 76.60% (33,261 attempts)
Away 75.84% (31,571 attempts)

4th Quarter:
Home 75.82% (40,616 attempts)
Away 76.01% (38,683 attempts)

At Saturday, February 26, 2011 10:28:00 AM, Blogger Phil Birnbaum said...

Wow, thanks! It's more HFA than I expected ... 2 or 3 percentage points in the first two quarters, 8 points in the third quarter.

I don't think the fourth quarter means much because of deliberate fouls ...

At Saturday, February 26, 2011 10:50:00 AM, Blogger Phil Birnbaum said...

If I'm not mistaken, the third quarter HFA is about 2.2 SDs from zero.

The overall HFA for the first three quarters is a little over .004 (just eyeballing).

So the HFA for a single free throw is about the same as for a single player on two or three possessions.

For a team, HFA on a single free throw is about the same as on 1/3 to 1/5 of a team possession. Put another way, it takes about 4 free throws to give the same HFA (in points) as a single team possession (on offense or defense).

If I've done the arithmetic right.

(Thanks again to King Yao for the data.)

At Saturday, February 26, 2011 4:08:00 PM, Blogger White Boner said...

I thought that this was great research and analogy, Phil. It's funny how epic the lapse in logic was (the assumption that the disparity in free throws should be the same as the disparity in home/road W%) and, yet, if I were reading the book, I'm pretty sure that I'd have just accepted it without a second thought.

Also, thanks to King Yao for his follow-up.

At Saturday, February 26, 2011 9:57:00 PM, Anonymous Anonymous said...

Phil, let's not get carried away with the results of King Yao's numbers. In 90,000 attempts or so (first 3 quarters), one SD of the H/R difference is around .2%.

The actual difference found is a little over .4%, which is barely significant at the 2 sigma level.

So we cannot say that it is the equivalent of "one player's 2 or 3 possessions" with much certainty...


At Saturday, February 26, 2011 10:36:00 PM, Blogger King Yao said...

I wish I had something to add, but I don't. I'm looking forward to more comments, thoughts, research on this topic. Thanks Phil.

At Sunday, February 27, 2011 12:29:00 AM, Blogger Phil Birnbaum said...


Did I get carried away? :)

Sure, there's a fairly wide error band around the estimate. Still, what's wrong with going with the point estimate?

Unless you're arguing that we should consider the possibility that HFA is zero (since we're barely significant). Is that what you mean?

At Sunday, February 27, 2011 9:06:00 AM, Blogger King Yao said...

Looking at preseason games in the NBA, MLB and NFL, it strikes me that the HFA in those three sports are pretty close in the preseason as they are in the regular season. This is surprising for different reasons in each sport. In the NFL - they play mostly backups. In MLB - they play in different stadiums than their regular season stadiums. In the NBA - the crowd shouldn't be in a frenzy as they may be in the regular season, so there shouldn't be nearly as much ref bias if ref bias exists (this should hold in the other two sports too). So why is the HFA in preseason games so close to the HFA in regular season games? I don't know, but I wonder if answering the HFA question, one needs to also consider the preseason HFA.

The numbers I have span different years, but I have no reason to think they are biased one way or the other.

Home team records
NFL Preseason: 932-685 57.6%
NFL Regular: 3086 - 2409 56.2%

NBA Preseason: 669-463 59.1% (I tried to exclude non-NBA games)
NBA Regular Season: 12,103-7996 60.2%

MLB Preaseason 1920-1660 53.6%
MLB Regular Season 10,473-8,922 54.0%

At Sunday, February 27, 2011 9:21:00 AM, Blogger Brian Burke said...

One reason why we wouldn't expect to see HFA in things like free throws, penalty kicks, or shoot outs might be due to the nature of the events. Unlike the rest of the game, they do not require exertion. Instead, they are muscle-memory exercises. And in the case of penalty kicks and shoot outs, the outcome is almost completely dependent on a rock-paper-scissors type of strategy mixes.

Related thought: I wonder if fastball velocity is higher at home than away.

At Sunday, February 27, 2011 9:29:00 AM, Blogger Phil Birnbaum said...

Brian: On page 121 of "Scorecasting," the authors say they couldn't find any PITCHf/x differences between home and road pitching.

King Yao: Very interesting results about preseason. I never thought about checking that. Very, very nice.

At Sunday, February 27, 2011 3:08:00 PM, Anonymous Alex said...

Phil, do you know if there's a difference in HFA for home runs versus some other kind of hit? From the way you set up the discussion, home runs should have a small HFA because it's an interaction between just the pitcher and the batter, but other plays should have a larger HFA because it involves the other defensive players.

At Sunday, February 27, 2011 3:27:00 PM, Blogger Phil Birnbaum said...

Hi, Alex,

HRs involve the hitter and the pitcher, which between them have a lot more confrontations than between the hit ball and the fielder. So you wouldn't expect that much difference.

Also, HR hitters are chosen for the park, at least a little bit, so unless you control for that, it could easily wash out the results, just like deliberate fouls washed out the results before King Yao broke it down by quarter.

I think you'd have to do a fair bit of work to get the pitcher and batter HFAs per pitch, then throw in fielding HFA on top of that and see what happens.

It doesn't seem to lend itself to an oversimplified model as easily as the NBA does, but maybe if you started with pitches and worked up?

At Monday, February 28, 2011 11:44:00 AM, Blogger Mike Fast said...

Brian Burke, yes, fastball velocity is higher at home than away. Most of the difference is in the first inning. I suspect this is because the home pitcher comes in warm from throwing in the bullpen whereas the visiting pitcher goes and sits on the bench.

At Monday, February 28, 2011 3:05:00 PM, Anonymous Anonymous said...

Mike, Can you print some numbers for home and away fastball velocities and perhaps break it down by inning (and overall of course)? Again, the authors of Scorecasting say that the velocities (and movement and location) for every single pitch (fastball, curve, etc.) are exactly the same, emphasizing that there is NO home/road difference in actual pitcher performance, which I find hard to believe. Do you have any data on home/road pitch locations?


At Monday, February 28, 2011 3:06:00 PM, Anonymous Anonymous said...

Mike, if you have an article which includes that data, you can just reference the article of course...

At Monday, February 28, 2011 3:16:00 PM, Blogger Mike Fast said...

I didn't separate relievers from starters, which you would obviously need to do for later innings, but shouldn't matter in the first inning. Results were published here:

At Monday, February 28, 2011 3:19:00 PM, Blogger Mike Fast said...

And no I don't have any data on home/road pitch locations. That's damn hard, if not in fact impossible, to do by pitch type because of classification issues. Overall pitch location, all pitch types lumped together, doesn't vary between home and road. But what you say about individual pitch types depends heavily on how you classify them to extent I think that information would be meaningless.

At Monday, February 28, 2011 5:57:00 PM, Anonymous Jim Kelly said...

Great insight Phil. I hope you don't mind that I will refer to your site on my blog later. I would like to let my readers know the good research you are doing.
Jim Kelly

At Monday, February 28, 2011 5:58:00 PM, Blogger Phil Birnbaum said...

Thanks very much! Sure, refer away!

At Tuesday, April 05, 2011 10:19:00 PM, Anonymous Anonymous said...

As far as mlb preseason, most "home" teams have more projected starters/stars in the lineup than the visiting teams do as the visiting teams choose not to travel with many of the starters. I'm not sure if this is the same for the NBA, but don't think it is for NFL. NFL would be subjective to must "umpire bias" however, as they have the largest crouds I'd think preseason.

At Tuesday, April 05, 2011 10:21:00 PM, Anonymous Anonymous said...

As far as the MLB preseason HFA, alot of that HFA advantage may be because most home teams have more projected stars/starters in the lineup than the away team. I'm not sure if this is the case for NBA or NFL.

At Saturday, October 01, 2011 8:27:00 PM, Anonymous Chris said...

The reason that preseason and regular season could be the same even w/ different players, different ballparks can be fairly easily explained. Effects of travel. Which team has been in town the longest. I think it would be an interesting study to see if HFA is different in strength for home teams that are coming back from a road trip, as opposed to home teams that just completed a series at home. Can we notice a difference between game 1 of series and game 3 of series? Just things to ponder.


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