Referee Bias in the NBA

It gets asked from time to time here why there is a home field advantage in every sport. I have answered this question with referee bias towards the home team for years. "Why are the refs biased?", you might ask. It is because people will pay more money for a ticket for good teams. When the home team wins, it drives up the value of that team and how much they can sell future tickets for. Ultimately, it is the fans who butter the ref's bread and I contend that subtle influence on the refs is why they call more penalties against visiting teams. I know any ref will vehemently deny this, so let's look at some statistics, shall we?

The following data is take from the five NBA seasons starting in 2013 to 2017. In 6,567 games played those five years, here are the number of personal fouls called by side:

Side	Total Personal Fouls	Average per Game
Road	135278	20.60
Home	130787	19.92
Total	266065	40.52

Maybe just random variance, you might argue. The average number of fouls per side per game is 20.26. Road team exceed that by 0.342 per game.

You should be asking at this point, what is the probability of that?

To help answer that, the following table shows a count of the number of personal fouls per side per game.

Total fouls per side	Number
7	2
8	9
9	21
10	51
11	109
12	205
13	267
14	440
15	599
16	838
17	951
18	1117
19	1269
20	1268
21	1140
22	1053
23	933
24	788
25	614
26	435
27	327
28	220
29	177
30	101
31	66
32	50
33	27
34	21
35	16
36	6
37	7
38	2
39	1
40	2
41	1
42	1
Total	13134

Some math will show the standard deviation of personal fouls per side per game is 4.342.

The variance of the mean is the standard deviation per game divided by the square root of the number in the sample. In this case 4.342/13134^0.5 = 0.0379.
.
As I showed before, the average either side is off from the mean is 0.342 points per game. That is 0.342/0.0379 = 9.025 standard deviations from expectations. The probability of results that skewed if home and road teams were expected to have the same average number of personal fouls is 1 in 11,138,867,028,804,600,000.

With that, I welcome the forum to ask questions or poke holes in my math.

The question for the poll is why do you think is the reason home teams perform better in all major professional sports?

Can you test the hypothesis that losing teams commit more personal fouls and visiting teams are losing more (for reasons other than ref bias), so losing more often would explain the personal foul discrepancy between home and away?

This is an easy one Mike. If one believes that just being home is an advantage, then the home team will be more likely to be ahead near the end of a game. What do teams behind do? INTENTIONALLY foul. So if the reason home teams do better is their fans’ cheering, they will be fouled more than their road counterparts. Often times 3, 4 or even more times in the last two minutes of a game.
There’s your answer.

To be fair, I do believe there is a bias not only against road teams but also in favor of ‘stars’.

I agree with Soopoo 100%. Fouling intentionally when you are behind at the end of a close game has always been part of the game at every level of basketball. Since road teams do lose more frequently, it is completely unsurprising that you have found this effect.

There are plenty of other reasons to suspect for the home advantage, which some thoughtful analysts have dubbed as a "traveling disadvantage."

1. Fatigue from travel.
2. Differences in time zones.
3. Differences between arenas in the background behind the nets that affect shooting accuracy for the visiting team
4. Different diet when traveling.
5. Different night-time leisure activities when on the road (drinking, wenching.)
6. Differences in elevation at selected cities that cause visiting teams to more quickly become tired
7. Psychological effects of a noisy, partisan crowd

I never liked that chapter in the Sportscasting book that advocated this theory of referee bias.

Being at home, sleeping in your bed, not traveling, very familiar with all aspects of the field/court is an advantage in itself. There is probably also a slight subconscious bias to the home crowd.

I umpired baseball, including State Finals and Spring Training games. Now, that's not a regular season professional game or playoffs, I admit, but during play, I didn't even pay attention to which team was which. Between inning I knew. During a break in action i knew. But during a play, it had absolutely no influence on my calls.

I'd say there is almost no chance that the refs in basketball want the home team to win for economic reasons.


ZCore13

I agree with the posts above , the home team has an advantage for a variety of reasons but referee bias is not one of them. That parade to the free throw line in the last minute of an nba game is the reason for the foul discrepancy

As a common sense check, it would be worthwhile to talk to professional athletes about why they think their team does worse on the road.

Also, does it seem possible that an average margin of 0.6 fouls per game would be responsible for the point differential between home and away teams (whatever it is), or for the win/loss discrepancy between home and away teams? My answer would be no, no way, absolutely not.

Quote: SOOPOO

This is an easy one Mike. If one believes that just being home is an advantage, then the home team will be more likely to be ahead near the end of a game. What do teams behind do? INTENTIONALLY foul. So if the reason home teams do better is their fans’ cheering, they will be fouled more than their road counterparts. Often times 3, 4 or even more times in the last two minutes of a game.
There’s your answer.

That's a very good point. I can't of a good argument to refute it.

somebody might check on this but I believe the home team in the NBA wins close to 60% of the games, a higher % than in any other sport and also considerably higher than in college b-ball.

I think in the MLB and NHL and the NFL the number is very close to 55%.

In baseball there are actually a group of umpires, who when they are behind the plate, have a very strong road team bias consistently year to year.

Ben May is one of them. Home teams are 8-18 in his games behind the plate this year. And you’re down 14 units if you bet the home team in his games

Hard to explain why. Could just be they take subconscious joy in shutting up a home crowd.

Quote: michael99000

Hard to explain why. Could just be they take subconscious joy in shutting up a home crowd.

Not true. Prior to this year home teams were 37-31 when he was behind the plate. You can't just take one year and say an umpire/referee is bias one way or the other.


ZCore13

Quote: michael99000

Ben May is one of them. Home teams are 8-18 in his games behind the plate this year. And you’re down 14 units if you bet the home team in his games .

If you call a flip of a coin 26 times, the probability of getting 8 or less right is 3.7759349%. I don't think there is enough data there to make any accusations. I'd suggest looking further back into his career if you want to make that argument.

Quote: Wizard

If you call a flip of a coin 26 times, the probability of getting 8 or less right is 3.7759349%. I don't think there is enough data there to make any accusations. I'd suggest looking further back into his career if you want to make that argument.

Totally agree with your conclusion (and it looks like the deeper history cuts against his argument), though to be fair, I think your example should be flipping a slightly biased coin that hits heads [55]% of the time hitting heads 8 or less times of 26. To account for home field advantage.

Quote: Wizard

If you call a flip of a coin 26 times, the probability of getting 8 or less right is 3.7759349%. I don't think there is enough data there to make any accusations. I'd suggest looking further back into his career if you want to make that argument.

By considering each game as a coin flip for that hypothetical , you’re assuming every game was a -110 moneyline on both sides. It’s possible some of the games the home team was favored

Quote: unJon

I think your example should be flipping a slightly biased coin that hits heads [55]% of the time hitting heads 8 or less times of 26. To account for home field advantage.

Good point.

I agree with previous posts about the structure of the NBA game could explain this (late 4th quarter fouling by road teams). I guess if you had the data on fouls by quarters/halfs/final 2 minutes, you may be able to dig into this idea more...

There are lots of theories for why home field advantage exists. There are only two or three reasons with any data to support them that I know of. One is referee bias. Fouls in basketball in the first three quarters would be something to look into. Interestingly, in basketball and football home advantage is generally stronger in the first quarter / first half. In baseball it is stronger in the first game of a series.

The best place to look is baseball. Can start with umpires calling balls and strikes and comparing it to pitchf/x. I'm surprised that information isn't easy to find. Next place would be to compare things like pitcher velocity by pitch type, that really can't be affected by the umpires in any way. It seems there really is no difference between home and road, which suggests strongly that athletic abilities aren't really affected much by the location of the game (https://www.isportsweb.com/2016/06/29/mlb-analytics-statistical-discrepancies-home-away-games/)

The idea that this is money driven so that the fans can be happy is probably horseshit. The money from ticket sales is so much smaller when compared to TV ratings. But it might be interesting to compare home advantage in non-televised games (where revenue is coming mostly from ticket sales) to games that are on TV. But now everything is broadcast, so that ship may have sailed. The one place I think money might matter is when it comes to extending a playoff series -- especially in the NBA.

The other thing that might matter is travel. This can be supported by showing how home field advantage changes based on how far the road team has to travel. Hawaii always seems to have the biggest home advantage (and the biggest road disadvantage).

Another possibility might be a team being able to build their roster and strategies to best fit their home stadium. The Rockies have the most unique environment, and like Hawaii, always seem to have the biggest home advantage (and biggest road disadvantage). Also, as baseball parks have become more uniform over the 100+ year history, the home field advantage has become less and less. The exception being interleague play where road teams are playing differently than how they built their team.

If anyone has any other theories, feel free to produce your own data, it could be pretty interesting. This is all the stuff I've been able to steal over the years that passed the bullshit test. Rarely helps with betting anymore as it all seems to end up as part of the odds anyway. Until about 10 years ago betting against teams traveling from one coast to the other was usually profitable. In recent years getting points on the home team in the 1q and 1h in the NBA playoffs has been great.

Quote: TomG

The best place to look is baseball. Can start with umpires calling balls and strikes and comparing it to pitchf/x.

Sportscasting puts a big emphasis on this. Somehow they got data showing where every pitch crossed the plate. They showed the borderline pitches were called in favor of the home team much more than the road team.

Quote:

The idea that this is money driven so that the fans can be happy is probably horseshit. The money from ticket sales is so much smaller when compared to TV ratings.

Not that I'm challenging that, but I would be interested to see some data.

Quote: Wizard

Quote:

The idea that this is money driven so that the fans can be happy is probably horseshit. The money from ticket sales is so much smaller when compared to TV ratings.

Not that I'm challenging that, but I would be interested to see some data.

https://en.wikipedia.org/wiki/National_Football_League_on_television

https://en.wikipedia.org/wiki/National_Basketball_Association_on_television

$4.4 billion and $2.7 billion per year. So ticket sales and TV revenue are close. (At 17 million NFL tickets per year that would require an average face value of $258 to be equal https://www.statista.com/statistics/193420/regular-season-attendance-in-the-nfl-since-2006/). (Also, the NFL figures is lower than it should be because the NFL Network gets to broadcast games for way below market rate)

Which means there is almost no chance that profits from customers who watch the game in person represent the majority of revenue for the leagues after merchandising, other broadcast rights, and all the other sources are considered.

From just this sports fan's perspective, I feel like the NBA referees won't blow the whistle against the home team when it's late in the game (unless it's flagrant), so in a close contest, a visiting team has to also overcome the refs.

When I watch the NFL, I've noticed that the refs will call pass interference on the home team even when it's late in the game, so I feel like there's less officiating bias in football.

Quote: TomG

$4.4 billion and $2.7 billion per year. So ticket sales and TV revenue are close. ...

Thanks Tom! I hope Paco sees that.