What Contributes to Home Field Advantage in the NFL?

Note: I originally published this on PhillyInferno.com, but given this is Chip Kelly's first home game in Philadelphia, I thought it would be appropriate to re-post. Scroll to the bottom of the article to skip to the interactive graphs.

I will never forget "Fourth and 26". It was early in the morning when we arrived. The parking lots at Lincoln Financial Field were already filling up and it was brutally cold. My friends and I dressed for it – I wore twelve layers – and we brought plenty of food to grill and plenty of beer. The beer we had to drink quickly, because at eight degrees a layer of ice formed on the surface. More than once I tilted a half- full can to take a sip and nothing followed. It was a cruel joke. Regardless, the twelve layers and amount of beer I drank made taking a leak a torturous endeavor. But in reality, there was no better place I would rather have been than that frozen hell. All because of Freddie’s hands. God bless them.

After Donovan McNabb delivered a hard-thrown wobbler that Freddie Mitchell stopped and secured for that critical first down, the Linc erupted. It’s a sound I will never forget. It was a deafening roar. My buddy and I screamed in disbelief and hugged everyone within, and just out of, reach. The Eagles were losing to Green Bay by three points at the time, and that miracle play gave the Eagles a new set of downs, which McNabb used to get into field goal range. There was not a doubt in my mind that David Akers was going to kick the 37 yard field goal needed to force overtime, and the Eagles were going to win it.

There were other great plays in that game (like Brian Dawkins’ interception of Brett Favre in overtime), but would these plays have happened if the game were played in Green Bay instead? Does this game illustrate the importance of home field advantage? It’s actually a question I didn’t intend to ask. This post was initially going to be about whether Chip Kelly’s offensive success formula can be applied to the NFL. In short, it does. But during my research I noticed that home teams have a decided advantage, so my attention shifted.

REVIEW

Home advantage in sports has been a popular research topic. A quick comparison of home team wins to away team wins will demonstrate that the phenomenon exists. For example, in their 2011 book Scorecasting, economist Toby Moscowitz and Sports Illustrated journalist Jon Wertheim looked at NFL wins from 1966 through 2010 and concluded that home teams win 57.3% of the time. The bigger question, and one they address, is why does home field advantage exist at all?

According to Freakonomics.com writer Stephen J. Dubner, Moscowitz and Wertheim discounted, through research, many of the popular reasons we think home field is an actual advantage:

When athletes are at home, they don’t seem to hit or pitch better in baseball … or pass better in football. The crowd doesn’t appear to be helping the home team or harming the visitors. We checked ‘the vicissitudes of travel’ off the list. And although scheduling bias against the road team explains some of the home-field advantage, particularly in college sports, it’s irrelevant in many sports.

Instead, Moscowitz and Wertheim adopt a theory proposed by a German economist, Thomas J. Dohmen. Dohmen addressed how decisions are influenced by social factors that often contradict our own best interest by looking at how decisions by referees in Germany’s Bundesliga are affected by the home crowd. He concluded that it’s not the crowd’s impact on the players that matter, but it’s the referees who are subconsciously affected. Dohmen found that German referees award more extra time during games in which the home team is behind by one goal, and more time when the game is tied but the home team is in a good position to score.

Sabermetrician Phil Birnbaum summarized Moscowitz and Wertheim’s adoption of this theory to the NFL, in terms of penalties and instant replay decisions:

In the NFL, "Home teams receive fewer penalties than away teams — about half a penalty less per game — and are charged with fewer yards per penalty. Of course, this does not necessarily mean officials are biased. But when we looked at more crucial situations in the NFL … we found that the penalty bias [increases]."

Away teams have their challenges upheld 37 percent of the time, versus 35 percent for home teams. But when the home team is losing, the visiting team wins 40 percent, versus only 28 percent for the home team. So it looks like the referees favor the home team more when they need it more.

RESEARCH

I don’t have data to support replay decisions, but on the surface, my own research seems to support Moscowitz and Wertheim’s suggestion that there may be a penalty bias, however subconsciously. From 2009 to 2011, NFL home teams averaged 6.08 penalties (offense plus defense) per game, while away teams averaged slightly more, 6.18. Offensive penalties were nearly identical, with home teams averaging 3.35 and away teams averaging 3.34 per game. The largest difference in penalties appears on the defense, where away teams average 2.84 penalties per game and home teams average 2.73. In addition, NFL home teams won 434 games (56.5%) by an average score of 23.12 to 20.67. Is this enough to explain home field advantage?

To answer this question, I’m using what I call an offensive efficiency rate (OER). This is not to be confused with the Defense-adjusted Value Over Average (DVOA) that FootballOutsiders.com uses to calculate offense efficiency. Instead, my efficiency rate is a bit simpler (if you’re familiar with my work, you may remember that I subscribe to a Gladwellian "less is more" kind of philosophy). I define offensive efficiency as:

(rushes + pass completions) / total offensive plays,

where total offensive plays is the sum of rushes, pass attempts, and offensive penalties.

I calculated OERs for home and away teams for the 768 games in my sample, then performed a logistic regression to determine if OERs could predict game outcomes. The results were very conclusive (p-value <.00001). When the home team has a higher OER, the home team wins 89% of the time. When away teams have a higher OER, away teams win 80% of the time. Since the results were significant, I converted the individual team/game OERs to home and away win probabilities. And this is where I observed something I thought interesting. When both the home and away teams have identical OERs, the home team has a higher win probability. For example, when the OERs are equal to 75%, the home team has a 62.6% chance of winning, while the away team has a 46.2% chance of winning. Is this evidence of home field advantage?

I wasn’t sure so I sought help. I reached out to Phil Birnbaum, the sabermetrician who wrote a great review of Scorecasting and provided some interesting insight into Moscowitz and Wertheim’s findings. He suggested to me that, since home teams win more often, they may rush more often to protect a lead, which would in turn inflate their OERs. Since my data does not include play types per quarter, I randomly removed 100 home wins from my sample so OER averages were weighted the same (334 wins) for both home and away teams. I also decided to control for offensive penalties in order to see if there was still a home field advantage in this "equalized" environment, a relative vacuum. According to these new results, home and away win probabilities are nearly identical:

Then, when penalties are included, win probabilities extend slightly in favor of the home team:

This graph is interesting because it shows a small away team advantage as OER decreases. However, when including penalties in an equalized environment, there does seem to be a slight home field advantage as OER increases. When both teams have an OER equal to 80%, the home team has an 80.8% chance of winning, while the away team has a 73.4% chance of winning. Since we know what HFA looks like in a controlled, equalized environment, and what it looks like in reality (Graph 1), what about turnovers?

In reality, turnovers are the great equalizer. If the home team has just one less turnover than the away team, then home teams have a decided advantage. When OERs are equal to 75% and away teams have one more turnover than home teams, home teams have a 78.5% chance of winning, while away teams have a 28.5% chance of winning:

And when home teams have one more turnover than away teams, home field advantage is all but erased:

Of course, there are exceptions. For more team-specific details, below is an infographic on NFL Home Field Advantage. Click on it to interact. I determined HFA by subtracting each team’s average Home Win Probability from their Home Opponent’s Win Probability. The larger the difference, the better the HFA. Using this rubric, the Green Bay Packers had the best home field advantage from 2009-2011, while the Washington Redskins had the worst.

CONCLUSION

Home field advantage definitely exists. As Moscowitz and Wertheim suggest and my own research illustrates, penalties do seem to have a slight influence. However, I cannot claim that this is caused by subconscious referee bias. I also cannot discount the power of the crowd. The fact that away team defenses average more penalties than home team defenses could indicate a referee bias, or it could indicate an away team defensive player’s reaction to a high pressure social situation (the home crowd).

Also, not quantified here, is the home crowd’s impact on the home defense. As Birnbaum suggests, and I agree, humans evolutionarily have a need to defend their home. In football, this is extremely applicable. My guess is, when the home defense is placed in a high pressure, high emotion, high adrenaline situation, they will more often execute its collective desire than the away team’s offense. In other words, even if both team’s may have the same OER, the home defense, feeding off the energy of the crowd, wanting to defend its home, is more likely to obtain that "key, timely stop" than when playing away. Perhaps this is why Darren Sharper did not defend Freddie Mitchell like he was supposed to. So Eagles fans, continue the deafening roar.

Special thanks to Phil Birnbaum. Check out his work at http://blog.philbirnbaum.com and http://www.philbirnbaum.com.