Hawks, Doves, and Home Field Advantage

Sports researchers have been studying home field advantage for decades. It’s a universal phenomenon found in virtually every sport, and professional football is no exception. Home teams win 57% of all regular season games in the NFL. Measuring it is easy. The question is, what causes it?

Several studies have tested theories about crowd noise, referee bias, time zone effects, climate, and peculiarties of ballparks. But these effects have not been shown to account for much if any of HFA.

Some recent research looked at when HFA manifests itself in games. In the NBA, HFA (or HCA rather)  is strongest in the beginning of the game and then diminishes as it goes on. I found the same phenomenon in the NFL. The first quarter shows the strongest HFA by far. Now, baseball research reveals the same phenomenon. It’s also been shown that HFA in the NFL is strongest between inter-conference games and weaker between intra-divisional games. With the advent of inter-league play, baseball also appears to have the same tendency.

I think these findings all point toward the same theory, namely that a significant portion of HFA comes from environmental familiarity. I’m not talking about the quirks of an outfield or the type of turf in a stadium. I’m talking about the whole picture—the way we all feel comfortable when we’re in familiar surroundings and often feel anxious in strange places.

I think that game theory can help explain why this is the case. I’m not referring to the usual run-pass or fastball-curve game theory we talk about in sports. Instead, I’m talking about natural selection and behavioral evolution. I realize this sounds a little out-there, but bear with me.

The Hawk-Dove Game

Evolutionary biologists have used game theory to help explain animal behavior since the early seventies when theorist John Maynard Smith created the Hawk-Dove game. Imagine a species of bird in which males compete for mates peacefully. Doves try to wait-out their competitor suitors calmly, just hanging around until the other doves give up and fly off. The lone male with the most patience wins the mating opportunity.

Now imagine that a male bird enters the gene pool with a hawk-like approach to competing for a mate. Hawks fight aggressively to win mating opportunities. The hawk strategy will obviously dominate the passive dove strategy because whenever a hawk encounters a dove, the dove flies off and the hawk wins. You’d think that after enough generations, the hawk behavior would completely wipe out the dove behavior from the population, but that’s not what happens.

Once there are enough hawks in the mix, hawks will begin to encounter other hawks, resulting in bloody battles that often maim and wound even the winner. This is a very costly strategy, and the result is actually an equilibrium between hawk-like and dove-like males within the species. This way hawks don't run into other hawks too often. This balance is what theorists call an Evolutionary Stable Strategy (ESS).

Here is what the payoff matrix of the game would look like, where V is the value of winning the competition, and C is the cost of a bloody battle. (An example on how to read the table: The bottom left quadrant's 0 says "the payoff to a dove when it encounters a hawk is zero.")

Hawk-Dove Payoff Matrix

Hawks would always beat doves and earn value V. When doves encounter other doves they win half the time for a long-run value of V/2. When a Hawk meets another hawk they win half the time, but always have to pay the cost of the fight--C. Victory in a hawk vs. hawk conflict would be a Pyrrhic one if C is greater than V.

The "Bourgeois" Strategy

What happens if there were another strategy? Imagine that along comes a smarter bird, which sometimes acts as a hawk and sometimes as a dove based on whether he's on his own territory. If he's in competition on his home turf, he'll act as a hawk. But when he is intruding outside his territory, he'll act as a dove. The resulting dynamic is a relatively peaceful process for resolving conflicts.

This kind of behavior is exactly what we see so often in nature, from butterflies to lions, and from dogs to humans. It's why your dog spends half its time marking and expanding its territory. In fact, much of human history is a never-ending conflict over territory. Even today, at every level of society, from the urban gang to the nation-state, marking and patrolling territory is vital. Conflicts can be extremely costly, even for the winner, so nature has developed a relatively safe process for resolving them.

Theorists call this territorial strategy the 'bourgeois strategy' because it closely mimics the middle-class entrepreneurial ethic of property rights. Game theory shows us that the bourgeois strategy is dominant over both the hawk and dove strategies. Here are the payoffs when bourgeois is added to the matrix:

Hawk-Dove-Bourgeois Payoff Matrix
Hawk(V-C)/2V(V-C)/4 + V/2

Ok, there's a lot of V's and C's and fractions in that table, and it appears complicated. Behind the notation however, it's very straightforward. For example, when bourgeois encounters a hawk (bottom-left cell), half the time it would be on the bourgeois' own territory, and we'd get hawk vs. hawk. And the half the time the bourgeois would be the intruder, and we'd and up with dove vs. hawk. The total expected payoff for bourgeois vs. hawk conflicts would be:

Hawk vs Hawk = (V-C)/2 * (1/2), plus
Dove vs Hawk = 0 * (1/2)
Total = (V-C)/4

Repeating the same calculation for each possible bourgeois encounter produces the matrix above. Next we can solve for the equilibrium. If you do the analysis, you find that the bourgeois strategy is the dominant and stable strategy. In the long run it has higher payoffs than hawk and dove or any mix of the two. Deferring to the owner of territory is nature's less costly way of resolving conflicts.

The bourgeois strategy reflects how we generally operate as a society. It's a near-universal value to respect the territory of others. Economic or social systems that tried to ignore property ownership were unnatural, and were ultimately doomed to failure. Unfortunately, it's when both competitors believe they are fighting over their own territory that the real bloody battles occur. That's when lions will maul each other, (or when Hitler and Stalin laid waste to an entire continent). Natural selection helps us avoid costly conflicts because those who lack the instinct to respect territory will eventually cost themselves dearly.

Explaining Home Field Advantage

Hopefully, now you are beginning to see the connection to HFA. If humans have evolved with an instinct to behave differently based on territory, remnants of it would still be with us and would manifest itself even in the artificial conflicts of sports. My suspicion is that environmental familiarity triggers some kind of physiological response that heightens aggression, focus, or strength. Unfamiliar surroundings might trigger an anxiety response that softens our edge. When we are in a very familiar environment, our instincts say "be a hawk." And when we're in an unfamiliar environment, they whisper "be a dove."

Now, when I watch Ray Lewis play in Cincinnati, Cleveland and Pittsburgh each year, I don't exactly get the impression he's a dove. He'll take your head off if he can. The cognitive part of our brains would be able to overcome most of these "dovish" instincts and tell ourselves to try just as hard, but maybe not completely. Even if the bourgeois effect dulls the visitors' edge an by an imperceptibly small 0.2%, leaving the visiting team playing at 99.8%, that difference occurs in play after play. The cumulative effect is what becomes HFA, where home teams win a very noticeable 57% of the time.

A 2003 study (discussed here) found that prior to home games Canadian hockey players had highly elevated levels of testosterone, a hormone known to increase aggressiveness. So it's very plausible that physiological changes can occur based on territory, and we have reason to believe that it's familiarity that causes or enhances home advantage. Further, game theory tells us to expect a physiologically-based territorial advantage. Putting it all together, the bourgeois effect explains a lot.

I suppose the question now is, how do we design research to test the theory?

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36 Responses to “Hawks, Doves, and Home Field Advantage”

  1. Measure says:

    Fascinating stuff.

    I don't know about further research, but it would seem that teams should be working to attempt to mitigate the effect.

    I would suggest teams work at getting some practice in at the 'away' field/park/court in the days leading up to the game... which may not always be possible.

  2. Phil Birnbaum says:

    Hmmm ... here's one way to test part of the theory. Find a player who played for X last year, and Y this year. Find another player who played for Y last year and X this year. See if they have typical home field advantages.

    If they do, then familiarity with the park can be ruled out (since they have MORE familiarity with their old park). This makes the evolution bourgeois hypothesis more likely.

    Of course, you could also give visiting teams testosterone booster shots and see what happens to HFA.

  3. Jim Glass says:

    I've long known of the home field advantage patterns and long known of the hawk-dove analysis, but this is the first time I've seen them put together and never would have thought of it myself.

    Kudos on having a site full of great analysis and original ideas (even if I am not yet entirely convinced by all of them).

  4. Anonymous says:

    How much of this effect could be self-fulfilling, that playing at home causes higher levels of testosterone and/or an advantage because the team is pumping itself up due to convincing themselves that they must defend home territory? Conversely, the same could happen to the away team, it might not feel the extra pressure/excitement to pump themselves up because they aren't at home.

    It's a chicken-or-egg scenario.

  5. Vince says:

    There was a study a few years ago showing that wearing red uniforms provides an advantage, with the theory being that red coloration is associated with higher levels of testosterone. I don't know if that mechanism has been tested, but if red clothing does work by boosting your testosterone levels (or lowering your opponents' levels), then that would provide some support for the testosterone theory of HFA.

  6. Ty Willihnganz says:

    Your theory makes a lot of sense, but when I looked at the NBA's "neutral game" era (prior to 1973), I found that teams winning percentages in "semi-home" games (games near their home city or within their natural fan base, such as the Celtics in Providence, Rhode Island) and "semi-away" games (just the opposite situation) closely mirrored their home and away winning percentages, whereas team's winning percentages in "pure neutral" games normally mirrored their overall winning percentage.

    Perhaps court familiarity explains this, but there were so few teams in the neutral game era, and teams played so few games at their "semi-homes" each season, that each individual team was apt to be just as familiar with an opponent's "proper home" as it would be with its own "semi-home".

    That's what led me to conclude the HCA must have something to do with the effects of partisanship, but that's just a guess.

    Good work, as always.

  7. Brian Burke says:

    Just another thought--If the response is highest at the beginning of games and then fades as the game goes on, then perhaps the signal is telling visitors to be reluctant to enter battle. But once the battle has begun, the response becomes muted.

  8. Dave says:

    Have you looked at the effect scoring first has? Obviously scoring first doesn't guarantee anything but it certainly helps take the crowd out of it if you're the visitor, and amplifies it if you're at home. I'm not sure how you'd qualify it though, because there's only 1 neutral site game a year.

  9. Tom G says:

    One problem with coming up with theories, is that, unfortunately, there is very little we know for sure. We know that homefield advantage is very real. We know it is stronger earlier in the game (and in baseball, earlier in the series). Other than that, there doe very much

    Is it weaker in divisional games because of familiarity or because of travel? In out of conference games isn't it stronger when the road team has to cross multiple time zones?

    Heard that it was also stronger on Monday night than Sunday morning/afternoon ... which makes sense based on survival / fighting / aggressiveness. But not sure if that is true or not

    Also would be interesting to see how much homefield advantage changes based on the strength of the team. When the Patriots were 16-0 and the Lions 0-16, there was obviously no difference in home record compared with road record. But has anyone broken teams up into groups based on their record and see if there were any differences?

    The survival / aggressive certainly does have merit. But I don't think it can fully explain the .580 winning percentage. I also wonder why this is one area of study that is based so much around guessing, rather than analyzing date. Especially when the data is so easy to see for anyone who wants to look at it

  10. Neily says:

    Just a small point which doesn't even affect the thrust of the argument (which is, as usual, excellent): I think you may have the Hawk-Hawk payoff wrong. If won, the payoff is V-C, but surely if lost, the payoff is -C, so the overall expected payoff is (V-C)/2+(-C)/2. As I say, it's a little pedantic.

  11. Brian Burke says:

    Yes. There's 2 ways of looking at it. The matrix above shows only the loser paying the cost of the fight, as if the winner were unscathed. If both pay the same cost, then it's V/2-C. This would halve the number of hawks in the population.

  12. Jeff Clarke says:

    Reminds me of the old Hawk n Dove bar on Capital Hill in DC.

    I think its an interesting analogy. I don't really buy it though. In war (or the animal kingdom) somebody risks their life in the invaded country because it directly affects their quality of life. There really are no realistic alternatives to war. People are largely homeless and starving and there is no realistic economy. They fight because they have to. In the invading country, the direct reason is typically much more convoluted and people go to a considerable amount of trouble to avoid fighting for something that doesn't directly affect them. Its not the same in sports. The reasons why you play are the same at home or on the road. Money and pride. I suppose you could make an argument on the high school or college level that people are more motivated to impress their friends and family at home but I doubt that makes any difference on the pro level.

    It is an interesting theory though. To be honest, none of the HFA theories makes a lot of sense to me but HFA clearly exists and there must be at least one reason.

  13. Jeff Clarke says:

    Not at all related to this topic but I want to talk about the Bills/Pats game and this is as good a place as any.

    The announcers are all talking about how smart Belichick was in not going for the onside. I totally disagree. Obviously it worked out for him but sometimes you just get lucky.

    The reason isn't entirely obvious. I haven't heard anybody mention it yet. The reason was that the onside kick came with an extra timeout. There was 2:06 left on the clock. An onside kick would have almost certainly been done in less than 5 seconds after first touch. That meant that even after a failure, Buffalo would have hit 2:00 after their first play from scrimmage. A regular kick was going to go all the way to 2:00. I couldn't believe it when he ran it out but I did know he couldn't take an immediate knee. He should have just run around the end zone for 6 seconds.

    Anyway after a regular kick, NE needed to stop Buffalo without a single first down. If they succeeded, they'd still have to go 70 yards in a minute and a half without any timeouts.

    After an onside failure, they still need to stop them. Buffalo could then try a 50 yard field goal or pooch punt. If they get the field goal, NE is in the same position as before except they need the 2 pt and they need to win in OT. In other words about 25% of the previous chance...which isn't big to begin with. If they don't try the fg (and frankly I don't think Buf would have tried the fg in that situation) they need to go 90 yards instead of 70 but with an extra timeout. I'm not altogether sure that is that much more difficult.

    The onside would have worked only 10% of the time. But I guess it comes down to 10% of scoring with plenty of time + 33% of scoring with a minute and a half and a timeout and 90 yards vs 33% of scoring with a minute and a half and 70 yards and no timeouts.

    The 33% comes from the assumption that Buffalo would get the gameending first down 67% of the time.

    I'd be curious to see numbers on all these scenarios and how much difference the extra timeout would have made.

  14. Ian says:

    I've long felt HFA wasn't to do with the crowd simply because in the amateur level sports I play there is a significant home-field advantage and we have practically no crowds at all (certainly not tens of thousands of angry Steelers fans waving towels).

    Of course, we have other issues such as travel conditions, the difficulty of getting subs out to away games etc but even when you think about the games when you travel early and with a decent strength squad, it is remarkably tougher playing away.

  15. Anonymous says:

    Tom G wrote: "We know it is stronger earlier in the game (and in baseball, earlier in the series). "

    Is there a paper, research or article written on baseball teams having a stronger HFA earlier in the series than later?

    I challenge you to come up with anything meaningful.

  16. John Candido says:

    Great eclectic post. I wanted to share some similarities to my own research that may help address the question a bit further. Games are almost entirely decided in the first two quarters, so the reduction of the effect is most likley due to the fact that the beginning of the game is most important regardless of home or away advantage. You may find it interesting that Edward Thorp and a Computer Science PhD actually built a statistical prediction model based on the variable of away teams enduring the stress of being on the road, staying in hotels and playing in unfamiliar stadiums. It was successful in Vegas. You can read about it in "Fortunes Formula" by William Poundstone or a paper Thorp wrote entitled "The Kelly Criterion in Blackjack, Sports Betting and the Stock Market". From a psychological perspective, I also believe that it has much to do with a concept called self-efficacy. That would explain the higher impact of HFA on Inter-divisional games as opposed to Intra-divisional ones.

  17. Anonymous says:

    John Candido wrote: "Games are almost entirely decided in the first two quarters..."

    What is your definition of "almost entirely"? What percentage of games where the team leading at the end of the the first half actually wind up winning the game? I'll be it is lower than 95% (which is what I'd define was "almost entirely".

  18. meixler says:

    Could someone explain to me what effect a home team's crowd BOOING that team could have over home field advantage? It's got to have negative consequences, right? Even if they want to behave hawkishly, the booing would suggest that they are doing something wrong, right? And then they'd be less inclined to perform hawkishly again? And maybe become something more like a turtle? Or an ostrich? At least a little bit, right?

  19. Anonymous says:

    This is all fascinating stuff but when it comes right down to actually playing the game of football perhaps we can tie some things together.
    Players and coaches in the NFL have always told me that the distinct advantage that the home team has is hearing the snap count and crowd noise. At home, their tackles can hear the snap count and since they know the count can get to the other guy a fraction of a second faster then the defense. When that same team is on the road, their tackles cannot hear the snap count and it allows the defense that split second advantage.
    Perhaps in the second half there can be two reasons that advantage may disapate. Crowd is growing hoarse, or they have been taken out of the game due to other factors and their team is losing due to turnovers etc.
    I know that this is a fact since it comes right from the field of battle so to speak.
    Also with inter-conference games the visiting teams fans are more apt to travel to the away venue due to familiararity and proximity.
    If you go and look at the the coaching theories of one of the best, Bill Walsh, he was always preaching one thing above all else. "Beat the other guy to the punch".
    No V's and C's but real X's and O's to perhaps tie in?

  20. Anonymous says:

    .570 is interesting for it equates to four wins out of every seven - gosh, what a surprise; to win the WS a team has to win best of seven and there is a very slim chance this can be achieved on home turf, and then only by one of the teams

    It would be nice to know how this translates across other sports as well

    A few years' ago I did a rough check on the Premier League in England; approximately 10% of the time the team scoring first went on to lose. I think this has increased but have not yet done a check for 2008-9

    The key point is territory. Attackers know they cannot win the "property" in the sense that a medieval castle could be captured, so they act as raiders or guerrillas. Conventional military wisdom requires at least a 2:1 advantage; up to 10:1 depending on the defenses

    So in most cases, unless very comfortable and familiar with the terrain, the raiding team is after what they can get and on balance the expectancy is that the home team will win

    Look how poor John Elway's stats were against divisional opponents compared to divisonal rivals particularly earlier in his career

    Given that the NFL generally thrives on competitive balance and there are rarely ties, four out seven is the minimum the home team should expect long term

  21. Eric says:

    This is most fitting in Seattle, where the "Hawks" have a pretty damn good winning percentage, thanks to their home field advantage :P

  22. Marver says:

    Two other things to consider:
    - Length/quality of sleep and concentration are related. Lack of familiarity with sleeping environment is related to length/quality of sleep, so there should be a relationship between the lack of familiarity with sleeping environment (road hotel) and subsequent concentration in the following day(s).

    - The fact that this occurs most in places/against opponents in which the teams are unfamiliar makes the first point more credible, but it also makes me think that perhaps this has to do with reduced preparation time. If you are going to be playing a team in which you aren't familiar, the loss of perhaps 5 hours of tape-viewing and/or practice time, could certainly be detrimental in game that week.

  23. SALVADORE says:

    I like Marver's thoughts. Time is finite.
    Travel requires more concerns that the home team does not have to account for. Anyone ever head over to the in-laws for an overnight or six? Yup, I'm always off my game, too. Now, if I did it eight times a season...

  24. Anonymous says:

    Swartz's work showed that HFA is *not* significantly stronger earlier in the series in baseball. This is an important finding, and really puts a dent in the original poster's thesis that HFA fades as a visiting team's familiarity increases. It's pretty clear that baseball HFA is stronger in, say, innings 1-3 of game 2 in a series than it is in innings 7-9 of game 1 in the series.

  25. Brian Burke says:

    Travel has been ruled out for the most part as the primary cause of HFA.

  26. Anonymous says:

    "it's when both competitors believe they are fighting over their own territory that real bloody battles occur. That's when lions will maul each other,"

    That comment is particularly insightful after a college basketball weekend featuring intra-city games involving Cincinnati/Xavier and Villanova/Temple. It's not hard to see it in another rivalries like Kentucky/Louisville or Alabama/Auburn in football either.

    I would expect this sort of theory to hold true more strongly in college or high school sports, where a territorial claim would encompass more than just a stadium and often overlaps. In professional sports, that territorial feeling probably ends at the boundary of your home field.

    Is the HFA more pronounced in college sports? I would expect so for both my reasons, but also because the larger, better schools schedule more home games against weaker opponents.

  27. mrparker says:

    How come home field doesn't seem to matter in other sports as much as basketball and football?

  28. Brian Burke says:

    I think the primary difference is due to the nature and structure of the sports themselves. NBA basketball features dozens and dozens of possessions, and the HCA is very strong. There is a tiny on every play, and it accumulates as the game goes on. By comparison, college basketball games are shorter and feature fewer possessions, and the overall HCA is weaker.

    Another factor is the degree of randomness in the sport. For example, MLB baseball is very random. (The Royals beat the Yankees 40% of the time. In contrast, the Lions would beat the Saints about 5% of the time.) It takes many more games for the better teams to come out on top in the MLB.

  29. Chris L. says:

    Where are you getting the 57% of all NFL home teams win # from? I ran my own analysis from 1993-2007 and found that home teams won less than 51% of their games. Maybe my data set was dirty? Based on those #'s I started to consider homefield advantage a myth (at least in the NFL, as those were the only games I ran the analysis on). Great stuff. Love the articles here. You are a champion.

  30. Brian Burke says:

    Chris, I suspect you made a math error somewhere.

  31. Anonymous says:

    I am a professional sports bettor, and also love to read books on evolutionary biology. Needless to say, I really enjoyed this article.

    Thanks for all you contributions.

  32. Ed Feng says:

    I met my friend's 5 year old son the other day at the park. The kid would not say a word to me. He does not say a word to anyone he meets.

    A week later, we were invited over to their house for a party. At his home, this same silent 5 year becomes the loudest kid among the 10 boys playing. He punctuates everything he says with an ear shattering shriek.

    If that doesn't convince people of your home field theory, nothing will.

  33. Brian Burke says:

    Ed-Too funny!

  34. tmk says:

    What about examining HFA in the first season of a stadium/arena's use, or individual EPA/WPA of players who have been traded playing in their old city. This might be better suited to baseball, due to sample size. Also, HFA in high school sports...the players slept in their own beds, and are surrounded by familiarity up until a few hours before game time.

  35. Tommy Valtin-Erwin says:

    Couldn't the fact that HFA is stronger at the beginning be explained by risk-taking? So, thanks to HFA, at the beginning of a game the home team jumps out to a lead. Then, as the game comes to a close, the away finds itself losing (thanks to HFA) and then takes more risks in an attempt to make a comeback. Or, it could even be explained more simply by the fact that teams with a lead (thanks again to HFA) is simply trying to run out the clock, while the away team needs points, and so scores them. Then, the away outscores the home team later in the game.

  36. Daniel B says:

    {{ Your theory makes a lot of sense, but when I looked at the NBA's "neutral game" era (prior to 1973), I found that teams winning percentages in "semi-home" games (games near their home city or within their natural fan base, such as the Celtics in Providence, Rhode Island) and "semi-away" games (just the opposite situation) closely mirrored their home and away winning percentages, whereas team's winning percentages in "pure neutral" games normally mirrored their overall winning percentage. }}

    You have found evidence that it's crowd-related. Specifically, most likely crowd effects on subconscious officiating bias.

    For example, officials in football call slightly more penalties on road teams. By itself, this could be b/c teams play worse on the road and thus commit more penalties. However, only "subjective" or "judgement" calls increase for the road team (except for - you guessed it - false starts and delay of games which are noise related). Road teams get called more for pass interference and offensive holding, but get called the same for intentional grounding or facemask.

    Similary, in baseball, the "true strike zone" (the boundary inside of which >50% of pitches not swung at are called strikes, and outside of which >50% are called balls - roughly a circle, not a square, for what its worth) is consistently very slightly larger for home pitchers and smaller for home batters.

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