tl;dr Sports fan behavior is explained by a combination of constant identity-forming team loyalty which is an end in itself, and status signaling by association which is modulated by team performance. These two factors differ between individuals and are associated with different cognitive styles, with constant loyalty more associated with moral foundations and intransitive preferences.
It's been observed that you can tell who a team's true fans are by noticing who remains loyal to the team even when that team is losing. I think this is meaningful, but it does beg the question: what are those fans getting out of it? Of course any speculation about this must mention the very real example of the Cleveland Browns, who over the past 2 years have a 1-31 record, and this year after going 0-16 they were on the receiving end of a sarcastic "perfect season" parade.
Humans get utility from associating with others with high status. Much of the happiness that a sports fan gets from their emotional connection to their team derives from this, and many observations are consistent with what a status-by-association theory would predict: fans are happier when their teams win because they feel high status and can signal higher status, they engage in extreme dominance displays when their teams win important contests (i.e., people acting like idiots as they come out of a championship game if their team won, yelling, jumping on cars, setting off fireworks) but not if they didn't win, they attend games more when the team is winning and less when the team is losing, and they wear branded gear to identify themselves with the team and otherwise let others know of their association.
But this theory falls short of explaining why, for example, there is any such thing as a team's consistent fanbase. By this model, everyone should just cheer for the best team, game by game (or even play by play!) It especially doesn't explain why the the Cleveland Browns have any fans left at all; supposedly they're a football team but I've seen a number of convincing arguments against that, for instance, every game of the 2017 season. During an 0-16 season you would expect that if fandom is about fully rational people maximizing utility by associating with high status teams, the fans would stop posting on forums, they would put their gear away and deny to others that they were fans, and the stadium would not just have lower attendance, it would be completely empty. Yet this is not what happened.
I think the answer here very likely has to do with the gap we see between two types of beliefs/behaviors that often produce apparent impasses in other domains of life, especially religion and politics, the intensity of which differs between individuals. This gap in rational and more instinctual behavior will seem very familiar to readers of books like Jonathan Haidt's Righteous Mind, or Simler and Hanson's Elephant in the Brain. Humans demonstrate some domains in their cognition which are inflexible and impervious to reason - to use Haidt's categories, harm, fairness, loyalty, authority, and purity. By "inflexible" I mean "not open to discussion, or conversion into money or other goods/services." For example, you likely do not believe that murdering children is morally acceptable. Are you interested in hearing arguments about why it might be morally acceptable? If you would never consider such a thing, and you're uncomfortable that I would even suggest it in a thought experiment, you're showing inflexibility in discussing it. Okay - would you kill an adult for $50,000? I see that also upset you, I'm sorry to have opened with such a low offer! $75,000 then? You're being inflexible (I hope!) in reacting by thinking "It's not about the number!" Okay, what's the conversion rate between adults and children? Forget murder, how about urinating on a picture of your family for money? etc., you get the point. "Inflexible" means it can't even be suggested as open for discussion, which includes not being allowed to convert between moral-foundation-violating acts and money, or between different types immoral acts. (A favorite of action movies or dramas to demonstrate the extreme evil of an antagonist is to have them force someone declare the relative value of immoral acts, e.g. Sophie's Choice.) To connect to the abstract - the philosophical term for having values that cannot be negotiated, and for which there is no relative value like this, is that they are intransitive.
I took you on this little tour of moral darkness to illustrate that morally normal humans do not adhere to consistent rationality, and the ones that actually do are psychopaths. (You may be interested to know that Haidt found that when he surveyed the business students he was teaching, they scored low on every single moral dimension, taught as they are that everything is negotiable.) So what does all this have to do with the Cleveland Browns? Many of us have noticed that "hardcore" sports fans - the ones who stick around with long faces even when the Browns are losing, and falsify the first model above - tend to have certain personality and cultural characteristics that fit well with some of these inflexible moral foundations: they tend to be more religious, more nationalistic, more conservative and more valuing of loyalty and authority. Sports fans rarely become hardcore about a team after entering adulthood, and very often there is a family lineage of fandom - and these are exactly the times and ways in which characteristics of core identity are formed. Also telling, while there were about 3,000 people who showed up for the Cleveland Browns parade, there were many fans who were quite angry about it - but online objections were mostly that it was "embarrassing". (No mention of the 0-16 record that inspired the parade.)
Before I put into words what might be motivating them and make predictions, here's a summary of the two kinds of of beliefs, producing two kinds of motivation. While these beliefs exist in everyone, there is going to be a distribution in the population, with one category of beliefs dominating the fandom-related cognition of some fans, and the other category dominating that of others.
|HARDCORE FAN||CASUAL FAN|
|motivated by moral foundations||by utility calculations|
|end in themselves||deliberate, external goal-oriented|
|higher value on loyalty||lower value on loyalty|
|adopted in childhood, maybe from family||adopted voluntarily in adulthood|
|central to identity||not central to identity|
|unwilling or unable to verbalize||position clearly verbalized|
|more often encountered in person||more often encountered online|
|sees casual fans as untrustworthy, sleazy||sees hardcore fans as stupid, gullible|
Of course it's a spectrum, and every fan is somewhere on this spectrum, but many of us clearly lean toward one or the other end. (If you're reading this, you're more likely in the right column than the left.)
To summarize the hardcore fan: he is motivated by more basic, instinctual moral drives, especially loyalty. Being a good fan is an end in itself, and an offer to burn a team jersey, to cheer for the other team, etc. in exchange for money is likely to not only be immediately refused but to provoke active offense. These fans consider their fandom a crucial part of their identity, to the extent of including team-related themes in their weddings or mentioning it in obituaries ("he lives and dies by the Browns"; "a Browns fan to the core.") He can get uncomfortable when the business aspects of a professional sport are discussed and overshadow the games on the field. Asking him to explain his fandom will be met with puzzlement, anger, or a jumbled set of team cheers and slogans, in the same manner as a person asked to explain why they are patriotic or follow a certain religion - "If I have to explain it to you, you'll never understand." And finally, because tribal loyalty sentiments are more warning-barks or team cheers than any kind of actionable proposition, you're more likely to hear such sentiments when talking to him in person, where the nonverbal (affect-laden and irrational) part of communication dominates. He will be a fan for life. When the bandwagon people disappear during losing seasons the hardcore fan says "Good riddance, good-time Charlie."
To summarize the casual fan: he is motivated by utility calculations about external goals (this team might win this year so I'll cheer for them, maybe I can make friends this way, maybe I'll look successful if I follow a good team.) He doesn't see what's impressive about staying loyal to losers, and really doesn't understand why making fun of your team when they lose is shameful or embarrassing. He probably picked up his fandom after college, maybe when he moved to a new city. He probably don't care either way about the business dealings of the team. If someone offered him money to stay home from a game or burn team logos, he would seriously consider the offer. He doesn't introduce himself to strangers as a fan, and five years from now he might not be following the team, or might not be following the sport at all. He can give clear reasons why he started following the team, and you're more likely to hear from people like him online. He shakes his head at the hardcores who keep shelling out cash for losing teams' jerseys.
Both the hardcores and non-hardcores gain utility in proportion to the team's performance. A team's performance can be negative, causing you to lose utility by associating with them. But there must be another source of utility for the hardcores, who somehow gain utility from the association no matter the team's performance - and that source of utility is a constant ability to demonstrate loyalty, period, to others as well as to themselves to reinforce their own identity. And this signal is most informative when your side is losing. Speaking quantitatively, in the utility equation for this model, there are two terms, loyalty (a constant for everyone, hardcore or not), plus the product of team performance times associative utility. Associative utility is how much your utility changes per team winningness. Both loyalty and associative utility vary by individuals, and team performance of course is determined by the team. The equation looks like this:
Team performance can be positive or negative. For the hardcores, loyalty is such a large term that it doesn't matter how negative team performance is, loyalty will alway be greater and the total utility will always be positive (this could be the definition of "hardcore", "rain or shine", etc.) Further toward the other end of the spectrum, the value of loyalty signaling decreases and the team performance makes more of a difference in whether people keep following the team. It's also worth pointing out that this explains people who don't care about sports at all, because they have zero loyalty and zero associative utility - that is, it doesn't matter how much the team wins, they still won't care.
Many of these predictions seem trivial, but the point is to relate these predictions to specific components of the hardcore fan's motivation structure as noted in the table above, which would be more informative.
- While utility is hard to measure directly, there are good proxies for it, like revenues, attendance, or Nielsen ratings. Given that there will be a distribution of hardcore to non-hardcore fans, there will be a non-zero floor to revenues so even 0-16 teams don't go to zero, as we observed. If we graph all of the teams on performance vs utility proxy, I would expect a mostly linear-looking scatter plot with an increase in the slope at the good end, for those teams with some expectation of a national championship, and possibly a flattening at the bottom. This may depend more on expected utility (if fans are pleasantly surprised by a win vs. they expect their team always to win.) I plan to try to collect some kind of utility-proxy data and see if this is in fact the case.
- In general a sport will be more successful in inspiring loyalty, the more similar it is to tribal warfare (always a reliable revenue stream for every team); maybe this is why football has eclipsed baseball as the national pastime.
- The more hardcore, the more they will pay attention to the outside charity activities of their own team, and the more outraged they will be by disloyalty-demonstrating acts, e.g. kneeling during the national anthem. They will also be more interested in the moral failings of opposing teams, especially rivals.
- The more hardcore, the less they will be interested in statistics, especially of other teams, even ones their teams are playing in important games.
- The more hardcore, the greater the difference in their interest in a player when he is on their team, vs. after he is traded. That is, hardcores think each of their players is a great person on and off the field - when he plays for their team - and any suggestion that they'll stop caring about him the second he is traded is likely to be met with hostility, but in fact this is the behavior they demonstrate. (He will also be annoyed when asked why, or when Seinfeld is cited - "Essentially you're cheering for clothing.")
- The more hardcore, the more they will feel sad or angry after a loss, and the more likely they are to attend or watch the next game despite having been very sad or angry at the last game's outcome.
- The more hardcore, the less tolerant they will be of fans behaving negatively toward the team, even when the team loses (very concrete and contra expectations here: you might expect hardcore fans to support a parade showing anger against the people making their Browns lose, but it seems to be exactly the opposite. Parallels to gay marriage here too: how exactly does the 0-16 parade degrade your fandom, when you didn't attend?)
- The more hardcore, the more they will confuse the team with a government agency or public good (i.e., demanding that the city finance a new stadium.) More recent teams with cities that have highly educated and/or mobile populations (i.e. the coastal Pacific) will therefore find that they can't get what they want from those cities, because the voters don't care (Seattle, San Francisco, San Diego) where other cities filled with less mobile, less educated people would crucify their mayor for allowing a team to leave on their watch.
- It's often been noted that the Midwest with its brutal early winters has far more rabid sports fans than the mild West Coast. One possibility is that the loyalty-demonstration value of attending every game is diminished when all of those games are 70 F and sunny, vs some of them being freezing cold. (Think of the people who still wait in line in the cold and dark on Black Friday morning to buy things for their families. They do know that Amazon exists. So what do you think they're really doing?) Of course there could be a climate-independent cultural difference between east and west coast, but the model's prediction would be that Miami has equally low loyalty.
- The more hardcore, the more they will be upset if a star player leaves for another franchise, or the whole team moves to another city, and they use words like "betrayal."
- The more hardcore, the less tolerant they will be of long-term, off-field strategies, especially ones that alter play and result in on-field losses. (Both the 2008 Detroit Lions and 2017 Cleveland Browns had 4-0 preseasons, then went 0-16. Tanking (here and here) and/or salary cap manipulation? Difficult to explain as mere incompetence. And if it were confirmed that this is what is happening, the hardcore fans would be angry; casual fans might say "Huh, that's kind of clever, although it means you've been putting a bad product on the field." "My team is not a 'product'!" the hardcore fan says.)
- I'm not sure what to predict about the impact of hardcoreness on betting. The hardcores' loyalty may make them become overconfident in their team's performance. On the other hand, moral foundations-related beliefs are often kept carefully separate from anything affecting real-world decision-making. By that I mean: sacred beliefs are often more tribal chant than actionable proposition, and in general, people desperately avoid any bet that touches their moral foundations (next time someone makes a verifiable statement about religion or politics that you disagree with, offer to bet them, and see what happens. Typically they backtrack to a non-verifiable version of what they said, and/or get very offended that you would "cheapen" such an important matter by betting on it - which are all moves to avoid testing their belief.) Then again, the hardcore fans presumably know more about their team than most others, which means they should be more confident in their predictions, and be more willing to bet. Consequently they may be less willing to bet proportional to their claimed confidence, than would a casual fan with equal knowledge of the team would be. In my one test of this during March Madness, I found that self-identified fans did more accurately predict the outcome of a game involving their team than non-fans, but I collected no information on willingness to bet.
 This very article is diagnostic. By trying to dissect loyalty, instead of taking it as an obvious good and discussing it in the context of a specific team, I mark myself as someone with a small loyalty term in my equation - whereas people whose sports utility equation is dominated by loyalty would not understand, and/or be actively be offended by, a question like "What do you get out of being a fan of your team?"
 One might argue that a purely rational human being would ignore sports altogether - what do a bunch of guys chasing a ball on a field somewhere else in my city have anything to do with me, I've never even met them! - and I'm sympathetic to that argument.
 I hope no one read the paragraph about the price of murder and thought, "Hmmm...What is my price to kill someone?" In the case of exemplar psychopath Richard Kuklinski, he got positive utility from harming people so he kept doing it even after he ran out of work.
 When people do not have VNM-consistent rationality (that is, they have these inflexible, non-negotiable, non-fungible beliefs - i.e., intransitive preferences) - they can be turned into money pumps, by observant and unscrupulous characters who can carve their motivation structure at the joints, i.e. focusing on the the inconsistencies. While this has been reproduced now in artificial settings, not only salespeople but politicians have been doing it since the dawn of civilization. The NFL and in particular the Cleveland Browns are doing exactly this to the fans by exploiting the intransitive preference of loyalty, and I would be very surprised if their marketing does not already have a model of their fans and spending patterns similar to what I've described here. Another follow-up is to look for literature on whether psychopathy allows one to see these disconnects more easily, or (hopefully) the ability to see them and the willingness to act on them are unrelated and therefore form a mercifully narrower sliver on a Venn diagram of the population.
 There's probably a Markovian/hedonic treadmill effect here too, where the utility multiplier from a team's win is not constant but rather influenced by expectations based on the team's record. Next year if the Patriots go 9-3, fans leaving a game after a win won't be as happy as Browns fans if the Browns have the same record.
 Remember Karl Rove dragging out the 2012 election night broadcast and refusing to accept the outcome, seeming a little nuts? But simultaneously advertising to ten million Republicans watching that he never ever gives up. Say what you will about Karl Rove, but "bad strategic thinker" was not among the many epithets hurled at him.
 When the Baltimore Colts were about to move to Indianapolis in 1984, the city actually tried to pass an eminent domain act (!) to take over the team, but the Colts escaped with the team's property under cover of darkness the night before. Other teams like the Chargers have found a much more lukewarm reaction on threatening to leave, and found themselves without many fans.
 While I wrote this post I was wearing a Garfunkel and Oates sportsball T-shirt, so you can guess which end of the spectrum I'm near.