So, are sports fans ready to cheer on openly gay players?

A body of recent research suggests they are. A number of studies published over the last three years have found a steep decline in homophobic attitudes among both athletes and fans.

There’s no question that NBA player Jason Collins took a risk in telling the world, via this week’s Sports Illustrated, that he is gay. But that risk is far less than it would have been even a decade ago.

“Research on masculinities and homophobia today shows that, even in the traditionally conservative institution of sport, matters have shifted dramatically,” Eric Anderson of the University of Winchester wrote in the introduction to a 2011 edition of the Journal of Homosexuality, focusing on sports. “Today’s youth exist within a much-improved social and sporting landscape.”

Anderson, who became America’s first openly gay high-school coach in 2000, knows this as well as anyone; he has been researching homosexuality in sports for well over a decade. During that time, he has seen a dramatic shift in attitudes, which he charts in another 2011 paper (this one in the journal Gender and Society).

In it, he describes 52 interviews he conducted with gay male athletes on school-affiliated teams in the United States. Twenty-six of them went public with their sexual orientation between 2000 and 2002; the other 26 did so between 2008 and 2010. Those in the latter group “have had better experiences after coming out than those in the earlier cohort,” he reports, “experiencing less heterosexism and maintaining better support among their teammates.”

Anderson’s tentative conclusion: “Either sport in America has ‘learned’ from pioneering openly gay athletes, or (much more likely) cultural homophobia has decreased among the local cultures that the 26 men of the 2010 sample inhabit.”

Another 2011 study found a similarly accepting attitude at one “mid-sized Eastern university in the U.S.” A team of psychologists led by Jamonn Campbell asked 276 students to name their favorite sports team. They then read a short news article about a fictional athlete, and were asked to imagine he was on the team they regularly root for.

In all versions of the article, the player was described as a hard-working, well-liked five-year veteran of the team. But some of the study participants also read that he had recently come out as gay. Afterwards, they rated him on positive and negative characteristics, and described whether he was right for the team or should be traded.

Surprisingly, “participants rated the gay male player significantly more favorably than the heterosexual team member,” the researchers reported in the Journal of Homosexuality. “These findings were primarily driven by the ratings of our female participants. Whereas males’ impressions of the player were unaffected by his sexual orientation, females formed a more positive impression of the gay athlete than the heterosexual athlete.”

OK, but that’s a group of college students. How about the hard-core sports fans—those who post comments on message boards? Surely we’ll find homophobia there.

Yes, but not as much as you’d think. At least, that’s the central finding of a 2012 study from the U.K., published in the International Review for the Sociology of Sport. Jamie Cleland of Loughborough University looked at over 3,000 anonymous posts on 48 soccer message boards, all of which dealt with fans’ reactions to openly gay players.

Despite “some orthodox views toward homosexuality,” he writes, “a majority of (a team’s) supporters demonstrate more inclusivity through the rejection of posts that they feel have pernicious homophobic intent.” He found that fans “frequently challenge” posts deriding players due to their sexual orientation, “and suggest that on-the-field performance is what is valued the most.”

Presuming Collins returns to the NBA next season, it seems likely that most fans of his new team will have a similar reaction: We’re happy to have you, so long as you help our team win.

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