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Peter Nelson, a Seattle Seahawks fan, will cheer every bone-jarring hit when the team's defense squares off against Denver Broncos quarterback Peyton Manning and his offense in this Sunday's Super Bowl.

But the 32-year-old engineering professor would be much less enthused if he ever had to watch his son, now 8 months old, deliver or receive one of those punishing blows.

Mr. Nelson counts himself among the 40 percent of American adults, and 37 percent of parents, who would encourage their child to play a sport other than football because of concerns about concussions, according to a new Wall Street Journal/NBC News poll.

"It just seems like everything that has come out over the last few years make it scarier and scarier to see what happens to people who have played football for years," Mr. Nelson said.

That puts Mr. Nelson in a distinct but sizable minority. Nearly 60 percent of respondents in the poll—and 62 percent of parents—said they wouldn't discourage their children from playing football.

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