Sport

If we turn up to spectate a sport for instance a football match is the outcome of the game any different to what it would have been, had we not been there?

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Alas, probably not, especially if (a) the crowd is very large and (b) your seat would have been filled by another fan, especially if (c) that fan would have been cheering for your team and about as loudly as you. But even if a-c are not true, it's not clear how much the cheering of the fans changes the players' performances and hence the outcome of the game. On the other hand, it always amazes me how significant the home field/court advantage is in every sport, including soccer (I presume that when you said "football match" you were referring to the beautiful game, not American football). What could explain the fact that a team is at least 10% more likely to win at home than away against the same opponent? (OK, I'm making up the 10% figure, but if anything I bet it's low, and Wikipedia says in English Premier League home teams are almost 40% more likely to score goals.)

Well, several things could explain home field advantage other than the crowds, such as familiarity with the environment and not having to travel. And as far as I can tell, contributing to the crowd noise is the only chance we have of influencing the outcome of a game. Hence if a-c are true, it's not clear how you could have an influence on the outcome, barring a belief in weird causal powers (e.g., you can give the opposing players cramps by looking at them funny) or exceptional circumstances (e.g., you are close enough to yell insults at David Beckham which make him perform worse--watch out, they may make him perform better!).

On the other hand, it's kind of like voting. You should vote even if it is unlikely that your vote will make a causal difference in the outcome, because if people stopped voting based on that belief, it would make a difference. If all the fans started thinking their cheers made no difference, the overall silence would make a difference.

Anyway, I still like to believe I can influence the outcome of a game ... even by watching it on TV! Hence, there's no way I'm going to Tivo an important Duke basketball game--they need my magical energy to flow in real time! (Yes, philosophers can believe irrational things, though I'm not sure it's accurate to say I believe something I know is false, but that's a question for another day...)

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