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BGonline.org Forums
statistics question (not really OT)
Posted By: Chuck Bower
Date: Tuesday, 12 July 2011, at 4:59 p.m.
Tonight is Major League Baseball's annual all-star game, and if that isn't exciting enough for you, take a look at the history of wins/losses for the two leagues winning team shown) for the 81 contests to date for American and National leagues:
3A, NANAN, 3A, N, 4A, 4N, A, 2N, 3A, 4N, (tie), A, 9N, A, 11N, ANNAN, 6A, 3N, 5A, (tie), 7A, N
(Total is pretty even: 41N, 38A, two ties.)
Most people (including most people who claim they can) in fact have extremely poor ability to distinguish a random sequence of events from a non-random one simply by using judgement. But I think this one still breaks that concern.
Before asking the questions, note that ties in baseball are technically not allowed. You're supposed to keep playing until one team wins. During the regular season that might mean continuing the game on a much later date. (I can't give an example but I suspect when that contingency is difficult, AND the outcome doesn't have an affect on the playoffs, even this requirement is broken.) In all-star games there are other concerns which can lead to a high frequency of ties, as is illustrated above.
1) How do you account for ties in this calculation?
2) For non-simulations, what are even the right questions to ask? I.e. how do you go about testing this sequence to get more than a simple "unlikely vs. not" answer?
Anyone have more than a guess as to the commonness/rarity of this sequence if each team is equally likely to win each game? (I.e. can you put some calculations behind your answer?) I suspect a tight upper/lower bound (preferably both) are the best that can be done with pencil and paper, but I'll be happy if I'm proven wrong.
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