Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.2 9/18/84; site lasspvax.UUCP Path: utzoo!watmath!clyde!burl!ulysses!mhuxr!mhuxt!houxm!vax135!cornell!lasspvax!rokhsar From: rokhsar@lasspvax.UUCP (Dan Rokhsar) Newsgroups: net.sport.baseball Subject: World Series Probabilities Message-ID: <538@lasspvax.UUCP> Date: Thu, 19-Sep-85 22:17:13 EDT Article-I.D.: lasspvax.538 Posted: Thu Sep 19 22:17:13 1985 Date-Received: Sat, 21-Sep-85 04:02:31 EDT Distribution: net Organization: LASSP, Cornell University Lines: 59 In preparing a text on probability for nonscientists, a professor of ours considered the possibility that the teams were equally likely to win, and computed the probabilities that the Series would go 4, 5, 6 or 7 games based on this assumption. A newspaper article from 1981 claimed that the Series has been tied at two games apiece 30 times in the 78 years of the World Series; this agrees well with the 3/8 predicted by the "equal probability" argument. The article goes on to say that in 22 out of these 30, the winner of the fifth game won it all, which is in agreement with the 3/4 prediction. Using the above assumption, the chance of a Series of a given length can be calculated; comparing with data from 1926-1975, we find 1926-50 Calculation 1951-1975 7-games 7 7.8 15 6-games 5 7.8 3 5-games 7 6.2 4 4-games 6 3.1 3 The 15 7 game Series lies more than 3 standard deviations away, and the 3 6 game Series is over 2 standard deviations away. To explain this anomaly we decided to test the assumption that the home team advantage was the cause. Since the Series is played with 2 games at home, 3 games on the road, and the last 2 (if needed) back at home, a significant home field advantage would tend to increase the number of games expected in a Series. In the last 30 years, the team which started the Series at home went on to win it 21 times (assuming that the advantage has alternated from league to league, and that the 2-3-2 format has been unchanged). Assuming that the probability of team A winning at home is the same as the probability of team B winning at home (i.e. the teams are evenly matched except for the home field advantage) this 21/30 ratio corresponds to a .87 probability of winning a home game. Using this .87 probability, the probabilities of 4, 5, 6, and 7 game Series are: 1926-50 Calculation 1951-75 7-games 7 13.1 15 6-games 5 6.9 3 5-games 7 4.4 4 4-games 6 0.7 3 This helps with the 1951-75 data but misses badly with the early data. One explanation is in that time the Yankees won 13 of the World Series casting in serious doubt the assumption of evenly matched teams. A dynasty would clearly lead to shorter Series' since the dominant team would win no matter where it played. In fact the Yankees' won 1 Series in 7 games, 1 in 6 games, 5 in 5 games, and 5 in 4 games. When all the Series' are removed in which the Yankees played, we are left with 6 7-game Series, 4 6-gamers,2 5-gamers, and 1 4-gamer, which matches the trend predicted by the principle of equally matched teams. Since 1955, no team has won more than 3 times in a row, and that only happened once (Oakland '72,'73,'74). We don't have statistics for individual games; this should be checked by those who can and are interested. Any other information relating to these issues would be appreciated. Dan Rokhsar Eric Grannan