rokhsar@lasspvax.UUCP (Dan Rokhsar) (09/20/85)
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
rokhsar@lasspvax.UUCP (Dan Rokhsar) (09/20/85)
Just one more note about our discussion of the home field advantage in the World Series: we realize that a .87 probability of winning at home is extreme (the home field advantage averaged over all teams for a season is roughly 0.53, but (a) the teams involved are not average, and the home field advantage is most pronounced for good teams and (b) the home field advantage could easily be enhanced by the excitement of the World Series). What is really needed is for someone to check the outcomes of individual games. We HOPE that it isn't a media induced phenomenon (TV did appear around 1950, after all!) Dan Rokhsar Eric Grannan :wq
abgamble@water.UUCP (abgamble) (09/22/85)
> 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. > 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. > ... In the last 30 years, the team which started the Series at > home went on to win it 21 times ... > ... this 21/30 ratio > corresponds to a .87 probability of winning a home game. > > 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 Between 1951 and 1975 there were 155 World Series games played. The home team won 89 (57%) of those games, far short of the 87% you guessed. I think a far more plausible explanation for all the long series, is pitching. The strength of a team (the probability they will win) varies a great deal depending on who their starting pitcher is. For an extreme example, see the 1972 Phillies. Thus if you have one "hot" starter, you may have an 70% chance of winning game 1, but only a 30% chance of winning game 2. More examples, - In the 1975 W.S., the Red Sox were 3-0 when Luis Tiant started, and 0-4 in the other games. - During the 1960's, St. Louis was involved in the W.S. three times. The Cardinals were 7-2 in games Bob Gibson started, and 4-8 otherwise. Whether or not this explains the large number of 7-game series, I don't know, but at the very least I think it's an important point you've overlooked. -- Bruce Gamble - abgamble@water.UUCP