Long Stretches of Alternating Wins and Losses

Some of you may recall a series of analyses I conducted back in January and February on the St. Louis University men's basketball team's remarkable pattern of alternating wins and losses for its first 19 games of the 2005-06 season (game-by-game log). In other words, the team won every odd-numbered game and lost every even-numbered game until it was 10-9 after 19 games. St. Louis then won its 20th game, which gave the team two straight wins, the first time two of its games had the same outcome.

Mathematically, I framed the problem as an "n choose k" question: If you had 19 little boxes lined up (one for each game) and 10 slips of paper with a "W" written on each (one for each win), where each box could hold either zero or one slip, in how many ways could you distribute the 10 slips into the 19 boxes? The answer, as obtained at this online "n choose k" calculator, was 92,378 different ways. This blurb mentions my analysis after SLU's first 17 games, at which point the team's alternation of a win, then a loss, then a win, etc., had roughly a 1-in-24,000 probability.

Frank Vaccaro has now looked into similar stretches in Major League Baseball history and he's also come up with a name for the phenomenon: Consistent Inconsistency. In an e-mail distributed to members of the Society for American Baseball Research's (SABR) listserve discussion forum, Vaccaro posted the following information (accurate as of the close of play on Friday, September 15, 2006):

You might notice that the Los Angeles Dodgers have been alternating wins and losses for the previous ten games. A loss tonight (very likely) will run their streak to eleven. [This indeed happened, then the Dodgers lost again, to end the alternation, as seen in their game-by-game log.] As I'm always on the lookout for regular-season predictors of post-season success, this caught my eye.

Consistent Inconsistency is not something that great, or even good teams, engage in... Other teams that engaged in long streaks of Consistent Inconsistency this year include Cincinnati, no surprise, 10 games, 6/19 to 6/29 and Atlanta, 10 games, 6/23 to 7/3. Toronto, already mentioned, would have also had a ten-game run of this stat had they lost yesterday -- but they won. This gave them two such streaks of nine games since mid-August.

Historically, there have been pennant winners who have had ten-game or more streaks of alternating wins and losses. Thirty-four teams, entering 2006, finished in first despite having alternating won-loss streaks of ten games or more, but this number jumps up as MLB adds divisions: 11 teams 1871-1968, 10 teams, 1969-1993, and 13 teams, 1994-2005...

Here are the number of occurences of these long streaks with only the most recent teams listed, entering 2006 (the date is the date of the start of the streak):

Streak--# of--
Length--Teams--Most recently accomplished by:

16--2--1981 LAn 6/7, 1974 PHIn 6/4.
15--3--1949 CHIn 8/16, 1913 CHIa 6/12, 1908 CHIa 4/28.
14--11--2005 COLn 9/17, 2001 MILn 8/22, 2000 CINn 6/20...
13--17--2000 FLAn 8/23, 2000 ANAa 8/18, 1992 OAKa 4/17...
12--29--2004 CHIa 8/24, 2003 HOUn 7/30, 2002 PITn 5/27...
11--77--2005 MILn 7/15, 2004 COLn 4/25, 2004 LAn 4/20...
10--118--2005 SEAa 8/28, 2005 LAn 5/2, 2004 PHIn 5/22...

257 STREAKS OF AT LEAST 10 G ALTERNATING WINS AND LOSSES

This makes the Dodgers the 249th team on the list. Eleven teams had two such streaks during their season.