The St. Louis Cardinals' 8 1/2 game lead over the Houston Astros in the National League Central with only 12 games left (after the close of play on September 19) has almost completely evaporated. The Cards' lead now is only 1/2 game, with the final weekend of play remaining -- Houston at Atlanta, and St. Louis hosting Milwaukee (game-by-game logs for the Astros and Cards).

Presumably in connection with this dramatic turnaround, CNN/SI has posted its list of the greatest Pennant Race Collapses of all-time. To refer to these occurrences purely as "collapses" tells only half the story, in my view. In many (if not most) cases, one team's collapse was accompanied by another team's getting extremely hot. In some instances, the team making the comeback only won the pennant (league or divisional) by a single game at the end or in a special play-off after the seasonal standings ended in a tie. Thus, both the collapse by one team and the hot streak by the other were necessary for the latter to win out.

From CNN/SI's list, for example, the No. 2 entry involved the following from 1993: "On July 22, the Giants led Atlanta by 10 games. The Braves went 49-16 down the stretch to win the NL West by one game..."

And the No. 8 entry, the famous 1951 showdown between the Brooklyn Dodgers and New York Giants had this storyline: "On Aug. 11, the Dodgers led the Giants by 13 1/2 games, but the Giants won 16 in a row at one point and went 37-7 overall before winning a three-game playoff, which culminated in Bobby Thomson's Shot Heard 'Round the World."

In 2004, on the previous incarnation of the Hot Hand website, I did a fairly extensive analysis to mark the 35th anniversary of the 1969 NL East race, in which the New York Mets overtook the Chicago Cubs (this write-up is no longer posted here, but is available from me upon request). The following graph shows that, once again, both a hot streak by one team and a cold one by the other were implicated. The Mets ultimately won the division by eight games, so in this instance, they could have gotten by with a bit less torrid of a winning stretch.















Will this year's Cardinals join the ignominious list of teams that squandered big leads and perhaps earn a special "honor" for doing it so late in the season? Stay tuned this weekend!

Byron Nelson, one of the all-time great golfers, died today at age 94. Among Nelson's many accomplishments was his record streak of winning 11 straight tournaments, which he did in 1945.

Tiger Woods is currently on his own streak, having won the last five tournaments he's played. In the above-linked article on Nelson's passing, Woods is quoted as follows:

"In this day and age, with this competition, to win 11 in a row would be almost unheard of," Woods said after his fifth straight victory when asked how Nelson's accomplishment compared with others, like Joe DiMaggio's 56-game hitting streak.

"What Byron accomplished, that goes down as one of the great years in the history of our sport. ... DiMaggio's record, I see that being broken more than winning 11 in a row."

In yesterday's pro football action, Washington quarterback Mark Brunell set a new NFL record with 22 straight pass completions. In looking over the play-by-play sheet (which can be accessed from the linked article), it appeared that many of Brunell's completions were short passes. Ultimately, however, a record is a record, and no one else had ever completed 22 in a row.

I didn't think the 2006 L.A. Dodgers could give us streakologists anything more to work with, beyond what they've already done this season! This is the team that, of course, lost 13 of its first 14 games after the All-Star Break, then immediately won 17 of 18, then later settled into a pattern one observer called "Consistent Inconsistency."

However, last night's Dodger miracle really takes the cake! Opening up the bottom of the ninth trailing 9-5 to San Diego, L.A. tied the game in a most unusual way -- solo homers by four straight batters. This particular feat had not been accomplished by any major-league team since 1964! (At the college level, though, we saw a team hit five consecutive homers earlier this year.)

Then, after the Padres took a 10-9 lead in the top of the tenth, the Dodgers won on a two-run homer by Nomar Garciaparra (ESPN.com article, play-by-play sheet).

Magnifying the significance of L.A.'s ninth-inning homer barrage further still, beyond the pressure of it being the ninth inning, the Dodgers and Padres are battling to the wire in the final weeks of the season for the National League West title (San Diego had entered the game 1/2 game up on the Dodgers, but Monday night's win now gives L.A. a 1/2 game lead).

The Dodgers most certainly don't have a Murderers' Row. In fact, they currently rank 15th in home runs out of the 16 National League teams.

To estimate the probability of the Dodgers' home-run burst, I first looked at the four batters who went yard (with their season-long home-run count and total number of official at-bats, which I found earlier today, in parentheses). In the order they batted, they are:

Jeff Kent (14 HR in 371 AB, ratio = .04)

J.D. Drew (17 HR in 460 AB, ratio = .04)

Russell Martin (10 HR in 378 AB, ratio = .03)

Marlon Anderson (9 HR in 244 AB, ratio = .04)

The probability of these four Dodgers putting together a string of four consecutive homers is thus:

.04 X .04 X .03 X .04 = .000002, or 1 in 500,000.

This calculation assumes independence of at-bats, like coin flips. One might argue that, if the same pitcher faced all four batters, he may have engaged in "streak pitching" to the same easy-to-hit part of the strike zone. An independence assumption may not be fully defensible, but it should be noted that the Padres changed pitchers after the first two homers, with relief ace Trevor Hoffman coming in (to no avail). The participation of multiple pitchers, along with multiple hitters, would seem to increase the independence of the events.

Can the Dodgers possibly top this?

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.

Jelena Jankovic, a tennis player I'd never heard of prior to today, has reached the semi-finals of the U.S. Open women's singles bracket. As with golf, there are so many men's and women's tennis players out there that it's not unusual for someone I've never heard of to do extremely well in a major tournament.

What makes Jankovic's case unusual -- and interesting to me as an observer of streaks -- is that, in the early months of 2006, she lost 10 straight matches. Given tennis's single-elimination format, she thus went from city to city, getting eliminated each time after one match.

However Jankovic did it, she was able to turn things around, making the quarter-finals (final eight) or better in several later tournaments. I'll have to think about what kinds of analyses I could do. For now, though, her winning streak of five straight matches at the U.S. Open is something to behold.

My specialty on this blog is, of course, the statistical analysis of sports streakiness. It has not been my intention to exclude other, non-statistical perspectives on hotness and coldness; I just haven't seen much of other genres.

Now, however, I've just finished reading the book Confidence: How Winning Streaks & Losing Streaks Begin & End (excerpt), by Harvard Business School professor Rosabeth Moss Kanter. The original hardcover version came out in 2004, but the paperback, which I read, just came out this year. Focusing on the worlds of business and sports, the book examines long-term failures, successes, and turnarounds from one to the other, through the lens of organizational culture.

In the athletic realm, Kanter uses two women's collegiate teams, North Carolina soccer and UConn basketball, to present the most extensive case studies of winning cultures, the Prairie View A&M football squad to illustrate a losing culture, and the Philadelphia Eagles' ascension to Super Bowl-quality in recent years to demonstrate positive turnaround. Dusty Baker's Chicago Cubs, who at the time of the book's initial publication looked to be turning around the franchise's longstanding losing ways (although they're not doing so at present), are discussed more briefly, as are several other teams.

What I take to be Kanter's major points are as follows:

*An organization's most visible results -- on the scoreboard or in financial data -- will tend to be reflected at a deeper level by other markers, such as a leader's communicative skills and ability to innovate (and spur innovation) and a team's work ethic, quality of facilities, community support, etc.

*Winning -- or losing -- can launch "chain reactions," thus perpetuating the original trend. Winning gets a team on television, helps attract better players (either through free agency in the pros or recruiting at the college level), builds fan support, etc., which fosters further winning, brings in money to improve facilities, etc. Losing sets the opposite types of events in motion.

*The ideal psychological environment for an organization seems to be one in which employees know they'll be held accountable for maintaining productive output, but feel supported enough that they will be comfortable taking risks, innovating, and reaching out to colleagues in a collaborative spirit. Failure of a promising idea to bear fruit will not trigger a cycle of criticism and blame, but rather a coming together of employees to improve the next time.

These ideas certainly seem valid. The tricky part -- which Kanter readily acknowledges -- is in untangling the causality. Yes, a positive attitude (or nice facilities or fan support) can help a team win, but winning will also likely promote a positive attitude (and the ability to construct new facilities and to attract fans).

Implementing Kanter's suggestions could well spur a winning streak, but even if a team doesn't end up winning as much as it had hoped, the changes could still be a net positive. One example I've thought of is that a university that attempts to improve its national academic ranking by building a new libary, will still have a nice new library, regardless of what happens with the rankings. Ultimately, however, there are no guarantees. I suspect there are many sports teams Kanter did not talk about that work hard in practice, assess player performance via objective "metrics," have nice facilities -- and still lose.

Statistical hot-hand research, that is, whether outcomes of successive trials on sports tasks are independent or not, is discussed occasionally in the book -- including citation of the Gilovich et al. study and a reference to Duke men's basketball coach Mike Krzyzewski's philosophy that players should always focus on the "next play," without carrying over any reaction from the previous one (p. 351). Most of the book's subject matter deals with long-term trends, however, and not moment-to-moment performance.

At 380 pages, the book will require dedication from the reader. Many portions seemed redundant to me, and full of platitudes. Often, the text jumps from one team/organization to another. My favorite parts were the extended discussions of single case studies, such as Prairie View football, Continental Airlines, and Nelson Mandela's leadership in transforming South African society.