10th Anniversary of Hot Hand Website

Today marks the 10th anniversary of the launching of the Hot Hand in Sports website. The page has gone through a few different looks, as shown below. From 2002 to 2006, I used just a very basic FrontPage HTML format for the site, which was hosted on my college's server at Texas Tech University.

In 2006, I transferred the site to Blogger/Blogspot, where it has remained ever since. However, I've changed the template somewhat during the past six years. Here's how the page looked in its early years on Blogger.

Finally, 2011 and 2012 have brought major new developments. The book Hot Hand has now been published (see upper-right column). Also, I have started issuing brief updates on streaky performances right as they occur, via Twitter (http:/www.twitter.com/alanreifman), reserving the blog for more elaborate analyses.

As long as athletes keep going on streaks and I enjoy writing about them, this blog and associated activities will keep on going!

New York Giants Bring Unusual Stat into Super Bowl

The New York Giants are the first team with a four-game losing streak during the season to make it to the Super Bowl, since the 2002 Oakland Raiders. No other team in American football's Super Bowl era (beginning with the 1966 season) has lost four straight and made it all the way to the title game in the same season.

I find it very surprising that a team with four straight losses during a 16-game season could make the Super Bowl, for two reasons. First, because the season is so short, it doesn't give teams much time to recover and compile a playoff-worthy record (although it is possible to make the playoffs with a weak record). Second, if a team loses four straight, one has to wonder how good that team really is. A lot of Super Bowl teams didn't even lose four games the entire season!

In fairness to New York, the four straight losses were to three eventual playoff teams and a fourth team (Philadelphia), which was good in spurts. Plus, the losses were mostly close. The Giants lost on November 13 to San Francisco (27-20), Nov. 20 to Philadelphia (17-10), Nov. 28 to New Orleans (49-24), and December 4 to Green Bay (38-35). In the playoffs, however, the Giants avenged their losses to the Packers and 49ers. (Click here for the Giants' 2011-12 game-by-game log.)

Interestingly, the Giants played their upcoming Super Bowl opponent, the New England Patriots, during the season. New York won that game, 24-20 on Nov. 6, and immediately went into its four-game skid!

Looking at this all-time chart of Super Bowl teams (with won/loss records during the season and links to game-by-game logs), we see that a few teams during the past decade nearly lost four straight the season they made the Super Bowl. The 2005 Pittsburgh Steelers and 2003 Carolina Panthers each lost three straight, whereas the 2008 Arizona Cardinals lost four out of five.

In 1978, the NFL adopted a 16-game schedule to replace the previous 14-game docket. Also, prior to 1978 there was only one wild-card playoff team per conference, making it extremely unlikely that a team with four consecutive losses could even make the playoffs.

College Hoops Hotness and Coldness

It's only late afternoon, and we've already seen instances of pronounced hot and cold shooting in men's college basketball.

Florida State's Deividas Dulkys hit 8-of-10 on three-pointers in Seminoles' 90-57 shocker over No. 3 North Carolina. Dulkys, a senior guard, has made almost exactly one-third of his shots from behind the arc during his junior (.333) and senior (.321) years, making this afternoon's 8-of-10 performance extremely unusual. How unusual?

Using what is known as a binomial probability calculator, we can answer the question of how likely a long-term .333 three-point shooter is to make 8 (or more) out of 10 attempts from downtown. The answer is .003 or roughly 3-in-1,000.

Jaron Nash is a Texas Tech sophomore forward who plays about 10 minutes per game (Nash stats). He doesn't get to the free-throw line much, but when he has, he hasn't shot well. In fact, before making a pair from the stripe late in the Red Raiders' 67-54 loss to Texas A&M, Nash had missed 11 straight free throws.

It's not like Nash got flustered and missed several free throws in one game while in a funk. Rather, he compiled the streak gradually over five games.

• Against Oral Roberts, he missed his last free-throw of the game, after two previous makes (box score, play-by-play).
• He then went 0-for-4 against Cal State Bakersfield (box score).
• And 0-for-3 vs. Southeast Louisiana (box score).
• He had no free-throw attempts in Texas Tech's next two outings, against Oklahoma State and Baylor.
• He missed his only attempt against Kansas (box score).
• Finally, this afternoon vs. Texas A&M, he missed his first two before making a pair (box score, play-by-play).

Hot Hand in Volleyball?

Science News has just published an article on research by German and Austrian investigators purporting to document a hot hand in volleyball spiking, and the reporter was nice enough to contact me for comment. A hot hand in this context would mean that a player who has successfully put away a few spikes in a row (known as "kills") would have a higher likelihood of a kill on his or her next spike than the player's long-term kill percentage would suggest. A cold hand would represent the opposite, that a player whose last few spike attempts have resulted in errors (e.g., ball hit out of bounds) would have higher than usual odds of an error on the next attempt than his/her long-term percentages would suggest.

Within the constraints of the data set to which the authors had access (partial game-sequence data from top players in a German men's professional league), the analyses were conducted with full rigor and in a manner consistent with previous hot hand research. However, as I elaborate below, I feel there was at least one major limitation in the available data.

One type of analysis done by the authors used the runs test. This statistical technique requires the researcher first to list the sequence of events, in this case, a given player's order of kills (K) and errors (E). A "run" is an uninterrupted sequence of the same outcome, either all K's or all E's. The following hypothetical sequence, with few runs, would indicate streaky performance (i.e., clustering of K's and of E's):

KKKKEEEKKKKK (3 runs)

Another hypothetical sequence (with the same number of total attempts), this time with many runs, would indicate less (or absent) streakiness:

KKEKEEKKKKEK (7 runs)

According to the Science News piece:

An analysis of playoff data from the 1999/2000 season for 26 top scorers in Germany’s first-division volleyball league identified 12 players as having had scoring runs that could not be chalked up to chance. Hot-handed players’ shots contained fewer sequences of consecutive scores than expected by chance, the result of a small number of especially long scoring runs.

As volleyball fans know, however, there is a third category of outcome for spike attempts, namely the ball is dug up (or otherwise kept in play) by the defense, and the rally continues. As I told the reporter, I definitely think those hit attempts should have been included in the analyses, but they apparently were unavailable in the data set the authors received. Hitting errors were very rare in the data, so balls kept in play may have been a better measure than errors of unsuccessful spike attempts.

(Cross-posted with VolleyMetrics.)

Doug McDermott's Three-Point Shooting Highs and Lows

I heard on ESPN Radio the other morning that Creighton University's Doug McMermott has been hitting at a .580 clip on three-point attempts so far this season. The sophomore's high success rate behind the arc is surprising for a couple of reasons. Typically, guards are the main outside shooters and McDermott is a 6-7 forward. Also, his percentage from long-distance a season ago was much lower (though still good) at .405 (47-for-116)

To see if there were any interesting trends this season, I plotted his game-by-game three-point shooting percentages (below), based on his seasonal log. The size of each data point corresponds to his number of three-point attempts in a given game (see graph's legend) and opponents are listed along the horizontal axis. You may click on the graph to enlarge it.

First off, McDermott doesn't attempt that many threes, just 50 (of which he's made 29) in 14 games. In his most recent outing, against Drake, McDermott didn't try any treys, despite playing 32 minutes. Twice, against Northwestern and Wichita State, he didn't miss from behind the arc, but he was only 2-for-2 in each of these games.

His steadiest stretch of hot three-point shooting occurred in Games 3-8. In each of these contests (except vs. San Diego State), McDermott shot within a range of .667-.750. Accounting for number of attempts, his most impressive game was against St. Joseph's (5-of-7, .714).

Otherwise, he's had a lot of ups and downs, but not any prolonged stretches of poor three-point shooting.

Creighton and McDermott are next in action on Saturday at Bradley.

Follow My Hot-Hand Tweets on Twitter

Happy New Year! Something new for 2012 is that I've started a Twitter feed and will use it from now on to "tweet" brief statements about streaky sports performances. For more in-depth analyses, I will still be writing here on the blog.

Follow me at: http://twitter.com/#!/alanreifman.

Bulls Red-Hot Down the Stretch as NBA Season Gets Late Start

Christmas Day was Opening Day in the NBA this season, thanks to the owners' lockout. Among the marquee match-ups was a Chicago Bulls visit to play the L.A. Lakers. For most of the second half, Chicago's shooting showed the rust of a longer-than-usual off-season. However, the Bulls caught fire in the closing minutes to pull out a stunning 88-87 victory.

Below is a shot-sequence chart for Chicago, based on the play-by-play sheet. I haven't done one of these in a long time, but it seemed fitting for the Bulls' second half. (You may click on the graphic to enlarge it.)

For roughly the first 20 of the 24 second-half minutes, Chicago's missed shots (blue) greatly outnumbered its made baskets (red). As shown in the legend at the bottom of the chart, longer line segments indicate greater distances of shot attempts. For the stretch highlighted in pale yellow, the Bulls missed 21 of 22 field-goal attempts. However, the Bulls came back to score 18 points in just the final 4:13 of the game, which was enough to win.

Streak-buster Sunday in the NFL

Not only did the Denver Broncos' six-game winning streak -- powered by quarterback Tim Tebow's frantic rallying of the team -- come to an end today. So did two other major streaks in the National Football League.

Denver lost 41-23 to New England. Tebow worked as feverishly as ever to bring the Broncos back, but Denver's defense allowed the Patriots to score enough to maintain comfortable leads.

The Green Bay Packers, who entered today's play with a 13-0 record, lost to Kansas City, 19-14.

Finally, at the other end of the spectrum, the previously 0-13 Indianapolis Colts got their first win of the season, with a 27-13 victory over Tennessee.

Tebow Leading Broncos to String of Improbable Wins

American football fans are abuzz with what has been termed "Tebow-mania" or "Tebow Fever." The reference is to Denver Broncos' quarterback Tim Tebow, whose unorthodox playing style, his "mixing faith with football" (in the words of one writer), and his team's winning ways have garnered him great attention.

As seen in the Broncos' game-by-game log, Denver won in Tebow's first start, October 23 at Miami, lost the next week to Detroit, and then went on a still-ongoing six-game winning streak. Amanda Rykoff, writing in an ESPN-W "roundtable discussion" captures the essence of Tebow-mania:

...I'm not going to try to explain why he's 7-1 as a starter for the Broncos this year. Or why Denver has been able to come from behind late in the fourth quarter in five of those seven victories. Or how the Broncos managed to win what seemed to be an absolutely unwinnable game on Sunday against the Bears, trailing 10-0 with two minutes left in regulation.

The blog "This Given Sunday" has a detailed summary of each Broncos/Tebow win during the stretch.

The improbable nature of many Bronco wins has led probability analysts to estimate the likelihood of Denver's comeback-heavy winning streak. The key element is the win probability in each game, based on historical data. If you click here to get to the Advanced NFL Stats website and then scroll down to the graph with all the wavy lines, you'll get an idea of win probability. First, you would select one of the lines, corresponding to how your team is doing with regard to score (e.g., leading by 7, trailing by 3). Once you have your line, then follow it along the horizontal axis corresponding to how many minutes remained in the game. For example, a team trailing by 7 entering the fourth quarter tends to win about 10% of the time.

Using a chart like the one above, analysts would then find the win probabilities for Denver in each of its victories, given the depth of Denver's dire circumstances in a given game (i.e., when it trailed the most with the least time remaining). One can then multiply the probabilities together to get an overall probability estimate of the Broncos' streak. (This is analogous to calculating the probability of rolling double-sixes with a pair of dice by multiplying 1/6, which is the probability of a six on one die, by 1/6, the probability of a six on the other die, to yield 1/36.)

Using this methodology, ESPN's Statistics and Information Blog estimates a probability of Denver winning its last six straight at "approximately one in 137,000. The odds are better that a flipped coin comes up heads 17 consecutive times."

"This Given Sunday" (the blog cited above) calculates the probability of the Broncos winning the seven games with Tebow as starter (ignoring the one loss). The verdict: "the odds of the Broncos winning all seven games from their lowest odds in each particular game situation [are] 1 in 27 million."

If you're going to use seven as the win total, you must take into account the one loss, in my view. The seven game-specific probabilities from "This Given Sunday" are as follows:

.01, .15, .58, .17, .18, .14, .01

If you throw out the high and low values, the Tebow-led Broncos typically faced around a .15 probability of winning in many of the games during the stretch. Using an online tool known as a Binomial Probability Calculator, we can ask the question: For a team that faced only a .15 probability of winning each game, what is the likelihood of that team winning seven or more out of eight games? The answer, given these assumptions, is .00001 or 1-in-100,000.

As many writers have acknowledged, Tebow obviously should not get sole credit for Denver's winning stretch. However, his contribution appears to be great. One metric is quarterback efficiency ratings, which attempt to boil down many passing statistics (e.g., completion rate, yardage gained, touchdowns, interceptions) into a single number.

ESPN's Statistics and Information Blog notes that Tebow has the highest score (96.3) on one such metric, the Total QBR, of all NFL quarterbacks this season in the final 7 minutes of the fourth quarter (using a certain minute-mark rather than, say, the fourth quarter as a whole seems a little arbitrary; would Tebow still lead if we used the final 8 minutes or 6 minutes?).

Along with Denver's defense, which has had to shut down opposing offenses, another key figure in the Broncos' recent success is kicker Matt Prater. Without his hot foot, the winning streak would be over. According to Adena Andrews's commentary in the aforementioned ESPN-W roundtable:

Prater, who was recognized as the AFC special teams player of the week after his performance against the Bears on Sunday (a 59-yard field goal to tie the game, and then a 51-yarder for the overtime victory), has hit 28 of the 29 career field goals he has attempted in the fourth quarter or overtime.

One final factor to consider is that, as unusual as the Broncos' stretch appears, maybe in the larger historical scheme it is not so unexpected. The National Football League has been around for roughly 90 years. Initially, the league had around 10 teams, and increased over the years to the teens and mid-twenties (with the NFL-AFL merger), and continued to expand to the present 32 teams. The number of games per team per season has increased from roughly 10-12 in the early years to the present 16.

Let's say that, in a given season under the modern schedule, each team would have 10 opportunities to begin a winning stretch for six games (e.g., right from the start, beginning after Week 1, beginning after Week 2, etc.). Once Week 11 had gone by, of course, it would no longer be possible to start a six-game winning streak.

As a simplification, let's say further that within each of the most recent 30 seasons, there were 300 opportunities for a six-game winning streak (roughly 30 teams X 10 opportunities); that for each of the prior 30 years, there were 200 opportunities; and for the first 30 years of the NFL, there were 100 annual opportunities. That yields roughly 18,000 opportunities. Considering the above likelihood estimate of the Broncos'  winning six straight in the comeback fashion they did (i.e., 1-in-137,000), it seems that Denver's recent feat goes beyond the ordinary course of events.

Penn State's Streak of Women's Volleyball National Titles is Over

Penn State's run of consecutive NCAA women's volleyball championships, which reached four last year, is now over. The Nittany Lions were eliminated this evening in three straight games by UCLA in the Sweet 16 round.

Photos from Book Signing

Today, I did my first-ever book signing, in the bookstore of my home university, Texas Tech. Several people, mainly friends and colleagues, came by. Thanks to everyone who came by to chat and/or buy the book!

Woods Ends Winless Tourney Streak

Tiger Woods yesterday ended his streak of 26 golf tournaments without a win. For most of Woods's career, it seemed the only long streaks he would record would be of the winning variety. But, times have changed.

Red Wings Putting Together Strings of Wins and Losses

Last night on the NHL Network's highlight show, it was pointed out that the Detroit Red Wings have been very streaky in their wins and losses thus far this season. Based on the team's ESPN.com game log, I created the following graphic of Detroit's streaks of wins (red) and losses (grey). If you want to see the little notations for games decided during a five-minute overtime (OT) period or a post-overtime shoot-out (SO), you probably need to click on the graphic to enlarge it.

As can be seen, the Red Wings won their first five games, then lost their next six, and so forth. One of the statistical methods of detecting streakiness is known as the runs test. A "run" is an uninterrupted sequence of entirely wins or entirely losses. The fewer runs a team has, the stronger the evidence of streakiness. After 24 games, Detroit has only five runs. Based on an online runs-test calculator, into which I typed a 1 for each win and a 0 for each loss, the Red Wings' number of runs was fewer than would be expected by chance (with a significance of .00082 for those of you with some statistical training).

In this type of analysis, one must be careful to check if the team's schedule contained stretches of easy or difficult opponents, which could inflate the amount of apparent streakiness. This may be the case to some extent for Detroit, but not totally. During the Wings' string of six losses, two were to Columbus and Calgary, both of which today are in last place in their respective divisions. Conversely, during its current seven-game winning streak, Detroit has beaten some of the league's better teams, such as defending Stanley Cup champion Boston, Los Angeles, and Buffalo. The November 25 win at Boston, in fact, snapped the Bruins' 10-game winning streak.

Losing Streaks in College Football Rivalries Coming to an End

On this rivalry weekend of college football, some teams that had lost many consecutive games to a particular opponent have ended their string of setbacks.

Michigan ended its seven-game losing streak to archrival Ohio State, with a 40-34 win in Ann Arbor.

Kentucky, which had lost 26 straight to Tennessee, finally vanquished the Vols today, 10-7.

Baylor snapped a 15-game losing streak to Texas Tech, outscoring the Red Raiders 66-42.

South Alabama 0-for-24 on Treys

The South Alabama men's basketball team went 0-for-24 on three-point shot attempts last Sunday against Florida State. South Alabama now shares the record for most three-point tries without a make, as Dayton's men also went 0-for-24 behind the arc in a 2008 game. In doing some research today, I discovered that I had previously missed the fact that there is a third school with an 0-for-24 day on treys, namely South Carolina State in 2004.

Baylor Gets First Football Win Over Oklahoma After 20 Straight Losses

Baylor's football team ended the school's 0-for-20 all-time drought against Oklahoma (dating back to the teams' first meeting in 1901) with a 45-38 win over the No. 5 Sooners last night. The Bears also had lost 33 straight to teams ranked in the Associated Press Top 10, since a 1986 win over then-No. 10 Arkansas.

Hot Hand, the book, is here!

I am pleased to announce the arrival of my new book, Hot Hand: The Statistics Behind Sports' Greatest Streaks. It represents the culmination of many years of writing about sports streaks on this blog and elsewhere. I have picked out what I consider the most interesting streaks I've written about on the blog for inclusion in the book, plus I've added some new stuff. On Amazon.com, you can "Look Inside" for a free preview of Chapter 1 (here's a direct link to Amazon's information about the book).

Yaari & Eisenmann Article on Free-Throw Shooting

Gur Yaari, a researcher at Yale School of Medicine, recently notified me of an online article on free-throw shooting and the hot hand that he co-authored with Shmuel Eisenmann. The study focused on whether basketball players have a higher probability of making the second of two free throws after making the first than after missing the first.

The classic Gilovich, Vallone, and Tversky (1985) article failed to find evidence of streakiness in free-throw shooting, but Yaari and Eisenmann noted that they were using a much larger sample than that of Gilovich and colleagues -- 308,862 free-throws taken from 2005-06 through 2009-10 in the National Basketball Association (situations in which shooters were awarded three shots after being fouled behind the arc were studied, but I don't discuss them).

Some of the statistical concepts cited were beyond my expertise, such as the hypergeometric distribution. The basic finding was clear, however. Players made around 72-75% of their free throws (depending on the season) after missing a free throw, whereas they hit on around 76-80% after making the first. The paper is full of technicality and subtlety. The authors precisely characterize their findings as: "essentially that the results are unlikely to emerge from a collection of uncorrelated sequences each with a constant probability of success and no auto correlation."

Yaari and Eisenmann also raised two possible explanations for their findings: what I would consider a traditional hot-hand scenario ("success breeds success and failure breeds failure"); and fluctuations between "better and worse periods." The authors found that players' hotness levels were uncorrelated from season to season, thus going against the idea that some shooters possess inherent streakiness.

The website "Sweat Science" also reviewed the Yaari and Eisenmann study. The review ended with the following call for caution, with which I concur:

...we’re usually referring to time frames that are longer than two back-to-back free throws [for a sequence to be considered a hot or cold hand] ... but far shorter than game-to-game variations. So in the end, I’m going to keep believing that the hot hand doesn’t exist until better evidence emerges.

NFL Streak Tidbits

This weekend's play in the National Football League had several streak-relevant developments.

The defending Super Bowl champion Green Bay Packers advanced to 8-0 on the season. With wins in the team's final two regular-season games of the 2010 campaign and four postseason games, Green Bay has now won 14 straight.

A team heading in the opposite direction is the Indianapolis Colts, who today fell to 0-9 on the season. It doesn't seem so long ago that the Colts were playing in Super Bowls (following the 2009 and 2006 regular seasons), but with star quarterback Peyton Manning not playing this season due to multiple neck surgeries, the team seems totally adrift.

Whereas the Packers' and Colts' respective streaks continue onward, there were also some streaks that ended today.

The Miami Dolphins won their first game of the season, after starting off 0-7. Adding in losses in their final three games of the 2010 season, the Dolphins had lost 10 straight.

Finally, this Associated Press article on the New England Patriots' loss to the New York Giants notes a couple of streak-ending elements associated with the Patriots' defeat:

The loss ended several impressive streaks: wins in an NFL-record 31 regular-season starts at home for [quarterback Tom] Brady and in 20 regular-season home games for the Patriots.

Carryover from Winning Game 6 to Winning Game 7 in the World Series?

The 2011 World Series -- which concluded with last night's rather unexciting St. Louis victory in Game 7, after the Cardinals' dramatic comeback Thursday night over Texas in Game 6 -- had many streak-relevant aspects.

One issue that probably occurred to many people is the apparent momentum that carried over from the Cards' Game-6 win to Game 7 (or perhaps the Rangers' demoralization that did the same). It is an easy enough matter to examine World Series that went seven games to see if the team that won Game 6 seemed to have an increased likelihood of also winning Game 7. This online compilation details the game-by-game sequences of winning and losing teams in each World Series, but runs only through 2004. However, it turns out that the only post-2004 Series to go seven games was this year's. Below, I list all World Series from roughly the last six decades that went seven games (it is admittedly an arbitrary cut-off, but I wanted to have a relatively large sample without the chart getting too long).

Year	Team That Won Game 6 Also Winning Game 7	Team That Lost Game 6 Winning Game 7
1952	NY Yankees	---
1955	---	Brooklyn Dodgers
1956	---	NY Yankees
1957	---	Milwaukee Braves
1958	NY Yankees*	---
1960	---	Pittsburgh Pirates
1962	---	NY Yankees
1964	---	St. Louis Cardinals
1965	---	LA Dodgers
1967	---	St. Louis Cardinals
1968	Detroit Tigers*	---
1971	---	Pittsburgh Pirates
1972	---	Oakland A's
1973	Oakland A's	---
1975	---	Cincinnati Reds
1979	Pittsburgh Pirates*	---
1982	St. Louis Cardinals	---
1985	KC Royals*	---
1986	NY Mets	---
1987	Minnesota Twins	---
1991	Minnesota Twins	---
1997	---	Florida Marlins
2001	Arizona Diamondbacks	---
2002	Anaheim Angels	---
2011	St. Louis Cardinals	---

HTML Tables

*Won final 3 games in coming back from 1-3 deficit.

In total, there were 13 instances of the team that won Game 6 continuing on to win Game 7, and 12 of the team that lost Game 6 rebounding to win Game 7. Pretty even. However, nine of the last 10 times the World Series has gone seven games, the team that won Game 6 went on to win Game 7.

Among the instances of the Game-6 outcome appearing to carry over to Game 7, we have some of the most heartbreaking losses from the perspective of the team that failed to close out the series in six games:

• The 1986 Boston Red Sox, seeking the franchise's first World Series title since 1918, failing to get one final out to finish off the New York Mets in Game 6, after leading 5-3 with two Mets out and no one on base in the bottom of the tenth. The Mets won in seven.
• The 2002 San Francisco Giants, leading 5-0 at Anaheim in Game 6 as the Angels came up in the bottom of the seventh, giving up 3 in the seventh and 3 in the eighth to lose 6-5. The Angels won in seven.
• This year's World Series, in which the Texas Rangers were "one strike, twice" away from closing out the Cardinals in Game 6. A listless Ranger squad then fell in Game 7 by a score of 6-2.

Of course, not all teams that have suffered a near-miss loss in trying to close out the World Series in six games have faltered in Game 7. The 1975 Cincinnati Reds, who squandered a three-run lead in the eighth inning of Game 6 and lost on Carlton Fisk's famous extra-inning homer, did manage to win Game 7.

Another factor to consider is home-field advantage. With the Cards' win last night, the home team has now won nine straight Game 7's.

Other instances of hotness and coldness from the World Series:

• The Cards' Albert Pujols, who recorded what some consider the greatest offensive performance ever in a single World Series game, blasting three home runs and getting five hits overall in six at-bats during Game 3, went 1-for-19 in the remainder of his official AB's. He thus finished the Series 6-for-25 (he did get on base with six walks, though, five of them intentional).
• The Game 6 and 7 losses were the first back-to-back defeats for Texas since getting swept three games by Boston on August 23-25. Each of the next 13 times the Rangers lost, they immediately won the next game. (The losses in question were: Aug. 27 to the Angels; Aug. 31 to Tampa Bay; Sept. 3 to Boston; Sept. 5 to Tampa Bay; Sept. 7 to Tampa Bay; Sept. 10 to Oakland; Sept. 16 to Seattle; Sept. 22 to Oakland; to Tampa Bay to begin the postseason; in Games 3 and 5 in the American League Championship Series against Detroit; and finally, in Games 1 and 3 against St. Louis.)
• Josh Hamilton, the ailing Rangers slugger, ended a drought of 65 postseason at-bats without a homer in the 10th inning of Game 6, with a two-run shot. It looked like it might be enough to give Texas the series, but the Cards tied the game in their half of the inning and won in the 11th.