Last night marked the conclusion of the Great Alaska Shootout, one of the many men's collegiate basketball tournaments taking place over the Thanksgiving weekend. The word Shootout was particularly apt, as the two finalists, champion Butler and runner-up Texas Tech, lit things up from behind the three-point arc all tournament long.

Here is Butler's report card on three-pointers:

Quarter-final vs. Michigan: 17-32, .531, with the top individual performances coming from Pete Campbell (6 of 11) and A.J. Graves (5 of 10).

Semi-final vs. Virginia Tech: 14-33, .424, including Campbell at 7-13 (Graves was a little off at 4-13).

Final vs. Texas Tech: 16-24, .667, with Campbell 4-7, Graves 6-8, and Mike Green 4-4.

Overall, the Bulldogs were thus 47-89 (.528) in the Alaska Shootout.

On Texas Tech's side:

Quarter-final vs. Alaska-Anchorage: 7-13, .538, largely based on John Roberson's 6 of 7.

Semi-final vs. Gonzaga: 8-18, .444, led by Alan Voskuil's 5-7.

Final vs. Butler: 3-PT FGS: 6-12, .500, with Voskuil going a perfect 4-4.

Overall, the Red Raiders were thus 21-43 (.488).

Historically, I don't know how often two teams in the same tournament (of at least three rounds) have maintained three-point shooting percentages this high, but I doubt it's very often!

Hot three-point shooting to start the season is nothing new for the Red Raiders. Almost exactly one year ago, the Texas Tech men were leading the nation in three-point shooting percentage (.504). As I discussed back then, the team's three-point percentage was likely to go down over the course of the season, purely as a matter of two statistical principles, regression to the mean and the small sample size for early-season statistics.

Indeed, the Red Raiders ended the year with a .412 three-point percentage, for eighth in the nation (because other fast-starting teams were also susceptible to the same statistical considerations, I did not predict that Tech would necessarily fall out of first place, just that the team's absolute percentage would go down).

As of this moment, according to ESPN.com's statistics page, Butler is fourth in the nation in team three-point shooting, making 77-164, for a .470 percentage.

Last year's three-point leader was Northern Arizona at .426 and, as I documented in a posting last year, from 2002-2006 no team led the nation in three-point shooting with anything higher than a .440 percentage. Thus, we'll see if Butler can exceed that level for a full season.

Texas Tech currently sits tied for 53rd in the nation from behind the arc (35-86, 40.7), due to some poor pre-Alaska shooting. From the Red Raiders' perspective, we'll see if their hot shooting in Alaska was a temporary blip or part of an incipient trend...

The story coming out of the University of Nebraska volleyball building tonight, quoting from this news release, is that:

Tracy Stalls tied an NCAA record by putting down 13 kills on 13 swings for a perfect 1.000 attack percentage, as the Husker volleyball team sent Stalls and NU's three other seniors out in style Saturday night with a 30-18, 30-10, 30-11 sweep of Texas Tech.

For those not all that familiar with volleyball statistics, what this means is that 13 times the ball was set up for Stalls to swing at, and all 13 times she delivered balls that the Red Raiders could not field. Stalls hit no balls into the net, nor out of bounds, had no balls blocked back in her face by Texas Tech, and did not even have any balls dug up by the Red Raiders in the backcourt.

Now, that's a hot hand!

[Cross-posted at my VolleyMetrics blog.]

I hope everyone is having a great Thanksgiving! One person who definitely has had one is Green Bay Packers quarterback Brett Favre. The 38-year-old signal caller completed 20 consecutive passes, a team record and only two away from the NFL record, as the Packers knocked off the Detroit Lions.

Looking at the play-by-play sheet (the streak starts right after the two-minute warning before halftime), one can see that most of the passes were for short yardage, but even short passes can go awry.

The yardage gains, in the order the plays occurred, are as follows:

10, 13, 20*, 9, 7, 7, 10 (sets up field goal)

5, 7, 9, 4, 8, 43*, 4 (last one for touchdown)

24*, 0 [complete but no gain], [incompletion negated by defensive pass interference], 7, 3 (last one for touchdown)

2, 41^

*Play-by-play sheet lists pass as "deep," suggesting most of gain was through the air.

^Play-by-play sheet lists pass as "short," suggesting most of gain was via run after the catch.

I have been fortunate in recent months to have a couple of sports journalists take an interest in my “hot hand” research and in applying some fairly subtle statistical concepts to sports, more generally.

One of these journalists, Jerry Crasnick, contacted me in August about an article he was writing for one of the Major League Baseball post-season souvenir programs (which turned out to be for the World Series) and interviewed me for his piece on “Baseball’s Law of Averages.”

The other writer, Kenneth Shouler, contacted me back in the spring about an article he was writing for Cigar Aficionado magazine on NBA basketball players being “in the zone” when they make several shots in a row. This article is now on the newsstands in the December issue of Cigar Aficionado (I do not smoke, and my cooperation with the writer should not be seen as an endorsement of smoking).

If you would like a copy of one or both of these articles, just e-mail me through my faculty webpage (link in the upper right of this page) and I'll send you a copy.

Happy Thanksgiving to everyone!

Texas A&M's 7-foot frosh DeAndre Jordan set a Big 12 men's basketball record Saturday night by making his 16th straight shot from the field. What's unusual about the record is that it took four games to reach it. According to the above-linked ESPN.com article:

Jordan hasn't missed a field goal since the first half of Texas A&M's opener against McNeese State. The prized recruit was 6-of-6 on Saturday, made his last two shots against McNeese, was 5-of-5 against Oral Roberts and 3-of-3 in a win over UTEP.

Thus, contrary to the popular image of a player just going wild in a single game, Jordan has methodically been making his shots -- in small quantities each game -- and building his streak incrementally.

The article alludes to a couple of his shots in Saturday's game being layups. Given Jordan's height, I would guess most -- if not all -- of his shots during the streak have been from close range. I can probably track down shot charts of the Aggies' games, but due to the late hour, I'll do that some other time.

Even if the shot attempts have been heavily or exclusively from near the basket, everybody suffers an unlucky bounce off the backboard and rim here and there, so Jordan's run of perfection is certainly to be commended.

At this moment in time, it seems like pro sports teams in Boston can't lose, whereas those in Miami can't win (the respective NHL teams, excepted).

In the Boston area, the Patriots are 9-0, the Celtics are 7-0, and the World Series champion Red Sox, after falling behind 3-1 to Cleveland in the American League Championship Series, ran off seven straight wins to close out the play-offs.

Down in Miami, meanwhile, the Dolphins are 0-9 and the Heat has gotten off to a 1-7 start.

This morning, I was listening to the ESPN radio show "The Herd" with Colin Cowherd. Colin was giving a commentary about how success stories such as the Patriots and disasters such as the Dolphins don't happen by accident. Regarding the latter, years of poor drafting, a merry-go-round of coaches, and bad management decisions have taken their toll.

Cowherd's commentary reminded me of a book I read a while back, Confidence: How Winning Streaks & Losing Streaks Begin & End. Written by Harvard Business School professor Rosabeth Moss Kanter, the book presents several case studies from corporate America and the sports world (including the Patriots) and argues that success and failure are heavily rooted in organizational culture.

Getting back to the day-to-day sports world, the Miami Heat will take on the Celtics tomorrow night in Boston, so look for each of these teams' respective streaks to continue.

The National Basketball Association season is barely underway, and already we have a new league record for streak shooting, in this case of the cold variety. Playing at Boston, the Washington Wizards went 0-16 on three-point attempts, which according to this ESPN.com article is "an NBA record for most attempts without making one."

Welcome World Series fans!

The big story of Game 1, to me at least, is the continuing run barrage of the Red Sox. Last night, they scored double-digit runs for the third straight game (post-season game-by-game log):

vs. Cleveland (Game 6) 12-2
vs. Cleveland (Game 7) 11-2
vs. Colorado (Game 1) 13-1 

I did a posting in late August about how the Red Sox had accomplished the extremely rare feat during the regular season of scoring double-digit runs in all games of a four-game series (against the Chicago White Sox). Thus, it seems the Red Sox are now up to their old tricks!

The pitching of Boston's Josh Beckett shouldn't be overlooked, either. As this ESPN.com game summary from last night notes:

Beckett also lowered his career postseason ERA to 1.73, placing him third behind Mariano Rivera (0.77 ERA) and Chrisy Mathewson (1.15 ERA) among pitchers who have thrown at least 70 postseason innings.

Welcome to visitors who've found their way here via Carl Bialik's "Numbers Guy" blog for the Wall Street Journal. I invite you to browse through my write-ups and the links section on the right. Feel free to add comments to my postings, if you'd like.

If you have no idea what I'm talking about, click here.

The Tennessee Titans at Houston Texans game completed earlier this afternoon had two major streakiness story lines. Houston, trailing 32-7 entering the fourth quarter, went on a 29-3 burst in the final period to take a 36-35 lead with 57 seconds remaining. Tennessee moved the ball down the field in the closing moments, however, to set up kicker Rob Bironas for a game-winning 29-yard field goal as time ran out (ESPN.com game recap).

The other streaky element was the "hot foot" of Bironas. His winning kick was his eighth successful field goal of the game, which sets a new NFL record (he had no misses). The yardage distances of the field goals in the order in which they occurred are as follows:

52, 25, 21, 30, 28, 43, 29, 29

Looking at Bironas's career statistics from various distances (which appear to be from before the Houston game, given that shortly after the game, his distance-specific stats for this season hadn't been updated, so I would doubt his career ones had been), they are as follows (career stats offer a bigger sample size than just those from 2007):

20-29 yards 21/23 (.91)
30-39 yards 18/19 (.95)
40-49 yards 11/18 (.61)
50+ yards 3/7 (.43)

To estimate the probability of Bironas's making all eight field-goal attempts he took, given that he would be receiving these opportunities, we multiply the component probabilities together:

(.43) (.91) (.91) (.95) (.91) (.61) (.91) (.91)

which yields .155. If we also factored in the likelihood of an NFL team having so many drives stall in fairly close proximity to the goal line, the probability of Bironas's accomplishment would probably get even smaller.

A couple of cautions are in order about this analysis. First, it is the unusual nature of the feat (or in this case, foot) that drew me to conduct the analysis; I did not seek a random cross-section of games. Second, the equation I used assumes independence of observations, that the outcome of any one kick had no impact on the next.

The independence assumption is typically associated with sequences of coin flips and dice rollings, which unlike humans, cannot experience momentum and other associated psychological states. However, having conducted numerous analyses over the years for this website, I consider the independence assumption to hold pretty well for athletic performances, too.

As for Houston's team-comeback element, which unfortunately for Texans' fans did not hold up, I would direct you to my statistical analysis of a relatively recent, similar comeback by Texas Tech (where I'm on the faculty) against Minnesota in last December's Insight Bowl.

The Colorado Rockies have just swept the Arizona Diamondbacks in the National League Championship Series, four games to none. Building upon a sweep of Philadelphia in the opening round (which has a three-out-of-five format), Colorado is 7-0 in the post-season and, factoring in the close of the regular season, has won an amazing 21 of its last 22 games.

Since the advent of the three-round/wild-card play-off system in 1995, the most dominant post-season performance by a World Series champion is shared by the 2005 Chicago White Sox and 1999 New York Yankees, each with an 11-1 record. The Rockies will thus seek to become the first team to go 11-0.

The baseball media naturally have been abuzz with Rocky talk, including comparisons to other hot teams down the stretch in baseball history. Another team I heard about tonight was the 1977 edition of the Kansas City Royals. From August 31 to both games of a September 25 double-header, inclusive, the Royals won 24 out of 25. Ultimately, however, Kansas City lost a heartbreaking American League Championship Series to the Yankees.

Just a few brief notes on the Major League Baseball play-offs:

With their opening-game win over Arizona in the National League Championship Series, the Colorado Rockies have now won 18 of their last 19 games (which also includes a three-game sweep over Philadelphia in the opening round). A couple of entries down, I conducted an elaborate analysis of the Rockies in the regular season.

A streak-within-a-streak is that Colorado pitcher Jeff Francis improved to 5-0 lifetime at the Diamondbacks' Chase Field. I was pleased to see, via this game article, that Francis appears to have some statistical savvy:

"I really can't explain that," said Francis. "It's just a small sample size of me not being here that long and just having a good run against one particular team."

Over in the American League, the championship series between Cleveland and Boston starts tonight. As pointed out in an ESPNews graphic on television yesterday, Cleveland hit .444 (12-27) in two-out situations with runners in scoring position (RISP) in its opening-round win over the New York Yankees.

Alex Rodriguez's streaky stretches, both hot and cold, have been chronicled on this blog. With the Yankees' elimination from this year's MLB play-offs at the hands of Cleveland last night, here's an accounting of his post-season woes from a Yahoo! Sports article...

He is mired in an 8-for-59 (.136) playoff spiral dating to his Game 4 home run against Boston in the 2004 ALCS.

New York's biggest bopper is hitless in his last 18 playoff at-bats with runners in scoring position.

Rodriguez hit a solo homer [in the finale of the Cleveland series]... ending a streak of 57 postseason at-bats without an RBI...

Hitless in his last 27 postseason at-bats with any runners on base, A-Rod is certain to again face some criticism after his up-and-down postseason.

With last night's exciting, extra-inning, come-from-behind win over San Diego in the National League one-game tie-breaker for the wild-card play-off slot, the Colorado Rockies are riding a hot streak (14 wins in their last 15 games) into the first round of the post-season (Rockies' game-by-game log).

Colorado's first sign of streakiness this season came when it won 7 straight in late May after starting out 18-27. I have plotted a graph of the Rockies' cumulative winning percentage after each game, starting with the 7-game winning streak, as shown below (you can click on the graphic to enlarge it). The late ending of the Colorado-San Diego game, plus all the little embellishments I added to the chart, kept me up until 2:00 AM last night!


As it says in the caption, the Rockies' last 118 games of the season included a combination of streaks (both hot and cold) and relatively steady, incremental gains.

A statistical technique that's appropriate in this context is the runs test. A "run" is a stretch of all wins (without interruption by a loss) or all losses (uninterrupted by a win). The following hypothetical sequence [WWLWWWLLL] includes four runs.

Given that streakiness entails winning (or losing) games in bunches, and not merely alternating wins and losses, evidence for streakiness would come in the form of a team exhibiting fewer runs than would be expected by chance. During their last 118 games of the season (the part I'm focusing on), the Rockies indeed exhibited fewer runs (55) than would be expected (57), but the difference is not very large.

A lot of teams (or individual players, when it comes to hitting or pitching) appear to be streaky performers. However, finding statistical evidence for such is more difficult than many fans would imagine.

For an earlier example of the runs test, where I went into greater detail, click here.

The Rockies' first-round opponent, the Phillies, have exhibited hot play, too, of late, though not quite as dramatically, closing out the season 13-4 (log). If both teams continue their hot offense, the scoreboard operators should get a real workout!

A couple days ago, Sports Illustrated's Tom Verducci published a column on "Debunking the biggest myths of MLB's wild-card era" (which I learned about via the ESPN radio show, The Herd). Myth No. 2 was that, "The 'hot' teams -- the ones that play well down the stretch -- are the ones to fear in the postseason." Take a look at Verducci's evidence by clicking here.

This upcoming Saturday, September 29 will mark the 20th anniversary of a major article in the St. Louis Post-Dispatch's Science section, on whether there was any evidence of streakiness -- either in wins and losses, or in batting performance -- in the city's beloved baseball club, the Cardinals. The article was written by Charles Franklin, then a relatively new professor at St. Louis's Washington University.

My connection to Dr. Franklin -- including a span of 22 years between any in-person contact -- and how I obtained the images of his article interspersed throughout this write-up make for an interesting story, if I do say so myself. (By the way, you can click on any of the images to enlarge them and be able to read them more easily.)

As with many developments in my life, it all starts with the University of Michigan. During the summer of 1985, after I had completed my first year of social psychology grad school at UM, I took a statistics course (linear models) through the university's ICPSR program.

The instructor of that course was the aforementioned Charles Franklin, who had just completed (or was just completing) his Ph.D. in political science at Michigan and had come back from Wash U to teach the summer class.

After that class, roughly 20 years passed without Charles's and my paths crossing in any way. In 1992, Charles moved to the Univesity of Wisconsin, Madison. Then, in 2005, he founded a blog called Political Arithmetik (yes, it ends with a "k"), which is devoted to quantitative expositions on public-opinion data.


Armed with his palette of graphing software, Charles might track, for example, presidential job-approval ratings over time, or systematic differences between survey firms in whether their polls tend to give higher or lower job-approval readings than other firms (known as "house effects"). Charles now also grinds out his analyses for the website Pollster.com, in collaboration with Mark Blumenthal, himself a Michigan undergraduate alumnus.

I don't remember exactly when I first discovered Charles's blog, but once I did, I e-mailed him about being in his class in 1985, and I've submitted comments on his postings from time to time.

This past summer 2007, I was fortunate enough to get the opportunity to teach a course at Wisconsin-Madison, as a visitor in human development and family studies (the same department I'm in at Texas Tech for my regular, full-time job). Here are some photos from my time in Madison.

Once I knew that I would be going up to Madison for a summer term, I contacted Charles about getting together, which would be our first visit in 22 years. He was agreeable, so we met in his office, just north of the campus's famous Bascom Hill. Charles told me that he had just returned from teaching in the Michigan summer stats program, and that he was calling it quits after 25 summers in Ann Arbor.

We chatted about Michigan, statistics, polling, and blogging, the latter of which led to my mentioning the Hot Hand page. As if we didn't have enough connections between Michigan and all the statistical stuff, Charles then told me about his 1987 Cardinal streakiness article for the St. Louis Post-Dispatch, of which I was completely unaware.


He didn't have any copies around. However, compounding our coincidences in a manner worthy of a Seinfeld episode, I was heading to St. Louis over an upcoming weekend to attend the annual SABR conference, and it seemed likely I could find a microfilm of Charles's article at the downtown St. Louis public library.

I, indeed, found the microfilm of Charles' article, and you're now seeing some excerpts of my discovery. The staff members in the microfilm room were extremely helpful, for which I thank them.

As you can glean from the inserted newspaper images, Charles didn't find any evidence of streakiness on the part of the Cardinals.

Matt Holliday of the Colorado Rockies is currently on a home-run explosion, having hit 11 in his last 12 games. Holliday is known for the gaudy distances of some of his homers, as immortalized in this 2006 blast I found on YouTube.

It took Holliday until September 2 to get his 25th homer of the 2007 season. He's now, of course, up to 36 homers, a 44% increase from when he was at 25 (11/25) in less than three weeks.

Holliday's streak has prompted me to seek out other similar ones.

The Yankees' Alex Rodriguez, whose tendencies to hit homers in bunches I analyzed in an earlier posting, began the 2007 season by hitting 12 homers in 15 games.

Another seemingly good place to look was at players who had set (or come close to) single-season records. During Barry Bonds's 73-homer season in 2001, his most scorching stretch appears to have taken place from May 17-22, during which he hit 9 homers in 6 games (game-by-game log).

Mark McGwire and Sammy Sosa in 1998 also seemed worth looking at. A few years ago, I found a copy of Race for the Record: The Great Home Run Chase of 1998 (a fancy magazine-type volume with side-binding) on sale for $2.99, so I was able to consult the charts within. In the eight games from May 18-25, McGwire had 9 homers. Sosa, of course, had the 20-homer month of June; at his hottest during that month, he hit 11 dingers from June 15-25.

By focusing only on big-name home-run hitters in the last decade, I'm sure I'm missing other great homer binges. I invite readers to add other big homer stretches (with documentation please) via the Comments link, below.

Pete Ridges just sent a message to the SABR e-mail discussion list, pointing out that this past Sunday, while playing at Cincinnati, Milwaukee became the first team in Major League Baseball history to start off a game by hitting three consecutive home runs (box score and play-by-play sheet)

Ridges offered the opinion that:

Unusually, some reports have undersold this, by saying that the Brewers were the third team to start their first inning with 3 HR. However, the other two cases came in the bottom of the first...

The other trifectas were by San Diego in 1987 and Atlanta in 2003.

Offensively, of course, only a visiting team can start off a game. From this perspective, Milwaukee's feat is technically unique. However, for a home team to lead off its half of the first inning with three straight homers is pretty darn impressive, too.

Whether any given reader considers the Brewers to be in a class by themselves or to share the record with two other teams, Ridges's conclusion helps put everything in context:

By my addition there had been 188,835 major league games through Sunday, so I was extremely impressed by this.

Charlotte (NC) Independence High School has just had its 109-game football winning streak come to an end -- but it took an out-of-state opponent to do it.

As part of former Ohio State quarterback Kirk Herbstreit's Ohio vs. The USA Challenge, Charlotte Independence ventured to take on Cincinnati Elder in the latter's home city, and dropped a 41-34 overtime decision.

As noted in the above-linked ESPN.com article, "Most of the wins weren't close. Independence had beaten opponents during its win streak by an average of nearly 35 points per game entering the 2007 season."

Independence's situation appears to fit a very simple "theory" of super-long streaks. A team (or individual) is physically superior to its competition, thus winning most of its games in dominant fashion. Then, in the rare circumstance of a tight game, the team with the winning streak benefits from good luck to keep the streak going, until the luck runs out.

One recent memorable example, from college football, was USC's 2005 win at Notre Dame to extend the Trojans' winning streak to 28, a victory that required some favorable bounces of the ball at the end.

When one thinks of other historical streaks, such as Joe DiMaggio's getting a hit in 56 straight games, the UCLA men's basketball team winning 88 straight games, and Tiger Woods making the cut at 142 straight PGA golf tournaments, it should not be surprising that the teams and individuals who accumulated these streaks were already at the top of their crafts.

It was a Sox vs. Sox weekend, with Boston visiting Chicago for a Friday doubleheader and single games Saturday and Sunday. In the end, one team did a lot more "socking" of the ball than the other, as revealed in the following scores:

Red Sox 11, White Sox 3
Red Sox 10, White Sox 1
Red Sox 14, White Sox 2
Red Sox 11, White Sox 1

According to the Sunday game article, for a team to put up double-digit run totals in each game represented:

...only the fourth time that has happened in a four-game series since 1900, according to the Elias Sports Bureau. It's the first time it has happened in the American League in 85 years.