In Brad Ziegler's brief major-league pitching career, he has not given up a run. Period. According to this news article:

Athletics rookie reliever Brad Ziegler stretched his scoreless-inning streak to 30 - extending the major league record to begin a career...

The prior streak of scoreless innings pitched to begin a career is 25, dating back to 1907. Heck, the Cubs have even won a World Series championship more recently than that!

The overall record for scoreless innings pitched is, of course, 59 by the Dodgers' Orel Hershiser in 1988.

Tonight's baseball game between the L.A. Dodgers and the Colorado Rockies featured the following nine-inning line score:

LA.....8 1 2...1 4 0...0 0 0 -- 16
COL...0 0 1...2 1 2...1 1 2 -- 10

According to this article, "The Dodgers began the game with five straight hits..."

Also, how often does a team score in seven straight innings and still lose???

The men's British Open golf tournament (or just "The Open" as it's sometimes called) ended today, with two of the leading final-day contenders exhibiting streaky play in various combinations of hot and cold.

Padraig Harrington ended up winning the tournament for the second straight year, but early on today, that didn't seem very likely. This chart of his day-by-day, hole-by-hole performance in this year's Open illustrates why.

Entering today's play trailing sentimental favorite Greg Norman by two strokes, Harrington shot a par on each of the first six holes, but then bogeyed hole numbers 7, 8, and 9. Granted, Norman wasn't doing too well himself at the time (discussed below), but Harrington certainly wasn't giving any sign that he was revved up for a big finish. The back nine holes would go a lot better for him, however, as he shifted from coldness to hotness.

Harrington birdied hole 13 (which he had not done in any of the initial three rounds) and 15, and eagled 17. He had no bogeys on the back nine and, in context, even some of his pars were impressive. For example, he had bogeyed hole 11 each of the first three days, but got a par today. All told, Harrington recorded a score of 69 for the final round to finish four strokes ahead of runner-up Ian Poulter.

For Norman, a lot was at stake as he unexpectedly got back in the spotlight. He had won the 1986 and 1993 British Opens (his only Grand Slam tournament titles), but he also had an extensive history of blowing leads entering the final day of major tournaments (discussed here and here). All of this set the stage for Norman's round today, as noted in this ESPN.com/AP article:

This had all the elements of a fairy tale like few others in golf. Norman, 53, married tennis great Chris Evert three weeks ago and was on the tail end of his honeymoon when he wound up with a two-shot lead going into the final round and a chance to become the oldest major champion. Instead, it ended like so many other majors when he was in his prime.

Norman got into immediate trouble, bogeying his first three holes. And unlike Harrington, Norman never turned things around, accumulating eight bogeys for the day (compared to only one birdie), and tallying a 77 to finish tied for third.

Harrington's performance earlier today may not quite rank up there with Phil Mickelson's amazing final round in the 2004 Masters, in which he birdied five of the last seven holes to claim his first victory in a Grand Slam event (discussed here). Still, considering that no golfer in this year's British Open came close to breaking par for the full tournament amidst the windy conditions and unforgiving greens, Harrington's finish should rank up there.

Picking up where my previous posting left off late-night Tuesday/early-morning Wednesday, the American League won its 11th straight Major League Baseball All-Star Game over the National League (excluding 2002's tie), thanks to a 4-3, 15-inning decision.

Last Friday, in the Wall Street Journal's "Weekend Journal," Darren Everson documented the AL's dominance over the NL -- not just in the All-Star Game, but also in recent years' World Series and interleague play -- and proffered some possible reasons for this state of affairs. These include ballparks, revenues, power hitters, and innovation.

I think we can safely say that the AL is superior and that the stretch of All-Star Games has not been like flipping a coin, with each team having a 50/50 chance of winning (the probability of a coin coming up the same way 11 straight times is .5 raised to the 11th power, or .0005; and even if we assume the AL had a .60 chance of winning each time, the probability of 11 straight would be .004).

It should also be noted that the NL had its own period of supremacy, losing only once from 1963-1982.

From one perspective, a lengthy winning streak by one league over the other is quite surprising. As Jim Albert and Jay Bennett argued in their 2005 Hot Hand web chat, baseball would seem to be much less of a "domination sport" than football or basketball. To a far greater extent than in these other sports, baseball teams are limited in how often they can deploy their top players -- starting pitchers can go only once every five days, and batters can take only one out of every nine at-bats for a team.

To the extent that baseball's rules (and the wear-and-tear on pitchers' arms) create parity between the teams, this trend would seem to be exacerbated by the traditions of All-Star play. Pitchers often throw just an inning or two, and players at the other positions might only play half the game, or so. Such shuttling in and out of players would seem to create a lot of volatility, making it harder for one league to dominate. This seems like an excellent theory, except for the fact that it completely fails to explain the data!

In what I think is a rarity, Major League Baseball's All-Star break has given us a Home Run Derby and a game that have both been exciting.

The Derby, of course, was dominated by the Texas Rangers' Josh Hamilton, who hit a single-round record 28 homers in the opening round (in what undoubtedly will become an historical footnote, Hamilton actually lost the competition to the Minnesota Twins' Justin Morneau; with totals from the earlier rounds wiped off the board for the finals and both contenders presumably with tired bats, Morneau was victorious, 5 to 3).

Years ago, I used to conduct hot-hand analyses of the Home Run Derby, but I gave it up after finding little evidence of streakiness. Hence, I was not charting Hamilton's first-round sequence of home runs and outs. However, after viewing several videos from YouTube (just search on "Josh Hamilton") and consulting some articles, I'm able to reproduce his sequence.

In particular, Jayson Stark's ESPN.com column provided some helpful descriptions of Hamilton's homering:

He hit a home run on 13 swings in a row. And 16 of 17. And 20 of 22. And 22 of 25.

Here's Hamilton's first-round sequence (shown in blocks of 10 for ease of viewing, where H = home run, and O = out).

HOHOOHHHHO
OHHOHHHHOH
HHOHHHHHHH
HHHHHHOO

Early on, Hamilton was hitting homers only a little over 50% of the time (6 homers, 5 outs), so he clearly lifted his home-run rate in the latter portion of his sequence. The problem with hot-hand analyses of the Home Run Derby, in general, is the small sample size. That probably was a factor for Hamilton, in particular, as this online runs-test calculator (with a 1 entered for each homer and a 0 for each out) showed a non-significant result.

Another factor to consider, as has been suggested by observers in the past, is "streak pitching." Indeed, the 71-year-old Clay Counsil, who used to pitch batting practice to Hamilton when the latter was a high-schooler and reprised this role on the Yankee Stadium mound Monday night, seemed particularly adept at consisently putting the ball in the same location for Hamilton. From there, Hamilton's beautiful swing did the rest...

***

As for the All-Star Game itself, it has just ended at around 1:40 a.m. Eastern, with the American League taking a 15-inning decision. Excluding the infamous 2002 tie game, the AL has now won 11 straight Mid-Summer Classics. That's a streak worthy of its own examination, but due to the lateness of the hour, I'll have to do it later!

The New York Mets won their ninth straight game tonight, shutting out the visiting Colorado Rockies, 7-0. What's more interesting, I would say, is a streak-within-the-streak. Specifically, during Games 4, 5, 6, 7, and 8 of the winning streak, Mets opponents had a hard time getting a hit, let alone runs.

According to ESPN.com's "Elias Says..." feature from the Elias Sports Bureau:

The Mets held the Rockies to one hit on Saturday, after Colorado had three hits on Friday and the Giants had three hits in each of the Mets' previous three games. It's the first time in modern (since 1900) major league history that a team has held its opponents to three or fewer hits in each of five consecutive games.

In tonight's ninth game of the winning streak, New York pitchers gave up seven hits, thus ending the three-or-fewer-hits streak. Slippage!

Phil Birnbaum's Sabermetric Research blog reports on a new study (originally from an L.A. Dodger fan site) of winning streaks in Major League Baseball and their consequences. Specifically, the new study asks whether short winning streaks raise a team's probability of winning its next game, beyond the team's established (baserate) winning percentage from large numbers of games.

Such a comparison is one of the earliest approaches to defining and testing for the existence of the "hot hand," as used by Gilovich, Vallone, and Tversky (1985, Cognitive Psychology). Gilovich and colleagues studied basketball shooting (for details, see the following PowerPoint lecture, especially slides 20-23).

The recent baseball winning-streak study -- like Gilovich and colleagues' earlier basketball-shooting study -- failed to find evidence of a hot hand. Specifically, quoting Phil, "...after winning three, four, or five consecutive games, [teams] won the subsequent game far less often than you'd expect from their record."

These findings also are similar to those for an older NHL hockey study that I discovered recently. The authors of this study concluded that, "NHL teams do indeed play better than normal after a few los[s]es and worse after a few wins."

Thus, contrary to the impressions of many athletes and sports fans, a number of studies suggest that putting together a string of successes (e.g, games won; shots made) does not appear to give performers momentum, in the sense of raising their probability of success on the next trial beyond established baselines.

LPGA golfer Paula Creamer had an amazing opening round Thursday in the Jamie Farr Classic near Toledo, Ohio. In shooting a 60, Creamer "birdied nine of the last 11 holes," according to this ESPN.com article. The LPGA single-round record is 59, held by Annika Sorenstam; one must take into account differences in courses' difficulty before putting too much stock in overall tour records, in my view.

Today, Creamer "cooled off" to a 65.

Cincinnati's batters were hot, "red hot" if you will, as the team outslugged the Cubs in Chicago, 12-7. In doing so, the Reds homered in six straight innings, the second through seventh; they added another in the ninth, as well.

Here at the Hot Hand page, we try to get an idea of how unlikely something is, through either a statistical or historical lens. In this instance, an historical reference point is readily available. According to this MLB.com article:

More breathing room came as [catcher David] Ross led off the seventh with his second homer of the game -- this time a shot to left field. It gave the Reds a home run in six straight innings, marking the first time they'd done so since Sept. 4, 1999, when they slugged homers over seven consecutive innings at Philadelphia.

OK, so we have an answer. For the Reds, at least, nearly nine years had elapsed since the last time this happened.

This ESPN.com article has an accompanying chart of all the scoring plays in the Reds-Cubs game.

This Baseball Almanac page lists a number of different kinds of home-run records, including each franchise's record for most homers in a single game. Several teams have hit eight (or more) homers in a game. Visual inspection of box scores would be needed, of course, to see over how many consecutive innings a team's homers were hit, in a particular game. The more homers hit within a single inning, the fewer innings would be needed to accumulate a bunch of dingers.

I recently finished reading Leonard Mlodinow's book The Drunkard's Walk: How Randomness Rules Our Lives, which I'd like to discuss. In the name of full disclosure, in case this may have colored my reaction to the book, I want to note that Dr. Mlodinow contacted me, offering a free review copy of the book, and I accepted.

Perhaps the foremost task of hot-hand analysts is trying to determine whether streaky sports performances simply reflect random variation on established generating processes (i.e., like a tossed coin coming up heads several times in a row due to chance) or something beyond chance. The relevance of The Drunkard's Walk is thus clear, and in fact, the book cites hot-hand research (pp. 178-179).

I actually found The Drunkard's Walk to be like two books, the first reviewing the subleties of probability calculation and the second, discussing how people can be mislead by random processes, consistent with the book's title.

The first major part of the book, on probability calculation, matches closely with how I teach probability in my introductory graduate statistics course. I have boiled probability down into one simple question: "How many possible ways can something turn out?" and Mlodinow presents the subject matter in much the same way (Chapter 3).

Then, after shifting to the second major topic, how randomness can mislead, the book finishes strongly, in my opinion. Concepts covered during this latter part of the book include hindsight bias, the arbitrariness of starting and ending points when measuring someone's success, and the distinction between a specific, named person experiencing some type of coincidence or unusual accomplishment and someone, somewhere doing the same (here's an additional example of the latter, beyond what's in the book).

On a somewhat negative note, the central message of The Drunkard's Walk is not exactly new. The book Fooled by Randomness, written several years ago by Nassim Nicholas Taleb and which I reviewed in the Journal of Behavioral Decision Making, plowed similar ground, and many of the ideas in that book had some history.(Parenthetically, Taleb has a follow-up book in the stores, entitled The Black Swan.)

There was only one assertion by Mlodinow that raised questions of accuracy in my mind. Specifically, on page 138, he stated that the "normal" (bell-shaped) curve is "the most widespread manner in which data have been found to be distributed." I am not prepared to say that this statement is flat-out wrong, but it does contradict the evidence of which I'm aware. The textbook I use in my introductory statistics class (King & Minium, 2008, Statistical Reasoning in the Behavioral Sciences, 5th ed.) cites a 1989 Psychological Bulletin article by Theodore Micceri, who:

“…examined the distributions of 440 measures of achievement and psychological traits… Nearly 70% included samples of 1,000 or more. Only 19 of the 440 distributions were found to approximate the normal curve” (p. 101).

Mlodinow has a lively writing style. If, like me, you've enjoyed the recent genre of relatively non-technical books on mathematics and statistics for a general, educated audience, the The Drunkard's Walk is for you; however, if you haven't yet read either of Taleb's books, that might be a better place to start.

Today's Wimbledon tennis men's singles final between Rafael Nadal and Roger Federer -- one that former champion John McEnroe has been quoted as calling the "greatest match I've ever seen" -- also had plenty to offer on the streakiness front (ESPN.com article). With Nadal's 6-4, 6-4, 6-7, 6-7, 9-7 victory, here's what the men's tennis landscape now looks like.

*Federer had his streak of five consecutive Wimbledon men's singles titles snapped, keeping him in a tie with Bjorn Borg for the modern record. William Renshaw won six straight between 1881-1986.

*Federer had also won 65 straight matches overall on grass surfaces.

*Nadal became the first male player since Borg in 1980 to win both the French Open and Wimbledon titles in the same year (these, along with the Australian and U.S. Open tournaments, comprise the "Grand Slam" of tennis). Nadal, in fact, has won the last four French Open titles, the last three by beating Federer in the finals.

*According to the statistics of the final match (which can be accessed via this scoreboard), Nadal won every game except one on his own serve, with Federer going only 1-for-13 on break-point opportunities (Nadal was 4-for-13).

*Had Federer been able to successfully complete his Houdini-type comeback attempt, what would have stood out as a turning point is the eighth game of the third set, with Federer trailing two sets to none and 3-4 in games. As described in this "Minute-by-Minute" journal from the UK's Guardian newspaper:

Big points win matches, and at the key moments of this final Federer has been found wanting... But this game could change everything. Nadal opens with a brilliant improvised backhand pass and quickly races to a 0-40 lead. But Federer - effectively staring defeat in the face - gets himself out of trouble with some big serving, reeling off five points in a row to hold. Courageous stuff...

Recently in Mansfield, Texas, another golfing hole-in-one oddity occurred. As reported in this article from the Fort Worth Star-Telegram, two men aced the same hole, one day apart from each other. The Star-Telegram writer was kind enough to consult with me and cite an analysis I did two years ago about a similar incident in Lubbock that involved the same golfer acing the same hole on back-to-back days.

Happy Fourth of July everyone, and enjoy the fireworks!