By finishing off the Tampa Bay Rays in Wednesday night's rain-delayed World Series finale, Philadelphia Phillies' closer Brad Lidge achieved relief-pitcher perfection on the "Save" statistic.

Combining regular-season (41 games) and post-season (7 games) play, every time Lidge had the opportunity to protect a Phillies' lead at the end, he succeeded. He thus ended up a perfect 48-for-48 on save opportunities.

A few years ago as a member of the Houston Astros, the 6-foot-5 right-hander was so powerful at the end of games that the team's middle/set-up relievers knew that their job was to provide a "Bridge to Lidge." As noted in this article:

With Houston in 2004, [Lidge] averaged 15 strikeouts per nine innings. In the seven-game National League Championship Series loss to St. Louis, he held the Cardinals to one hit in his eight innings...

The Astros and Cardinals met again in the next year's NLCS, and when Houston was one out from the World Series, Lidge gave up a game-deciding homer to Albert Pujols. Houston won the pennant in the next game, but somehow, Lidge seemed to become better known for that Pujols homer than for all his good work.

For now, at least, it looks like the "Heartbreak Lidge" moniker he obtained in Houston will likely be a thing of the past.

One week from tonight, two of college football's hottest teams (both undefeated) and most hot-handed quarterbacks will do battle when the University of Texas plays at Texas Tech.

The Red Raiders' Graham Harrell hit on 22 of his first 24 passes today, as Tech routed Kansas 63-21. The game was once tied 14-14 before the Red Raiders scored 49 straight points. The Jayhawks, fans will recall, won the Orange Bowl and finished as the No. 7-ranked team in the nation last season. Although clearly not as good this year, KU came into the game ranked 19th in the nation, thus serving as a quality opponent for Texas Tech.

The Longhorns' Colt McCoy has been similarly scintillating. As this ESPN.com article notes:

Through Texas' first six possessions Saturday [in a 28-24 win over previously unbeaten Oklahoma State], McCoy was ridiculously good. He led the Horns to four touchdowns and completed 30 of 33 passes including a school-record 18 straight at one point. Go back to last week's dissection of Missouri and McCoy was 59 of 65 (91 percent accuracy) across a span of 15 possessions, with a couple of drops and batted balls in there. On those drives Texas scored 77 points.

Inspired, presumably, by Boston's amazing comeback from a 7-0 deficit to win Game 5 of the American League Championship Series against Tampa Bay (although ultimately not the series), Tom Tango has just written a piece at Hardball Times probing the historical record of similar comebacks. Does evidence exist for comeback wins inspired by what the article calls "in-game momentum"?

Specifically, Tango identified games in which a team rallied from five or more runs down to tie a game, but not take the lead before the end of the inning. The idea is that the game would now have been back to square one -- dead even -- but one team would have had the momentum. Tango then investigated how often the latter team went on to win the game by scoring in a later inning, which might be seen as a sign of momentum on the part of the team that tied the game (or demoralization on the part of the team that squandered the lead).

Tango finds evidence that teams coming back from five or more runs have won games with a slightly greater frequency than that of teams coming back from smaller deficits (and thus with lesser momentum). However, he urges caution as follows:

...don't forget that we're talking extreme momentum here; in-game momentum in which the team scored five runs in an inning to tie the game. One must believe that the effect of momentum must be even less day-to-day.

Boston's postseason dominance over the California/Anaheim/Los Angeles Angels continued last night, with a 3-2 Red Sox victory to capture the first-round series, three games to one. According to a sidebar note with the above-linked article:

The Red Sox improved to 4-0 all-time against the Angels in postseason series, having beaten them in 1986, 2004, 2007, and 2008. Boston has also won 12 of the last 13 playoff games against Los Angeles.

The story begins, of course, with the 1986 American League Championship Series, in which the Red Sox, trailing three games to one, staged an unlikely comeback to take three straight and win the series, 4-3.

Boston then recorded 3-0 series sweeps against the Halos in 2004 and 2007, before winning 3-1 this year.

As I like to point out from time to time, streaks can arise from some combination of (a) sharp ability differences between the two competitors; (b) momentum and other psychological factors (though most statisticians are skeptical of this); and (c) random chance.

The idea that the Red Sox were substantially superior talentwise over the Angels -- for this year at least -- can be safely ruled out, as the Angels won eight out of the nine regular-season meetings between the teams.

Statistical research tends to show that athletes who have experienced consecutive successes (e.g., made baskets, hits in baseball) do not raise their probability of success on the next attempt, relative to their long-term baserates. For example, a long-term .50 basketball shooter will not be any more likely than .50 to make his or her next shot after making, say, three straight hoops. This runs contrary to the popular belief that the athlete is "hot" and therefore at an elevated rate of success. Another way of conveying the lack of a true "hot hand" is that athletes' instances of several successes in a row tend not to occur any more frequently than runs of several heads in a row (or tails in a row) from large numbers of coin tosses.

Despite most studies' lack of evidence for hot-handed performances beyond chance, however, I have never disputed that athletes may feel something special is going on during their runs of success. One type of perception, until recently (I thought) only in the realm of the anecdotal, is that relevant athletic stimuli (e.g., a basketball hoop, the baseball on the way from the pitcher) look larger or clearer than when the athlete is not in the midst of a streak.

An item from July on the "Nudge" blog, which I did not see until recently, cites evidence that successful athletes really do seem to see their targets as bigger.

The research in question is by Jessica Witt of Purdue University and colleagues, and is entitled "Putting to a bigger hole: Golf performance relates to perceived size" (published in Psychonomic Bulletin & Review, June 2008). The above-linked Nudge posting provides a concise description of the study's details.

In looking up Dr. Witt's faculty website, I noticed that she had published a similar study (with Dennis Proffitt) with recreational softball players ("See the ball, hit the ball: Apparent ball size is correlated with batting average," Psychological Science, December 2005).

The story does not end there, however. In their softball article, Witt and Proffitt cite a study by Wesp et al. (2004, Perception & Psychophysics) that "demonstrated that dart-throwing ability affects perceived size of the target. Participants who hit the target with fewer attempts selected larger circles as matching the size of the target than participants who were not as successful" (p. 938).

My apologies for not noticing these studies earlier, but better late than never!

With Boston's win over Cleveland last night, the New York Yankees have officially been eliminated from the postseason picture. The Yankees' streak of consecutive playoff appearances now ends at 13, one short of the Atlanta Braves' record of 14. The Bronx Bombers got more out of their postseason appearances, however, with four World Series championships to Atlanta's one.

The Houston Astros, whose hotness I wrote about in the posting immediately below, have now gone cold. In two games against the Cubs, the Astros were no-hit last night by Carlos Zambrano and then were held without a hit for six innings today by Ted Lilly. To provide some historical perspective, MLB.com reported several items of no-hitter trivia. The following appears most applicable to the Astros' latest futility:

According to the Elias Sports Bureau, the last time a team pitched or succumbed to a streak of 15 consecutive no-hit innings was June 2-3, 1995, when the Expos held the Padres without a hit for that span. On Sept. 25-27, 1981, the Astros held the Dodgers without a hit for 16 consecutive innings.

As they almost always seem to do, the Houston Astros are again pulling off a late-season hot streak. With a 6-0 win today against Pittsburgh, the Astros have now won 14 out of 15. As this ESPN.com/AP article notes:

Houston was 66-66 and 11 games back of Milwaukee, the NL wild-card leader, before the run began Aug. 27. The latest win closed the Astros within three games of the Brewers...

One method statisticians use to help determine if a given team's (or athlete's) streakiness is more than just a chance occurrence is to see if the team/athlete has shown any ability to repeat the special performance year after year. I recall the Astros' having had strong finishes in recent years, so I decided to look at the numbers for the last four completed seasons. Shown for each year are the Astros' records as of the last day of July, for the month of August, and for the month of September (plus any regular-season games played in October). You can click on the year to see the Astros' game-by-game log.

YEAR........THRU JULY..........AUGUST.........SEPT/OCT

2004........52-52 (.500)......17-11 (.607).......22-7 (.759)

2005........57-48 (.543)......13-14 (.481).......18-11 (.621)

2006........49-56 (.467)......17-12 (.586).......16-12 (.571)

2007........46-60 (.434)......15-14 (.517).......12-15 (.444)

Thus, with the exception of 2007, in recent years the Astros indeed have regularly put together strong finishes in August and/or September. Brewers, look out!

Leave it to those L.A. Dodgers to, once again, put together an amazing cold-to-hot pattern. In 2006, as I wrote about at the time:

The Dodgers started off the second half of the season, right after the All-Star Break, by losing 13 out of 14. They've now rebounded by winning 17 of 18...

Now in 2008, beginning August 22 with a loss at Philadelphia and culminating with today's 5-3 win at home against Arizona, the Dodgers have immediately followed up an eight-game losing streak with a winning streak of the same length (game-by-game log).

Given that a team has gone 8-8 during a 16-game stretch, how likely is it that such a record has been accomplished by losing eight straight and then winning eight straight (or vice-versa)?

Perhaps the easiest way to think about this problem is to imagine 16 boxes (representing the number of games) and eight cards, each of which has a "W" on it, for wins. Then we can ask: In how many ways can the eight wins be distributed into the 16 boxes? Obviously, there are lots of ways for this to happen. In addition to winning either the first eight or last eight games, a team might win games 1-2-4-5-7-10-11-12 or games 3-4-5-8-10-13-14-15, for example.

Fortunately, there's a relatively simple formula for determining how many ways eight wins can be distributed among 16 games. It's known as the "n choose k" formula, where in this case, n = 16 and k = 8. Using this online calculator, we find that there are 12,870 possible ways to distribute eight wins in 16 games.

So, indeed, the Dodgers' particular pattern is quite rare. Of course, it was the unusual nature of the sequence that drew me to analyze it in the first place, after the fact.

Perhaps it's a case of post-Olympic fatigue, but whatever the reason, the gold-medal beach volleyballers Misty May-Treanor and Kerri Walsh have had their 112-match winning streak snapped, in an Ohio tournament.

W.M. McEntire posted a message on the SABR members' e-mail discussion list, noting that the Cleveland Indians' current 10-game winning streak gives the team both 10-game losing and winning streaks this season (the losing streak occurred during late June and early July, whereas the more recent log of games is available here). According to McEntire, this is the 21st time since 1900 that a team has exhibited such a pattern.

A couple of major streakiness items from the Olympics:

The U.S. beach volleyball duo of Kerri Walsh and Misty May-Treanor won the gold medal for the second straight Olympiad. Overall, the pair has won 108 straight matches.

Another U.S. women's juggernaut, the softball squad, had its reign of three straight Olympic golds snapped by Japan. The gold-medalist pitcher, Yukiko Ueno, had quite a last two days. After pitching eight scoreless innings (seven innings is the regulation length) against the U.S. on Wednesday before losing in the ninth, Ueno came back later the same day to pitch all 12 innings of a 4-3 win over Australia. Then today, in a rematch with the Americans, she limited them to one run, the Japanese winning 3-1.

Given that Ueno gave up several runs during this stretch, I'm not sure we can say she always had the "Hot Arm," but I don't think anyone would dispute awarding her the title of the "Durable Arm!"

The Chicago White Sox hit four homers in a row Thursday afternoon, in a 9-2 victory over Kansas City. Such a feat has been accomlished six times in MLB history. Interestingly, half of these occurrences have taken place between 2006-2008 and the other half between 1961-1964 (see the linked article for a chart listing all the teams and players involved).

Baseball fans are still buzzing about Boston's 19-17 win over Texas last night, a game in which it looked like the Sox's 10-run first inning might go for naught. Obviously, several batters had big nights. The hottest hitter, though, appears to be the Rangers' Marlon Byrd who, according to this article, "went 5 for 6 and is 21 for 34 in his past eight games."

Trailing 10-11 early on against China, the U.S. women's Olympic basketball team closed out the first quarter on a 23-0 run (article, play-by-play sheet).

Deja vu, all over again. Similar to how he won the British Open last month, Padraig Harrington had the hot putter down the stretch to win the PGA Championship today.

"Manny's being Manny!" intoned legendary L.A. Dodger broadcaster Vin Scully in this MLB.com video, as the team's celebrated new acquisition Manny Ramirez belted a ball into the bleachers for a home run last weekend.

Ramirez's hot start in Dodger Blue has now continued on for several games. At the close of Wednesday night's play, according to this ESPN.com article, Manny "is batting .600 (12-for-20) with three homers and six RBIs in five games since joining the Dodgers."

Unfortunately for the Dodgers, they've had to face St. Louis the last few nights, and the Cardinals have some hot-hitting sluggers at the moment, as well. Quoting from the same ESPN.com article:

[Ryan] Ludwick tied a franchise record with a homer in his fifth straight game, only four pitches after [Albert] Pujols' grand slam, and the St. Louis Cardinals beat the Los Angeles Dodgers 9-6 on Wednesday...

Ludwick was 3-for-5 with three RBIs and Pujols finished 4-for-4 with a walk, while insisting being on the same field as Manny Ramirez served as motivation.

Tuesday night, Ludwick had homered in the 11th inning to give the Cards a 6-4 win over the Dodgers.

With Tiger Woods's absence from the golf scene due to injury, and other stories such as the upcoming Summer Olympics and the Brett Favre/Green Bay Packers saga garnering most of the sports media attention, relatively little has been made of the annual PGA Championship beginning tomorrow.

To the extent that commentators have addressed the PGA tournament, a good deal of the discussion has focused on how Phil Mickelson's career (in major touraments, at least) has turned on a dime, for the worse. What seemed to be a rise to greatness fell, just that quickly, into his being mired in mediocrity.

Having won the 2005 PGA and 2006 Master's, Mickelson appeared to be on the verge of making it three straight majors, as he neared the end of the '06 U.S. Open. However, as characterized by the Wikipedia, Mickelson ended up with:

...one of the most memorable final hole collapses in major championship golf. Leading by a stroke with one hole to play, he chose to hit driver on the final (72nd) hole of the tournament, and hit it well left of the fairway... He decided to aggressively go for the green with his second shot rather than play it safe and pitch out into the fairway. His ball then hit a tree... He was unable to get up and down from there, resulting in double bogey and costing him any chance of winning the championship outright or getting into a playoff... and also ending his bid to join Ben Hogan and Tiger Woods as the only players to win three consecutive professional majors...

Reflecting on his performance afterwards Mickelson admitted: "I still am in shock that I did that. I just can't believe I did that. I'm such an idiot".

In the nine majors he's played since then -- the '06 British Open and PGA, all four majors in '07, and this year's Master's, U.S. Open, and British Open -- he has finished in the top 15 only once (a tie for fifth in this year's Masters; see aforementioned Wikipedia link for his career finishes).

It's certainly tempting to say that Mickelson's collapse at the '06 U.S. Open threw his career into a tailspin, compared to how well he had been playing. Prolonged -- and unexpected -- slumps are not new for him, however. After recording three straight high finishes spanning 2001-2002 (second in the '01 PGA, third in the '02 Master's, and second in the '02 U.S. Open), he fell into the doldrums. Over his next six majors -- with the exception of a third in the '03 Masters -- his finishes were tie for 66th, tie for 34th, tie for 55th, tie for 59th, and tie for 23rd.

We'll see this weekend if "Lefty" can get back to contending for major titles again.

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???