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!