I wanted to tie a bow to wrap up three stories I had written about earlier this month:

With their 7-2 win over Boston this afternoon (and the day off tomorrow), the Oakland A's have completed their August games with a 21-6 record (game-by-game log). As I discussed originally in my August 8 posting, the A's have shown an amazing tendency to get hot in August, going back several years. From 2001-2006 inclusive, Oakland's record for games in August is 124-45 (.734)...

A couple of Sundays ago (August 20), I wrote about the Seattle Mariners' record 20-game losing streak within their own division, the American League West. In the time since, the M's have really turned things around (log). After August 20, Seattle went outside of the AL West, winning five out of six games (combined) against the AL East's New York Yankees and Boston Red Sox. These wins, of course, did nothing to end the Mariners' AL West losing streak, but seemed to suggest Seattle had righted the ship. The Mariners then returned to AL West play a couple nights ago, shutting out the Angels 2-0. And tonight, the M's go for a three-game sweep over the Halos...

The Houston Astros' Willy Taveras, about whom I wrote in the posting immediately below the current one, had his consecutive games hitting steak end at 30 on Tuesday night.

The Houston Astros' Willy Taveras has just extended his hitting streak to 30 games, beating out a dribbler toward third base in the first inning at Pittsburgh (I get most Astro and Texas Ranger games on cable TV in Lubbock, Texas, where I live).

The 30-game mark is when I'll generally start to write about hitting streaks. Thirty is a nice round number, and is a little over halfway to Joe DiMaggio's record of 56 games with at least one hit per contest.

It'll probably be several more games before I start presenting calculations of Taveras's probability of catching DiMaggio. To get a feel for the nature of these calculations, however, you can look at this write-up I did for the Phillies' Chase Utley, back when he had a nice streak going (which reached 35 games before ending).

The Seattle Mariners have closed out the weekend losing their 20th straight American League Western Division game, 3-2 to the Angels. In terms of consecutive losses within a team's own division, the Mariners have comfortably surpassed two other teams (the 2004 Diamondbacks and 1993 Rockies) who each lost 16 straight divisional games. It was not until 1969 that Major League Baseball -- having expanded from 20 to 24 teams -- introduced Eastern and Western divisions within each league. Prior to that, all the American League teams competed in one set of standings, as did all the National League teams, with the two first-place finishers going directly to the World Series.

The L.A. Dodgers' amazing turnaround continues. 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 (second half game-by-game log).

Jon Weisman at Dodger Thoughts conveys the strangeness of it all in this essay, a brief excerpt of which follows:

Why does the best Dodger 18-game run in 107 years and best National League run in 20 years feel so unreal? ... A .533 team playing .944 ball after an .071 stretch is hard to wrap the brain around.

(I interpret "best National League run" to mean by any NL team, not the Dodgers' best run through the NL.)

On the SABR members' e-mail discussion forum, the Dodgers' recent streakiness prompted an inquiry into other abrupt turnarounds (thanks primarily to Bob Timmerman and Frank Vaccaro for their messages). Examining the longest win-only stretches followed immediately by the longest lose-only stretches (or vice-versa), the most common patterns involved stretches of around 8 or 9 games won (or lost) and then 8 or 9 lost (or won). The greatest total number of games listed, in which a team's sequence consisted only of a fairly long winning and losing streak, was 21: The 1927 Detroit Tigers won 13 straight, then lost the next 8, from August 10-31 of that year (log).

A dramatic example I recalled is that of the 1987 Milwaukee Brewers. The Brewers started off the season with 13 straight wins. The losing streak did not come immediately thereafter, but it wasn't long before they lost 12 straight (log).

There were a couple of instances of hotness and streakiness in today's 13-0 Cleveland win over Kansas City.

Travis Hafner hit his sixth grand-slam homer of the season, tying Don Mattingly's MLB record. As the linked article notes, "Hafner is 8-for-13 with six homers and 29 RBI this season with the bases loaded." What this means is that, on nearly "Haf" of his bases-loaded at-bats, he has homered (6 of 13)!

The thing about a bases-loaded situation is that, in order to avoid walking in a run, the pitcher is under pressure to keep the ball around the strike zone. This, in turn, presumably allows the batter to concentrate on a smaller area in following an incoming pitch. I'm certainly not saying this accounts completely for Hafner's grand-slam rate, but it's probably a factor.

Hafner's offensive punch was not isolated, however. Cleveland took an 11-0 lead in the first inning, with "[t]he first 10 Indians to bat all reach[ing] base and scor[ing] against Luke Hudson (5-4)."

If it's August, it must be the Oakland A's getting hot again. As of this writing (mid-day Tuesday), the Athletics are 5-1 for August, plus they were also 5-1 in their last six games of July, for a 10-2 stretch overall (game-by-game log for second half of this season).

Looking at the records for previous A's seasons in Baseball Reference, here's how they've done each year of this decade in August:

2000 -- 11-16 (but 21-7 in September)

2001 -- 22-7 (along with 19-8 in July, 17-4 in September, and 6-0 in October)

2002 -- 24-4 (their 20-game win streak was mostly in August, but carried over into September, for which they were 18-8)

2003 -- 20-9

2004 -- 20-8

2005 -- 17-11 (although not as strong as June's 19-8 and July's 20-6)

Excluding 2000, Oakland is 108-40 (.730) in August since 2001.

I haven't decided yet what statistical analyses I might do of this trend. I, like many other people, did analyses to estimate the probability of the A's 2002 winning streak.

I'm pleased to note that in the July 2006 issue of Computers and Operations Research, Donald Martin has just published an article entitled "Hot-hand effects in sports and a recursive method of computing probabilities for streaks,"in which he cites and extends my analysis of the 2002 A's.

The Angels and Rangers are playing an afternoon game today, which will be starting shortly. As I've been documenting the last couple of days, the Halos' Vladimir Guerrero has gotten at least one hit in every game he's ever played against the Rangers, 44 games in all. Can the Texas pitchers finally hold him hitless in a game? We'll soon see. Below, I provide real-time commentary...

The Rangers intentionally walk Guerrero in the first inning, with two outs and a runner on second. I think that's a strategically defensible move. The FOX television crew puts up a graphic indicating that Guerrero has a .443 lifetime batting average against the Rangers! (The .443 figure is also documented here, in the Preview section below the box score.)

[As an aside, I'm curious whether all of Guerrero's games against Texas have been as a member of the Angels, for whom he has played since the start of the 2004 season. Vlad, of course, played many years for the National League's Montreal Expos (now Washington Nationals) before coming over to the AL. But, with interleague play, the Expos could have faced the Rangers.

I initially consulted Baseball Reference, finding the Rangers' game-by-game log for 2003. Sure enough, the Rangers played the Expos in a three-game series from June 6-8, 2003. I then looked up the box scores of these games on Retrosheet, and noticed Guerrero was absent from all three. Further research confirmed my guess that he had been injured, this MLB document showing a June 9 action in which Guerrero was placed on the DL, retroactive to June 5. There do not appear to have been any prior interleague Texas-Montreal games.]

Guerrero walks again in the third, the Rangers' John Koronka clearly seeming to be pitching around him. Vlad is known as a free-swinger at the plate, but some of the pitches he was just thrown were too far out of the strike zone even for him.

Another intentional walk in the fourth, in the same situation as earlier: man on second, two outs.

Yet another intentional pass in the sixth inning, with a runner on third and one out.

An amazing catch in right field by the Rangers' Mark DeRosa on a tricky fly ball thwarts Guerrero in the bottom of the eighth. DeRosa was running toward the wall in a somewhat circular path to keep track of the ball and may have been bobbling it as he fell to the ground, but there wasn't any argument over the "out" call. Baseball, of course, has no replay rule, and anyway, none of the camera views provided a conclusive view of what happened. If you look at the linked biographical page on DeRosa, he's listed as a second baseman, but he certainly showed a lot of dexterity in the outfield on Guerrero's fly ball.

That will almost certainly end the streak, as the Angels are unlikely to need their ninth-inning at-bats, leading 10-3.

Yep, the Rangers go down quickly in the ninth. Streak over.

Update: A video of DeRosa catching Guerrero's fly ball is available here. When the new page comes up, select "Top Play: 350 K." First, you will see a different play from the game. When that play is over, look over to the lower-right portion of the page, where some plays are listed (the first one being "Rivera's three-run homer"). Then, scroll down to "DeRosa's falling catch," and select it.

Utley-Guerrero Watch

Chase Utley has struck out in the first inning of the Phillies' game against the Mets.

Utley is retired in the third inning on a fly ball to center.

A fly-out to center again in the fifth for Utley.

The streak's going down to the wire -- Utley grounds out in the seventh.

Utley will be the Phillies' lead-off hitter in the top of the ninth. This will probably be his last at-bat, unless the game goes extra innings. Philadelphia currently leads 4-3 over the Mets.

Utley strikes out in the ninth.

Phillies-Mets game over. Utley streak over at 35 games.

Meanwhile, on the opposite coast, the Angels' Vladimir Guerrero has struck out in the second inning against Texas.

Guerrero singles in the third, so he now has at least one hit in all 44 games he's ever played against the Rangers.

According to this article, which I've added after the game, Guerrero "went 2-for-4 to extend one of baseball's most peculiar streaks. He has hit safely in all 44 games he has played against Texas in his career, the longest stretch by any player against one team since 1957 -- which is as far as Stats Inc. has been able to research it."

For background on these hitting streaks, see my Thursday, August 3, posting.

7:10 pm Central: Baseball fans will be keeping their eyes on two ongoing hitting streaks tonight, one front and center on the MLB landscape and the other more under the radar.

The prominent streak is that of the Phillies' Chase Utley, who last night extended his consecutive hitting stretch to 34 games. In fact, even before I can finish this write-up, Utley has singled in the first inning at St. Louis, extending the streak to 35 games [game article, added later].

He now is 21 games away from tying Joe DiMaggio's legendary 56-game hitting streak. I will analyze Utley's chances of reaching 56 games, later on tonight.

A little over 90 minutes from now, the Angels' Vladimir Guerrero will try to preserve the "other" streak I alluded to. Guerrero has gotten at least one hit in every game he has ever played against the Texas Rangers, 42 games in all.

This article from May, when the Angels and Rangers last met, documents the magnitude of Vlad's accomplishment: the next-longest actively going hitting streak by a player against the same opponent was 18 games (as of when the article was published), and the next-longest hitting streak of this type held at any time in the past by a currently active player is 35 games.

8:30 pm Central: With the Rangers at Angels game about a half-hour away, I thought I'd provide an estimate of Chase Utley's probability of equalling Joe DiMaggio's record 56-game hitting streak.

First, we need a prior (baseline) batting average for Utley. A good figure to use is .290. After his last game of the present season (to this point) without a hit, on June 21, he was batting .290. Also, his batting average for 2005 was .291 (year-by-year stats), so prior to the current hitting streak, Utley appeared to have a stable, long-term average of around .290.

The .290 represents Utley's probability of getting a hit on any single at-bat. However, because a player will usually get around four at-bats per game, the probability of getting at least one hit in a game is considerably higher than the batting average.

Fortunately, a chart exists that allows easy conversion of a batting average into the probability of at least one hit in a game. In Table 1 of the linked document, the closest shown batting average to .290 is .300, which translates into a probability of .745 of getting at least one hit in a game.

We then simply raise .745 to the 21st power (given that Utley's 21 games away from tying DiMaggio), which yields .002, or 1-in-500. This calculation assumes independence of observations, i.e., performance in one game does not affect performance in the next.

Also, as noted in the first linked article in tonight's entry (back up under the 7:10 pm heading), Utley is batting .401 during the streak. A .400 average converts to a .855 probability of gettting at least one hit in a game; .855 to the 21st power is .04, or 1-in-25. This latter estimate, though optimistic, still shows a small likelihood.

10:35 pm Central: A little while ago, Vlad Guerrero homered in the bottom of the fourth inning. He thus has gotten at least one hit in all 43 games he's ever played against the Rangers [game article, added later, which characterizes Guerrero's feat as "the longest such streak against an opponent in the majors for at least 50 years"].