Saturday, June 23, 2007

Friday night, the Atlanta Braves suffered their third shutout in a row, falling to the Detroit Tigers, 5-0. According to this recap (in the box entitled, "A Closer Look"):

The Braves were shut out for the third game in a row, their scoreless streak stretching to 28 innings. It was the first time since 1988 that Atlanta has been the victim of three straight shutouts.

Atlanta finally did score a run this afternoon (in the fourth) in losing 2-1 to Detroit, but that won't affect my analyses of the probability of a three-game scoreless streak.

So, how rare is it for a team to record what might be called a "Paula Abdul" trio of games -- my reference to her 1989 song Straight Up, which includes the phrase, "Oh-Oh-Oh..."?

I present two analyses, one historical and the other statistical.

First, for the historical analysis, I inspected every team's game-by-game logs (via's schedule/results page for each team, which can be accessed through here) for what's been played so far in 2007 and for all of 2006.

I found no instances of a team being shut out three games in a row during this (roughly) season-and-a-half span. Several teams came close, as seen in the following examples:

The Royals had a sequence during the first half of the 2006 season that went like this: May 31 at Oakland, lose 7-0; June 2 at Seattle, lose 4-0; and June 3 at Seattle, lose 12-1.

The Twins, during an April 28-30, 2006 sequence at Detroit, lost three games by the scores of 9-0, 18-1, and 6-0.

Later in the same season (August 10-12, 2006), Minnesota had the following losing stretch while hosting Toronto: 5-0, 7-1, and 4-0.

From May 2-5, 2006, the Cubs lost four straight games while scoring a total of only one run. The opponents and scores of the Cub losses are as follows: vs. Pittsburgh, 8-0; at Arizona, 5-1 and 6-0; and at San Diego, 1-0.

Finally, the Astros, on the dates of June 27, 28, and 30, 2006, lost at Detroit by scores of 4-0 and 5-0, and then at Texas, 3-1.

For the statistical analysis, I looked at every Braves' box score for their 20 games preceding the streak of three shutout losses. For each inning, 1 through 9, of every game, I recorded in a yes/no fashion whether Atlanta had scored one-or-more runs or not.

As David W. Smith shows in the recent SABR Baseball Research Journal (Volume 35) ("Effect of Batting Order..."), average numbers of runs scored tend to be higher in some innings than in others (e.g., more tend to be scored in the first inning). Therefore, I wanted to examine the Braves' probabilities of scoring (and not scoring) on an inning-by-inning basis, even though number of runs and scoring of at least one run are different quantities.

Listed below are the numbers of times the Braves scored one-or-more runs in each inning during the 20 games I coded. Each value was then subtracted from 20 to give the number of games in which the Braves were blanked in that inning, which was then converted to a percentage (number of games blanked in that inning, divided by 20).

Inning---#Games ATL Scored---% of Games NOT Scoring

First---4 games---.80 rate of NOT scoring in this inning
Second---4 games---.80
Third---5 games---.75

Fourth---5 games---.75
Fifth---7 games---.65
Sixth---6 games---.70

Seventh---4 games---.80
Eighth---6 games---.70
Ninth---5 games---.75

Multiplying these nine component probabilities together yields .069 for the overall probability of the Braves being shut out in any one particular game. This calculation assumes independence of scoring probability from inning to inning, which may be questionable (batting orders would typically lead to the batters in one inning being better than those in the next inning). Still, the estimate seems reasonable, as the Braves were shut out only once in the 20-game sample (.05, which is close to the estimate of .069).

Because Atlanta was blanked in three straight games, we then raise .069 to the third power, yielding .0003 (or 3-in-10,000) for the probability of the Braves getting shut out every time in a three-game sequence (again assuming independence).

Given enough opportunities to get shut out three straight games -- and the Braves certain had a huge number of them, going all the way back to 1988 -- it can happen. But in the short term, even across all of Major League Baseball, it seems very rare.

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