Thursday, August 03, 2006

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"].

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