Monday, August 06, 2007

In baseball action tonight, the St. Louis Cardinals tied a major-league record by getting hits in 10 straight at-bats (official at-bats, that is, as one batter walked in between the first eight and last two hits of the streak).

Much of the oddity centered around St. Louis starting pitcher Braden Looper, a converted reliever (I mention that, as relief pitchers would probably have among the fewest at-bats of any National League players and thus little opportunity to gain hitting experience).

For one thing, Cardinal manager Tony LaRussa had Looper batting eighth in the order, a ploy LaRussa tries with his pitcher from time to time. And, more amazingly still, Looper (who, as the above-linked game article noted, "began the game batting .161"), got two of the hits in the Cards' barrage (one of them a bunt single).

The comprehensive, batter-by-batter play-by-play sheet from is available here; your attention should be directed to the Cardinals' at-bats in the bottom of the fifth inning.

Due to the lateness of the hour (1:37 AM Central), I won't attempt any statistical analyses at the moment. I'll probably revisit the matter, though.

Update: One basic kind of analysis that can be done is to take the pre-August 6 batting average for each hitter who took part in the streak and multiply these together to obtain the overall probability of the Cardinals' accomplishing what they did.

As an analogy, if one wants to know the probability of rolling double-sixes with a pair of dice, one multiplies the chances of a six on each die together, (1/6) X (1/6), to obtain 1/36. This multiplication procedure assumes independence of events (i.e., no effect of one event on the other), an assumption that seems to work pretty well for athletic performance data.

Here are the St. Louis hitters who got at least one hit in the streak, along with the type of hit(s), and their batting averages prior to August 6 (for the position players, these averages are taken from the August 5 box score):

Looper (2: single, bunt single) .161 (use twice in multiplication)
Miles (2: infield single, single) .283 (use twice in multiplication)
Eckstein (single) .286
Taguchi (single) .298 (didn't play August 5, so taken from August 4)
Pujols (single) .316
Encarnacion (single) .289
Rolen (homer) .270
Ludwick (homer) .251

Thus, we're left with:

.161 X .283 X .286 X .298 X .316 X .289 X .270 X .251 X .161 X .283 = .000001

which, as an estimate at least, is 1 in a million.

Of course, each time a player makes an out in a game, his team has a new chance to start a hitting streak. Taking into account the large number of games each team plays in a year and the even larger number of outs it makes, those million opportunities probably come up every several years. Indeed, as alluded to above, there are other teams who share the record of 10 straight hits with the Cardinals.

No comments: