THE BOOK--Playing The Percentages In Baseball

Wednesday, September 20, 2006

Streaks

http://thehothand.blogspot.com/2006/09/i-didnt-think-2006-l.html

The probability of these four Dodgers putting together a string of four consecutive homers is thus:

.04 X .04 X .03 X .04 = .000002, or 1 in 500,000.

In MLB history…

...there has been almost 15 million plate appearances, meaning that many times to start a streak.  Of course, in many of those deadball years, the chances were virtually nil.  Assuming that this was not the case, what is the likelihood of getting 4 consecutive HR, if the true rate in each HR was .016 per PA (the historic average)?  Almost 15 million to 1.  That is, we should have expected this to have happened once.  In fact, there are four such games.

Like I said, I used the historic .016 HR per PA rate, when really, we should at least be using it on a year-by-year basis (and most accurately, on a player-by-player basis).

If we focus on the 11 million PA since 1919, the HR rate here is .02 per PA.  Now, our odds are 6 million to 1, or an expectation of having two such games since 1919 (and zero prior).

If we focus on the 2 million PA since 1993, the HR rate here is .028 per PA.  Now, our odds are 2 million to 1, or an expectation of having one such game, since 1994.  Between 1919 and 1993, there were 9 million PA, and the odds were 9 million to 1, or an expectation of one such game between 1919 and 1993.

So, if every hitter were league average, our expectation is for this to have happened twice in MLB history.  Not all hitters are league average.  And the four times that it did happened, they all occurred late in the game (6th, 7th, 9th, and 11th innings).  Bunching good hitters together, facing tired or ineffective pitchers, will bump up the odds.