Joe Morgan gets one right

I often disparage most of the comments Joe Morgan makes during a baseball telecast, but I have to (hesitantly) agree with a point he made during tonight's Red Sox - White Sox game.

Before the first pitch, the homeplate umpire came out to the mound to have RHP pitcher Freddy Garcia remove a black & white cloth bracelet from his left wrist. Before removing the bracelet, Garcia tried unsuccessfully to convince the umpire to let him tuck it under his long sleeved black undershirt.

Morgan made the point that this seemed ludicrous for a couple of reasons. First, if Garcia tucked the bracelet under his shirt, who even knows if he has it on? And second, the bracelet was black and white -- the same as the White Sox uniforms. After Morgan made this last point I was expecting the next sentence out of his mouth to be something like, "Maybe the umpire should make Garcia pitch naked since it's also black and white."

I grudgingly agree with Morgan on this one.

Later in the game after Mientkiewicz made a great play to end the bottom of the inning (and subsequently led off the top of the following inning), Morgan observed that when he was younger he was amazed at how often a player led off the inning after making a great play to end the previous inning.

If Morgan had paid more attention in math class, this phenomenon wouldn't be so amazing.

update: Apparently I didn't pay attention in class either. My know-it-all friend Doug, pointed out that it's not the probability of those players in front of Mientkiewicz getting a hit -- it's the probability of them getting on base. Anyway, here's the updated version.

Given the specific circumstances of Mientkiewicz's at-bat, the probability of Mientkiewicz leading off the top of the second inning was the probability of Damon, Cabrera, Ortiz and Varitek all getting hits on base in the first inning to allow Mientkiewicz the chance to lead off the second (it's their OBP: .382*.299*.371*.395) multiplied by the probability Mientkiewicz makes the final defensive out in the inning (which is 1/9). The answer? There's a 0.06% 0.20% chance that Mientkiewicz leads off the 2nd inning after making a great play in the field.

Of course, Mientkiewicz homered and the probability that he hits a HR leading off the inning after making a spectacular play in the field is 0.002*0.015 = 0.003% (where 0.015 is the probability that Mientkiewicz hits a home run).

Generally speaking, the probability that a player leads off the inning (after the 3rd inning) after making a great play in the field is just 0.11*0.11 = 1.23% in the NL and 0.11*0.125 = 1.39% in the AL (because of the DH).

Joe Morgan, be amazed no more.