Probability in Baseball Question

[pokeraz]

I realize I should probably put this in Probability but I like the forum and it can certainly use some Math balance the SMP scale -

Your watching a game and a guy makes an amazing play to end the inning. His team then comes up to bat, and as a baseball fan, we always note that, sure enough, the guy who just made the great play is now the first one up. And sure enough, he hits a home run.

Well the other night I'm listening to the game on the radio. Guy makes a great play. Sure enough he leads off the next inning...But the announcers say the following

Joe: "How many times have we seen it, The guy that makes the great catch leads off the next inning"

Dave: "Yup. Really what are the odds?"

Joe: "Well...One in Nine."

If you ask the question, what are the odds that the player who just made that out would lead off the next inning, that would be 1/9.

But if you ask, what are the chances that a random player would make the final out and then lead off the next inning, that would be 1/9 * 1/9, correct? Is it this simplistic?

How does this change if we ask these questions with a specific position player? How do we take into consideration the distribution of outs per position? Or frequency of at bats per position and the frequency of a specific batting order leading off an inning.

According to Elias Sports:

Here's the percentage of the time each batting order slot leads off an inning, with the top of the 1st removed for obvious reason.

1 -- 16.6 %
2 -- 9.3 %
3 -- 8.9 %
4 -- 12.5 %
5 -- 11.4 %
6 -- 10.2 %
7 -- 10.6 %
8 -- 10.6 %
9 -- 9.9 %

Considering that better players are playing more challenging positions and are more likely to be a leadoff hitter getting more at-bats

2007 Leadoff Hitters By Position, up to 6/18/2007

1. CF -- 39.4 %
2. 2B -- 21.2 %
3. SS -- 18.3 %
4. LF -- 9.1 %
5. RF -- 4.9 %
6. 3B -- 3.6 %
7. DH -- 1.5 %
8. C -- 1.0 %
9. 1B -- 0.9 %

I have yet to find a 'outs per position' number but it is probably important.

Other considerations?

[kerowo]

If you are talking big plays only then I think that would weight the chances a particular position makes that play to end the inning. For instance, the throw to first isn't usually the exciting part, the diving catch by short is, but I think the first baseman gets the put out.

[New001]

Also, while the "more challenging" positions to play defensively may be the most valuable, they often do not have the most prolific home run hitters. For those, you'd look towards 1B, RF, LF, etc. An average 1B who makes a big play and leads off is more likely to hit a HR than an average 2B who makes a similarly big play.

[evank15]

Joe: "How many times have we seen it, The guy that makes the great catch leads off the next inning"

My explanation? Logical fallacy - enumeration of favourable circumstances.

[lippy]

Either SI or ESPN.com had an article about this. They did a statistical analysis and said it was BS.