tag:blogger.com,1999:blog-11923437.post2133878912320057226..comments2007-10-18T15:25:56.559-04:00dakhttp://www.blogger.com/profile/02768386460112735397noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-11923437.post-80107999008433899132007-10-18T15:25:00.001-04:002007-10-18T15:25:00.001-04:00Markov Chain TremendousJuniorhttp://www.blogger.com/profile/12399868922850358920noreply@blogger.comtag:blogger.com,1999:blog-11923437.post-68239566254962024172007-10-18T15:25:00.000-04:002007-10-18T15:25:00.000-04:00Someone actually wrote in about this. I think it's 1+.whatever, because Tangotiger's system has to do with ... well, here:<BR/><BR/><B>I just thought I'd just chime in on the question about expected runs matrix when the lead off guy homers. So, if you assume that the inning is a Markov Chain <BR/>(http://en.wikipedia.org/wiki/Markov_chain) that is the state of an inning is <BR/>completely described by the number of outs and what bases are occupied<BR/>(not really true) then the answer to your question of what is the expected number of runs given that the leadoff guy homers is simply<BR/>1 + expected number of runs with no outs and no one on.<BR/><BR/>This is because you can separate what happens in the past (the lead off guy homers) with what happens in the future, due to the Markov property.<BR/><BR/>Of course, this is not exactly true, since other things change if the pitcher gives up a homer, such as the likelihood that the pitcher will get pulled. That make this model just an estimate.<BR/><BR/>Love your blog,<BR/>James<BR/><BR/>P.S. Simple proof that it must be 1+whatever and not whatever: (Lets call "whatever" the variable A)<BR/>Assume that the answer is A, then what if the first B batters (with B > A) all hit homeruns. Then we still have no one on and no outs, but we have B runs scored, this would mean that the expected number of runs (A) is less than the <BR/>number of runs actually scored, which is a contradiction.</B><BR/><BR/>???Juniorhttp://www.blogger.com/profile/12399868922850358920noreply@blogger.comtag:blogger.com,1999:blog-11923437.post-20505771442663868982007-10-18T12:20:00.000-04:002007-10-18T12:20:00.000-04:00I should have posted on this a long time ago, but then I left the country and just moved and blah blah blah. The point is, I got a few emails from people after my super snarky post about McCarver calling Stats. Inc. that showed he wasn't as crazy as I thought he was, and I never posted them. Pure neglect on my part. <BR/><BR/>Junior -- did we ever solve the mathematical accuracy of the Expected Runs Matrix for Bases Empty, No One Out when the leadoff guy homers? Is it (1+) .whatever? Or just .whatever?Ken Tremendoushttp://www.blogger.com/profile/15290167169845520176noreply@blogger.com