I'm betting the central element of Dexter's fourth season finale will be Trinity capturing Harrison and Harrison being reborn in a pool of blood, much like Dexter was. Dexter will kill Trinity and save Harrison's life, but in future seasons he'll have to raise a son with dark urges -- forcing Dexter to decide how far he accepts and rejects Harry's upbringing of him.
Come on, that's a good ending even if the prediction proves wrong.
Sunday, December 13, 2009
Saturday, October 31, 2009
Tuesday, October 27, 2009
Comment on MGL on Bunts
I planned on posting his on The Book Blog, but sadly it doesn't seem to want to take it. It is a comment on this, from a slightly more mathematical perspective. I'm not sure how much reader('s) of this basically dormant blog will enjoy it, but it seems like a reasonable place to put it. What follows is the comment.
This is very good, although I am not sure I agree with some of the details. I've been grading a lot of freshman calculus exams lately, so apologies in advance for this little model, which is obviously heavily inspired by MGL's discussion.
We suppose both managers behave optimally. Let t ranging from 0 to 1 be the possible positions the infielders can play, so t=0 means that the infielders are playing as far in as possible, and t=1 means that they are playing as deep as possible (or as deep as realistically possible, since I guess they could play as deep as the fences!) We assume for simplicity that there is only one free parameter in terms of how "deep" the defense can play, while of course there are many in reality.
For a given hitter, in a given game state, with a given defense, we have the functions b(t) and h(t), where b(t) is the expected value of the bunt with the defense playing position t and h(t) the expected value of hitting away. We assume that b(t) is increasing, h(t) is decreasing, h(0) > b(0) (so hitting is preferred to bunting with the defense playing in) and b(1) > h(1). At the Nash equilibrium, the defense will play some position t_0 between zero and 1 and the offense will bunt some fraction 0 < c < 1.
t_0 is easy to find, as MGL indicates. Namely, our assumptions about h(t) and b(t) guarantee that there is a unique point x between 0 and 1 where h(x) = b(x). MGL's argument in the link shows that if the defense is playing any position t' not equal to x, it cannot be in a Nash equilibrium (the offense would have to bunt or hit 100% of the time, and the defense could then improve by changing their position.) Of course, if the hitter is a good bunter then b(t) is bigger, so x is closer to 0, while if he is a poor bunter or a good hitter x is closer to 1, all of which obviously makes intuitive sense.
Now, what should the batter do? He bunts some fraction c of the time, and no matter what of c he picks the total value of his PA is c*b(x)+(1-c)*h(x)=(c+1-c)*b(x)=b(x) since b(x)=h(x). However, there is still a constraint: for the optimal value c, the function f(t) = c*b(t) + (1-c)*h(t) (which is the value of the PA as a function of t if the batter bunts with probability c) must have a local maximum at t=x. Otherwise, by either moving in or out, the defense can decrease the value of the PA, which contradicts the Nash equilibrium assumption.
So we must have c*b(t) + (1-c)*h(t) with a local max at t=x. From freshman calculus, we know that a necessary condition for a local max is that the derivative vanishes at that point. So
0 = f'(x) = c*b'(x)+(1-c)*h'(x)
Which gives
c = - h'(x)/(b'(x)-h'(x))
Our assumptions about b(t) and h(t) guarantee that this is always strictly between 0 and 1, which is obviously good.
Note, though, and this is the key point, that the optimal ratio is independent of how good a bunter the batter is! All that the matter is the LOCAL behavior of the two functions at the indifference point.
For instance, suppose ARod is a bad bunter and a good hitter, so the defense plays him very far back, say at .9. But at .9, it may well be the case that b'(.9) >> h'(.9), or in other words, that the marginal improvement in ARod's bunting value when the defense steps back is much bigger than the corresponding marginal decrease in his hitting ability. In this case, ARod should be bunting most of the time. Similarly, you can be a very good bunter and poor hitter, but still be advised to swing away when the defense is playing you optimally. So I don't think I agree with MGL's recommendations about how much different players should bunt
This explains why the offensive manager's job is much harder the the defensive manager's. The defense only has to know when the two functions are roughly equal, which is something that can be discovered implicitly through trial and error. It is very hard, however, to get a sense of the derivatives of these functions through trial and error. So it makes a lot of sense that offensive manager's make more bunting mistakes than defensive ones.
Does this make sense? Is there some other parameter that people think should be included in this ridiculously simple model?
This is very good, although I am not sure I agree with some of the details. I've been grading a lot of freshman calculus exams lately, so apologies in advance for this little model, which is obviously heavily inspired by MGL's discussion.
We suppose both managers behave optimally. Let t ranging from 0 to 1 be the possible positions the infielders can play, so t=0 means that the infielders are playing as far in as possible, and t=1 means that they are playing as deep as possible (or as deep as realistically possible, since I guess they could play as deep as the fences!) We assume for simplicity that there is only one free parameter in terms of how "deep" the defense can play, while of course there are many in reality.
For a given hitter, in a given game state, with a given defense, we have the functions b(t) and h(t), where b(t) is the expected value of the bunt with the defense playing position t and h(t) the expected value of hitting away. We assume that b(t) is increasing, h(t) is decreasing, h(0) > b(0) (so hitting is preferred to bunting with the defense playing in) and b(1) > h(1). At the Nash equilibrium, the defense will play some position t_0 between zero and 1 and the offense will bunt some fraction 0 < c < 1.
t_0 is easy to find, as MGL indicates. Namely, our assumptions about h(t) and b(t) guarantee that there is a unique point x between 0 and 1 where h(x) = b(x). MGL's argument in the link shows that if the defense is playing any position t' not equal to x, it cannot be in a Nash equilibrium (the offense would have to bunt or hit 100% of the time, and the defense could then improve by changing their position.) Of course, if the hitter is a good bunter then b(t) is bigger, so x is closer to 0, while if he is a poor bunter or a good hitter x is closer to 1, all of which obviously makes intuitive sense.
Now, what should the batter do? He bunts some fraction c of the time, and no matter what of c he picks the total value of his PA is c*b(x)+(1-c)*h(x)=(c+1-c)*b(x)=b(x) since b(x)=h(x). However, there is still a constraint: for the optimal value c, the function f(t) = c*b(t) + (1-c)*h(t) (which is the value of the PA as a function of t if the batter bunts with probability c) must have a local maximum at t=x. Otherwise, by either moving in or out, the defense can decrease the value of the PA, which contradicts the Nash equilibrium assumption.
So we must have c*b(t) + (1-c)*h(t) with a local max at t=x. From freshman calculus, we know that a necessary condition for a local max is that the derivative vanishes at that point. So
0 = f'(x) = c*b'(x)+(1-c)*h'(x)
Which gives
c = - h'(x)/(b'(x)-h'(x))
Our assumptions about b(t) and h(t) guarantee that this is always strictly between 0 and 1, which is obviously good.
Note, though, and this is the key point, that the optimal ratio is independent of how good a bunter the batter is! All that the matter is the LOCAL behavior of the two functions at the indifference point.
For instance, suppose ARod is a bad bunter and a good hitter, so the defense plays him very far back, say at .9. But at .9, it may well be the case that b'(.9) >> h'(.9), or in other words, that the marginal improvement in ARod's bunting value when the defense steps back is much bigger than the corresponding marginal decrease in his hitting ability. In this case, ARod should be bunting most of the time. Similarly, you can be a very good bunter and poor hitter, but still be advised to swing away when the defense is playing you optimally. So I don't think I agree with MGL's recommendations about how much different players should bunt
This explains why the offensive manager's job is much harder the the defensive manager's. The defense only has to know when the two functions are roughly equal, which is something that can be discovered implicitly through trial and error. It is very hard, however, to get a sense of the derivatives of these functions through trial and error. So it makes a lot of sense that offensive manager's make more bunting mistakes than defensive ones.
Does this make sense? Is there some other parameter that people think should be included in this ridiculously simple model?
Saturday, July 11, 2009
A perfect game
Jonathan Sanchez is getting gypped. Officially, he threw a no-hitter Friday. But because he allowed no walks and hit no batters, only third baseman Juan Uribe's fielding error separated Sanchez from a perfect game -- a far rarer and more prestigious feat than a no-no. Why should Sanchez be punished because his teammate choked? Not only was Sanchez's performance tantamount to a perfect game, but it was actually a bit better than perfect, because he had to record an extra out to make up for Uribe's screw up. The stat community should from now on determine perfect games independently of errors.
Wednesday, May 27, 2009
Bonzai
First Pearl Harbor. Now Dice-K.
How much bombing from Japan is this country going to take?
Truly, if the CIA had forced senior al Qaeda detainees to watch Daisuke Matsuzaka throw 100+ pitches in 5 innings, allowing 12 baserunners, serving up 690 wild pitches, all while wiggling his ass like an earthworm on a fish hook, Osama would have been toast on 9/12.
But to the detainees, it would have felt like forever.
How much bombing from Japan is this country going to take?
Truly, if the CIA had forced senior al Qaeda detainees to watch Daisuke Matsuzaka throw 100+ pitches in 5 innings, allowing 12 baserunners, serving up 690 wild pitches, all while wiggling his ass like an earthworm on a fish hook, Osama would have been toast on 9/12.
But to the detainees, it would have felt like forever.
Thursday, May 21, 2009
Travesty
You're a baseball announcer. How do you ruin back-to-back-to-back home runs? Right here. It comes naturally if you're John Asshat Sterling.
No amount of waterboarding could ever suffice to punish the use of the term "Swish-a-licious." But by golly we should try.
No amount of waterboarding could ever suffice to punish the use of the term "Swish-a-licious." But by golly we should try.
Sunday, May 17, 2009
Thursday, April 2, 2009
Time travel
Monday, March 23, 2009
Schilling Lumbers Off Into the Sunset
Curt Schilling's retirement announcement, with commentary from the very inner conscience of Curt Schilling:
“Turn out the lights, the party’s over” Totally nailed it.
“Turn out the lights, the party’s over”
Rather than simply state I am retiring, I will build this up like a prick. Because I am a self-indulgent prick.
I used to wait with bated breath for Don Meredith to start singing that on “Monday Night Football.” Normally, it was sweet music if the Steelers were playing.
I am a self-indulgent prick.
If I could get him to sing it again, I would. This party has officially ended. After being blessed to experience 23 years of playing professional baseball in front of the world’s best fans in so many different places, it is with zero regrets that I am making my retirement official.
I am a self-indulgent prick.
To say I’ve been blessed would be like calling Refrigerator Perry “a bit overweight.”
It would be like calling Curt Schilling "a bit overweight."
[...]Four World Series, three World Championships. That there are men with plaques in Cooperstown who never experienced one — and I was able to be on three teams over seven years that won it all — is another “beyond my wildest dreams” set of memories I’ll take with me.
I, one pitcher, Curt Schilling, believe I am solely responsible for the championships of all three teams.
The game always gave me far more than I ever gave it. All of those things, every single one of those memories is enveloped with fan sights and sounds for me. Without the fans, they would still be great memories, but none would be enduring and unforgettable because they infused the energy, rage, passion and “feel” of all of those times.
You can tell I'm disingenuous here, because this sentence makes absolutely no fucking sense at all, even for me: "Without the fans, they would still be great memories, but none [fans? memories? experiences?] would be enduring and unforgettable because they [fans? memories? donuts?] infused the energy, rage, passion and “feel” of all of those [wtf????] times." Totally nailed it.
I am and always will be more grateful than any of you could ever possibly know.
I am a sanctimonious prick.
I want to offer two special thank you’s.
To my Lord and Savior Jesus Christ for granting me the ability to step between the lines for 23 years and compete against the best players in the world.
Christ died for most people's sins. But because I have no sins, he died so I could play ball. And yes, my sanctimonious prickness is coming across loud and clear.
To my wife Shonda
I married a hatchback car.
and my 4 children, Gehrig, Gabriella, Grant and Garrison for sacrificing their lives and allowing baseball to be mine while I played. Without their unquestioned support I would not have been able to do what I did, or enjoy the life, and I am hopefully going to live long enough to repay them as much as a Father and Husband can.
See how I know the quantity and names of my children! First letter is always G, that's how I remember. But perhaps I was too forthcoming in acknowledging that my kids "sacrificed their lives" and that I never questioned their support.
Thank you and God Bless
Curt Schilling
Sunday, March 22, 2009
Tuesday, February 17, 2009
I Am Mankiw, I Am Douche
Greg Mankiw writes (translated from the Bullshit):
"Recently I found myself desiring to highlight how important I am. I noticed people were talking about how this other professor disclaimed any interest in debating the stimulus, saying: 'all I know on this issue I got from Greg Mankiw's blog.' Gosh! Look how important I am! So I contrived a post that speculated the professor was being tongue in cheek -- fanciful of me, because hey, if I were someone else, I'd parrot me -- in order to draw further attention to my own large, throbbing intellect. It's rock hard, my intellect."
"Recently I found myself desiring to highlight how important I am. I noticed people were talking about how this other professor disclaimed any interest in debating the stimulus, saying: 'all I know on this issue I got from Greg Mankiw's blog.' Gosh! Look how important I am! So I contrived a post that speculated the professor was being tongue in cheek -- fanciful of me, because hey, if I were someone else, I'd parrot me -- in order to draw further attention to my own large, throbbing intellect. It's rock hard, my intellect."
Monday, February 9, 2009
Pussy of the Day
Is Alex Rodriguez, for confining himself to a mea culpa, for not going after the player's union and the leakers, for not offering Peter Gammons to feel his testicles.
Tuesday, January 27, 2009
Updike
I cannot call myself an Updike fan, having read nothing of his other than a scattered few articles. What I can say is that he wrote beautifully about baseball; this is the article that has been getting a lot of play today. I particularly like this part:
"Baseball is a game of the long season, of relentless and gradual averaging-out. Irrelevance—since the reference point of most individual games is remote and statistical—always threatens its interest, which can be maintained not by the occasional heroics that sportswriters feed upon but by players who always care; who care, that is to say, about themselves and their art. Insofar as the clutch hitter is not a sportswriter's myth, he is a vulgarity, like a writer who writes only for money."
I also could not help but notice his mention of attending school "near Boston". I suppose it should count as little surprise to see this particular prevalent instance of Harvadian false modesty should be so old, but it was nevertheless quite amusing.
"Baseball is a game of the long season, of relentless and gradual averaging-out. Irrelevance—since the reference point of most individual games is remote and statistical—always threatens its interest, which can be maintained not by the occasional heroics that sportswriters feed upon but by players who always care; who care, that is to say, about themselves and their art. Insofar as the clutch hitter is not a sportswriter's myth, he is a vulgarity, like a writer who writes only for money."
I also could not help but notice his mention of attending school "near Boston". I suppose it should count as little surprise to see this particular prevalent instance of Harvadian false modesty should be so old, but it was nevertheless quite amusing.
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