Quote:
Originally Posted by rpriske
The question of pinch-hitting is a question of relative opportunity cost and is completely irrelevant to the discussion at hand.
|
2)
Tango's model gave zero consideration to the use of pinch hitters. This is an issue that must be considered before we can make the assertion that batting the pitcher 8th is, in fact, "optimal."
Before I go further I want to say, again, that I am a big fan of Tango. The stuff he does is really cool. I have no desire to go to his forum and simply cause trouble for Tom Tango.
"The Book" came out in 2007. I did not participate in his forum when the book came out, and I haven't been keeping up with it in some time.
I have no need to prove myself better than Tango, or anyone. What he does is great. However, this application of the model to a RL NL environment is flawed.
I could not have been the only one to have thought so over the course of 6 years.
I wasn't. So, instead of reinventing the wheel, I looked for material on this subject. What I found was head-slappingly obvious once discovered. The author of the paper was taken by surprise by it, also.
Instead of simply posting a link and saying "read this, you people and educate yourselves" (I don't know who makes posts like that on this forum...just can't think of one, at the moment), I will post an opening excerpt and my thoughts on the paper. Anyone is free to read it and agree or disagree with my take. I have not double checked the author's data, nor have I replicated the operations. I have not found anything indicating that the author's work is dishonest, in anyway, or that the data used is inaccurate. If anyone finds such information, I would like to know about it.
-----------------------------------------------------
"Tom Tango’s book (p. 147) uses his Markov runs per
game model for “typical” NL hitters by batting position
and finds an increase in scoring of 0.012 runs per game if
pitcher hits 8th and #8 hitter bats 9th. This advantage is 1.9
runs/season, which is not likely enough to produce an extra
win (based on 10 extra runs for one more win).
“A Markov Chain Approach to Baseball” by Bukiet,
Harold, and Palacios, Operations Research, 1997
“A Robust Heuristic for Batting Order Optimization Under
Uncertainty” by Joel Sokol, Journal of Heuristics, 2003
These papers also change how the top of the order hits.
Idea is to give better hitters more at bats and keep pitcher
away from them so they have more men on when they
come up.
I asked Bukiet and Sokol to analyze where the pitcher
should bat when pinch hitters are considered."
So, the author is not only using the same statistical methodology that Tango used in "The Book", he has enlisted the people whose work Tango used in "The Book" to base his model to work the same model used by Tango perform the same analysis Tango performed, only this time using pinch hitting frequency and data. Very cool, Mr Pankin.
What the author, Mark Pankin, found was that when pinch hitters are considered, NL teams (using 1984-1992 data) scored the most runs when the pitcher batted ninth.
Why? Precisely for the same reason that the model shows AL teams scoring more runs when the weakest hitter bats 8th. Once you pinch hit for the pitcher, the worst hitter in the line-up is no longer the pitcher.
Yes, you don't want your worst hitter batting in front of the top of your order. However, the pitcher typically bats twice a game. When you pinch hit for him, do you want the traditional 8th place hitter following him or your lead-off hitter following him? Using Tango's model
and adding pinch hitter data the model outputs that
more runs are scored by having the pitcher hit 9th.
When I started reading this I am thinking, "OK, the better my pinch hitters are, the sooner I want them in the game, so maybe hitting pitcher 8th is better in that case."
The opposite was demonstrated to be true. The better the pinch hitter is, the greater the benefit is of having him PH for a P batting 9th in terms of expected runs scored. The author used 1941 Ted Williams for an extreme test.
While Mr Pankin's model is Tango's, and does not account for the opportunity cost in terms of Game Winning Chances when removing a pitcher earlier with whatever frequency would occur by hitting him 8th, what this does show is that when the dynamic of pinch hitting is added to the model, the resultant "optimal" line-up from the same model that said hitting the pitcher 8th gains 2 runs a season now gives output that shows it is better to have the pitcher hit 9th.
Actually, it doesn't say that it is better for the pitcher to hit 9th, per se, but that it is better to have your
pinch hitters bat ninth. Why? For the exact same reason that model says it is best to not have your worst hitter batting 9th in a DH environment.
If there is a blanket strategy for a ML line-up without a DH, and you wish to base it strictly on expected runs scored, then this study indicates that the optimal place to bat the pitcher is 9th.
The Gorilla rests.
http://www.pankin.com/sabr37.pdf