Batting order

[VanillaGorilla]

Originally Posted by rpriske

I am just jumping back in and it see VG saying that my claim that this has been 'mathematically proven' is untrue.

Hypothesized.

Originally Posted by rpriske

I am sorry, but that is not the case. It is a very simple mathematical model, in fact. The only weakness is the side that will ALWAYS be a weakness: how accurate your prediction of results by individual players.... but that is the case no matter what model you use.

You plug in appropriate .OBP and .SLG and it calculate the average number of runs scored using that line-up. There is nothing magic about it.

Which is precisely the flaw. That is ALL that it does. And the conclusion that increased runs scored equals more won games is also a flaw.

What? Nonsense?

The earlier you pinch hit for your pitcher the more runs you score. This is based on actual data. It is also intuitive. Pinch hit for the pitcher, and subsequent relievers you should get better offense than if you let the pitchers hit (why pinch hit for them if they are better than your bench batters, otherwise?).

So, simply because more runs are scored by pinch hitting for a pitcher earlier, does that mean that the pitcher should be pinch hit for earlier? It increases runs scored, therefore it must be better, right? In fact, for each inning sooner that you pinch hit for the pitcher, you can expect about an additional 1 tenth of a run per ball game.

This is math.

The earlier a team pinch hits for a pitcher, the more runs that team is expected to score.

This is also demonstrable through math.

The earlier a team pinch hits for a pitcher the more games it will win because it will score more runs.

This is flawed logic.

When an AL manager pinch hits, he is not impacting the game, or his game winning chances on the pitching side of the equation.

In the NL game, this is not so.

If you pinch hit for Clayton Kershaw in the 5th inning you can expect to score an extra half run in the game than if you let him complete the game. So, why not pinch hit for him? You will score more runs.

The reason you don't is because there is an opportunity cost involved when you lift him for the pinch hitter, and that cost is that you are now going to have someone else pitch to the opposition for the next 5 innings (if it is a road game).

If a team pinch hits for the pitcher when he comes up in the 5th inning, that team will score more runs than if the pitcher is allowed to bat. If the pitcher is allowed to bat in the 5th inning and is pinch hit for in the 7th inning, that team has given up about 2 tenths of expected run production in order for him to have hit in the 5th inning.

Multiply that over 162 games and you find that there is an additional 32.4 runs that a team can expect to score over the course of a year by pinch hitting for the pitcher in the 5th inning vs the 7th (or the 6th vs the 8th).

Compare that to the approximate 2 runs that Tango's model says a team gets over 162 games by hitting the pitcher 8th vs 9th.



The Tango Model in "The Book" assumes the 8th place hitter will hit in the 8th place for the course of the game. For a the DHing AL, this assumption is a minor deviation from actual reality. In the NL, this is a huge discrepancy.

Note my original post on the matter in this thread where I said that I think the idea of hitting the weakest hitter 8th in a DH environment is of merit, but batting the pitcher 8th in the NL environment is suspect as the optimal blanket strategy.

Originally Posted by rpriske

What does that leave out? Intangibles? The outdated notions that you need speed at the top of your order? Line-up 'protection'?

There is much left out that is impactful. To be continued....

[Cinnamon J. Scudworth]

In other words:

Argument from Authority

[rpriske]

The question of pinch-hitting is a question of relative opportunity cost and is completely irrelevant to the discussion at hand.

[VanillaGorilla]

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.

This is simply not so. It is keenly relevant to the essential point of the discussion, on two points:

1) Baseball isn't simply about scoring runs and scoring more runs in 162 games than any other team. It is about scoring more runs than your opponent in a discrete game, and in discrete games over the course of a season/post season.

You can score runs forever. More importantly, your opponents can score runs forever. You need to get 27 outs before you claim the win. Saberheads will be familiar with this stunningly obvious concept put forth by Bill James (and a concept whose import was revolutionary to the study of baseball).*

This is key to the idea of what is an "optimal" line-up. It isn't only about scoring runs (defensive considerations of the players are assumed to be neutral for any exercise of this type). In the AL, it is. Put your starting 9 together in such a way that it maximizes your run output and you will win more games.

In the NL, this isn't so. The fact that one of your 'hitters' is the guy that has the singularly greatest effect on how quickly your team records the 27 outs needed to claim victory MUST be considered when constructing the "optimal" line-up to win games. Tango's model from "The Book" did not consider this, at all.

Second point to follow, which is a larger point and will require a bit of time.

[VanillaGorilla]

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