Game Theory Project

[sbrylski]

My game theory professor sprung a 4-page abstract on us today, due Thursday, outlining the game theory problem I will be solving for my final grade.

 

So, I need a topic. Obviously, I want to do something baseball related. So I'm here for your ideas. I'll probably post some of mine as they come to me for feedback as well.

 

I was looking forward to this, and I'm kind of put off on how short of notice he gave. I have to rush through the topic selection.

[endaround]

How involved is your game theory course? Obviously the easiest question is when to bring in a lefty specialist to face a hitter.

[sbrylski]

How involved is your game theory course? Obviously the easiest question is when to bring in a lefty specialist to face a hitter.

Isn't that basically a one player game though?

 

In general though, the problem doesn't have to be super involved.

[endaround]

No, because whether to do it depends upon the reaction function of the other manager. Its easy vs say Ryan Howard because they'll never lift him. But if its Jody Gerut and you bring in your Loogy? You're facing a RH Phitter off the bench. And unless your Ned Yost you don't usually want that. Now expand and say there are two lefty hitters in a row. Your manager B and a Loogy comes in. Do you ph your first LHander ensuring your 2nd lefty has to face the loogy? Do you let your 1st LHander hit, pH for the 2nd and get a RH vs RH probable matchup? You PH for both? Neither?

[rluzinski]

Do you have to just write about game theory being applied to a specific topic or also perform actual analysis?

 

I assume you've seen Levitt/Kovash's recent study related to baseball game theory?

 

http://tangotiger.net/files/kovash_levitt_w15347.pdf

 

http://www.insidethebook.com/ee/index.php/site/comments/game_theory_on_pitch_selection/

 

As you can see by the comments, many of the readers at insidethebook blog were skeptical of the findings. Perhaps you could improve or take a different approach on the pitch selection topic?

 

MGL wrote a recent fangraph article about when to attempt a sacrifice bunt but it only serves to illustrate how complicated that subject is and how little data there is to help answer questions. A lot of game theory in baseball has to do with forcing the defense to adjust their positioning, which is difficult/impossible to analyize, sicne their's no data on the actual positioning. Sacrifice bunt/suicide squeeze attempt, stolen base attempt. Bunting against a lefty supershift?

 

A pitcher throwing over to first has always bothered me, since game theory tells you to throw over 99% of the time (assuming no chance of an error, at least)?

 

If we assume the batter is completely guessing on pitch location and the only outcome is "strike" or ball", how often should a pitcher throw a strike at various pitch counts and how often should the batter swing? It would be a theoretical construct but might yield interesting information?

[endaround]

Well it doesn't help that Levitt has become a publicity seeking hack. Its not really a true game theory paper. It is also crappy research. They make assumptions, find that these assumptions then cause deviations from what observed data shows and then go on to say that the observed data is wrong and their assumptions are left alone.

[sbrylski]

Yeah, Russ, I had bookmarked that for further reading. Unfortunately that looks much to complicated to get a strong handle on and write up four pages by tomorrow morning.

 

I don't think the standard for complexity is too high for this class, so I'll probably do something like end's suggestion on LOOGY use, and specifically tailor it for the Yankees vs the Utley-Howard combo.

[sbrylski]

I can't seem to dig up the formula for calculating the expected outcome of an PA... i.e. the expected wOBA of the plate appearance given both the batter's and pitcher's wOBA.

 

Any help?

[rluzinski]

Log5 should approximate that:

 

ExAvg = ((BAVG * PAVG) / LgAVG) / ((BAVG * PAVG) / LgAVG + ((1-BAVG)*(1-PAVG)/(1-LgAvg)))

 

How are you going to handle expected platoon splits? I've just used league splits but I think that's wrong. Only the best lefties get to face everyone. So the average wOBA of the lefties facing righties is not equal to the average wOBA of the lefties facing lefties. The later's wOBA is higher.

[rluzinski]

Double posts are silly.

[sbrylski]

Log5 should approximate that:

 

ExAvg = ((BAVG * PAVG) / LgAVG) / ((BAVG * PAVG) / LgAVG + ((1-BAVG)*(1-PAVG)/(1-LgAvg)))

 

How are you going to handle expected platoon splits? I've just used league splits but I think that's wrong. Only the best lefties get to face everyone. So the average wOBA of the lefties facing righties is not equal to the average wOBA of the lefties facing lefties. The later's wOBA is higher.

Yeah, I found the Log5 equation. Thanks though.

 

As for the splits, I'm just going to have to be wrong - I'm just using each player's three year splits. That's why I'm kind of angry I have such short notice for this, I have to strip away so much and use bad projections just because I have to get it done by midday tomorrow. I don't really have time to scrutinize each step I make in calculating the projected payoffs, as long as the game theory itself is correct because that's what I'll be graded on.