I missed the comment about line-ups scoring runs exponentially when they are without gaps...but that absolutely confirms my belief that we need to score offense NON-linearly for individual players.,..accounting for their performance above and below the "super-margin" and the margin. If you are really...REALLY good you are causing a "gap" in the other team...if you are really...really bad...you are creating a gap in your own team and robbing other players of the chance to produce non-linearly as in this article.
I'm telling you folks...that is the number one problem with WAR.

...what happens when a pitcher is really bad? He raises everyone's OPS in a line-up by (say) .100. If you take a typical team with three gaps and 3 stars and 3 mediocre players...you will turn the gaps into regulars, the regulars into stars and the stars into beasts. Now the line-up with gaps becomes a line-up without gaps. Leading to non-linear scoring. Do you see why we need to account for the super-margin in great players as well as the margin (non-linearly) in bad ones?

Is really great. Matt I know the the idea of offense being non linear ties in with what you've been looking at lately but I'd really curious to hear your thoughts about his larger point...
Pretty much all sabremetrics (or at least the publicly available stuff) these days is based on the idea that baseball is made up of a series discrete events that we treat as independent of one another. But that's probably not true. Sequencing matters but we don't have the tools to really study and understand it. Because the database tools everybody uses look at individual events devoid of context, that's how we think about them. Even though there's probably some very important stuff buried in all those circumstances.
Arneson compares it Newtonian physics, it'll get you most of the way there and there's some important stuff in there but it doesn't capture the full reality of things.
The whole essay is fascinating and well worth everybody's time. Probably the best thing I've read about baseball in six months.
Some great thoughts about roster construction too. The idea that a lineup should be composed of different types of hitters makes a lot of intuitive sense to me.

Actually, Doc, you need to get more flying miles. PDX is Portland to the airlines - so, he's probably E.K.N. in Portland.
Joe Btfsblk, however, lives in Dogpatch, still, I hope. I do note that he used to be in Head and Shoulders ads - which are now done by C.J. Wilson and Josh Hamilton. Coincidence? I think not. Head and Shoulders ads now rank with an SI cover for jinx effect.
As to Mr. Mxyzptlk!, let's hope he stays away from our soon-to-be-super-Mariners as well!

It superbly underscores the inability of current publicly available models to adequately address the complexities of baseball. Intuitively we have suspected this is true, and we might have been able to illustrate some of our suspicions, but the article lays bare a fundamental oversight in the approach of those who merely adopt and parrot the ideas of those who have gone before. It also shows that sometimes managers may intuitively know more than we think they do.
It seems to me that not only are events within a single game are not both discrete and independent, but there are additional complexities in the histories of certain teams against other teams, certain batters against certain pitchers, and even in the day after day life of individual players. These are things managers are much more in tune with, things we have little or no access to. One can heap up complexities even more if one wants to. Suppose one player plays better in certain types of weather/climate than others?

I don't think I should post comments in response to this article...this is too important and too similar to my own basic thinking...I think I should take this article apart piece by piece in a feature article...so be ready to promote the article to viewable status when it appears.

It's been my handle since insidethepark.com and Seattle P-I days.
As for the article, I emailed the author with a thank you and opined much of his insight touched on the subject of an appropriate methodology on the study of the mysterious " line-up protection" debate.
For my educational background, I found the current ongoing argument of line-up protection to be focused on a results based analysis. Personally, I think the concept is best to be evaluated as a "tactical advantage."
That is to mean does having a diverse line-up create a tactical advantage not just during the at-bat, but a ripple affect on the game, the next game, the series, or a set of series, etc?
In symbolic interaction school of sociology there's a phenomenon called "self fulfilling prophecy." In short, when a group of people all believe something to be true (ex. The guy with the hot hand at the craps table) they harmonize a group expected outcome that has real consequences. The collective belief in line-up protection can be viewed in the same manner.
That would indicate managers and players base tactical decisions on line-up protection, leading to it having an affect on the game. So to examine the affect of line-up protection could also be measured, say by, bullpen management for the rest of the series and how that goes on to affect the next series. So line-up protection could have more of an effect on the team not equipped to deal with a strong diverse line-up in the wins and losses column over 162 games.
The author replied that he didn't concern himself with the current line-up debate, but agreed there could be a more methodologically sound way to understand the concept. Of which focused more on game theory - of course.
I agree with the comment that this was the most enjoyable read on baseball in a long time.

You finally shamed me into trying to register but it keeps telling me that it can't send me an email with my password and to contact the site administrator so... I'm not sure how to proceed.