All of the "intangibles" that may or may not exist in baseball are meaningless unless said player translates those onto the field.
Everything in baseball is finally determined on the field and as a matter of fact we can quantify every single thing that occurs there.
That is the very nature of Baseball Statistics, traditional, sabermetric, or otherwise.
A player with all the grit and heart in the world who hits 0.200 and walks one time out of twenty is still a player with a 0.200/0.250 slash line.
The "intangibles" need not be measured, as their results are measurable.
This is the equivalent to saying that one cannot prove gravity exists because we do not completely understand why particles have mass.
Jamiecballer and FNK would say that, until we know the absolute details of the causal mechanism, the results cannot be measured.
A scientist would tell you to jump and measure the result.
See the difference?
Allow me to make this distinction as I am not sure the two of you realize this.
Jeffy, Jej, et al are not making a claim as to the causal mechanism behind a player's performance.
Like any good scientists or adherents to basic logic they are merely demonstrating that there is no significant effect, independent of causal mechanisms, that would provide any evidence that the concept of line-up protection actually alters the outcome of a game.
If it does not alter the outcome of an at-bat, an inning, or a game, then it is irrelevant.
We know, as fact, that pitchers do not deviate from their approaches to certain batters based on the next individual in the line-up. Numerous studies have looked at Barry Bond's preceding hitters for instance and found zero correlation between his presence and the pitches the other batter saw.
Talk about "intangibles" all you want; until it effects the game in some measureable fashion they are meaningless.