Thoughts on the "impact bat" argument

I’ve been thinking lately about the question of whether a team needs to be more balanced in order to win more games –that the Mariners need a “big bat,” even if he blows a hole in our defense.  I’m convinced by the argument that balance doesn’t matter, that it is simply about addition/subtraction of overall talent, that the way a team achieves its run advantage over its opponent doesn’t matter.  However I’ve been wracking my brain, playing devil’s advocate, trying to come up with a way that the argument for more offense could work.  I first thought that adding a hitter at the expense of defense makes sense because defense cannot affect walks, home runs, or line drives that no human could get to.  However this is just restating the fact that offense is more important than defense, which doesn’t help at all.  I then considered that the effect of adding a hitter changes depending on the team’s existing offense –the number of runners that will be on base when he comes up, the likelihood that someone else will hit him in when he gets on etc.  Adding Chase Utley to the Yankees would have a greater effect on their runs scored than adding him to the Mariners.  However additional runs are more important to the Mariners, so he might have a greater impact on our win total than theirs.  This logic is the same for extra runs prevented. 

I’m wondering about two things that I don’t have enough information to figure out.

 First, because a player’s run output is dependent on other players being on base or hitting him in, the addition or loss of good hitter seems to have a greater impact on runs scored the better the team’s offense is.  For example, removing Ichiro from the Mariners would lower our runs scored less than removing a similar offense player like Robinson Cano from the Yankees would lower theirs.  Do defensive changes have a similar non-linear impact?  I know individual defenders don’t affect each other’s defense, but in overall run prevention, adding a good defender to a team already more likely to limit base runners makes it less likely on each pitch that a defender will face a batted ball that could change the score.  I know there’s a discussion about how pitching impacts the marginal value of defense (good defense being wasted on good pitching) but I want to focus only on defense.  If the run impact of changing defense is more linear than that of changing offense, then would adding more defense actually help the Mariners more than adding a bat.  Under this logic, wouldn’t adding Yadier Molina provide more value for what we’d give up than adding a similarly good offensively oriented player?

Secondly, if I am right that improving a team with a tendency towards close games adds more wins than the same improvement would a team trending toward larger single game run differentials, how far can that logic be stretched?  Does this mean that the low offense, high run prevention template for building a roster is better because when that team is able to improve itself, they will see more value in those close games from that marginal improvement?

To sum up my ramblings, would improving defense actually help the Mariners more than improving offense because the offense is already so hopeless it wouldn’t matter as much? And do teams like the Mariners see a greater change in record from marginal additions or subtractions because the games are so close?