Dave Cameron at FanGraphs writes about the Blue Jays adding Tulo to a lineup that already scores the most runs: "There are no diminishing returns to scoring more runs; there is no point on offense to where the marginal value of a run scored is worth less than preventing a run from being allowed on defense."
This is an excellent article with lots of research, so I hate to nitpick. But the above statement isn't completely true. For any team that scores more runs that it allows (which includes pretty much every team that makes the playoffs), preventing a run is more valuable than scoring an additional run.
It's because of the Pythagorean Theorem of Baseball, which states that the ratio of a team's wins to losses corresponds to the ratio of their runs scored to runs allowed (actually, to the SQUARE of these numbers, but that's not essential to this analysis).
Take a team that's on pace to score 600 runs and allow 550 runs. Their ratio of wins to losses should be (600 x 600) : (550 x 550) or 3600:3025. Or, to put it another way, their winning percentage should be:
(600 x 600) / (600 x 600) + (550 x 550) = .543
(that's a record of 88-74 over a 162-game season)
Let's imagine they have a choice to add a hitter that will give them 50 extra runs, or add a pitcher than will prevent 50 runs.
After adding the hitter, they score 650 runs but still allow 550. Their new projected winning percentage is:
(650 x 650) / ((650 x 650) + (550 x 550)) = .583 (94 wins)
After adding the pitcher, they still score 600 runs but now they allow only 500. Their new projected winning percentage is:
(600 x 600) / ((600 x 600) + (500 x 500)) = .590 (96 wins).
That's a difference of two wins. This may not sound like a lot, but the difference between making the playoffs and going home has averaged just 1.5 games in the American League over the last 4 seasons.
The interesting thing about this fact is that it doesn't matter if you are a great offensive team or a mediocre one. As long as you are a good team, one that scores more runs than it allows, it's always more valuable to prevent a run than to score a run.
And ... for fans of the Red Sox or Phillies ... the reverse is also true. If you are allowing more runs than you are scoring, you will improve your team more by adding offense than by adding the equivalent amount of defense.