Is a home run just a home run?

In sabermetrics, the statistical analysis of baseball, there is a lot of work done to estimate the value of players to team. How valuable is a player who hits .330 with an OBP of .387 with 12 HR? Is he more valuable than someone hitting .347 but with just a .365 OBP and 2 HR?

To make life simple sabermetricians generally try to answer questions like this by focusing on the player and his hits, walks, etc. and ignore what team he plays for and where he bats in the lineup. Stats like RBIs and runs depend on what other players do--unless you hit a home run someone needs to bat you in, and likewise you need someone on base to generate RBIs.

Traditionally this criticism is brushed aside as unimportant. The goal of asking "who is more valuable?" is to find our who is better and that question doesn't hinge on how good the other players are, does it?

But a home run isn't just a home run. The more people who are on base, the more runs you score when you hit a home run. Whether you play for a good offensive team or a bad one could have a big impact on how many runs a home run tends to be worth.

In fact, it DOES have a big impact on how valuable a player is by up to 40%. Replacing a replacement level hitter with Mike Trout would turn the Marlins' terrible offense (515 runs) into a merely bad one (584 runs predicted) for a gain of 69 runs. Doing the same trick for the Red Sox's potent offense could push a strong offense (853 runs) into the stratosphere (949 runs) for a gain of 96 runs.

96 runs is not "approximately" the same as 69 runs. It's important to take context into account when thinking about value.