If we were talking about any position but catcher, the answer would be, "Almost certainly nothing." The difference between an average defender at a position and a great defender is not enough to justify the gap between a good bat and a poor one. That is simply because the distribution of balls in play is not centered on any one position enough for the super-glove to make so many plays that he makes up for all the extra outs at the plate.
Following up on Tanya’s earlier post on Russell Martin, I wanted to respond to a reader comment, and I’m doing it up here because it’s a common enough expression that it’s worth digging into a bit. "Briceratops" says, "The Yankees can live without offense from one position."
This is often said, and by itself it might actually be true. However, the question is, "Why are you asking them to do so? What justifies doing without the offense?"
Derek Jeter has proved this every day for most of his career. Every other game a balls squirted past him into the outfield that an average glove would have picked up, but those were only singles and not all of them scored. Meanwhile, Jeter hit .330 and puts many more runs on the scoreboard than he allowed with his glove. Conversely, a player can strand more runs at the plate than he saves in the field.
Catcher is a little different because you have to consider pitcher comfort when evaluating his defense, as well as things like pitch-framing, which aren’t yet evaluated in defensive statistics. As Briceratops pointed out, citing an article published when I was E-i-C at BP, Martin has been shown to be quite valuable at framing pitches. What we don’t know is how consistent that ability is from year to year or if we’re really quantifying the impact perfectly.
More importantly, what we don’t know is the value of the hypothetical replacement and what his pitch-framing ability is. If Martin goes away and he is replaced by a catcher who is ten runs worse on defense but 20 runs better on offense, doesn’t the team come out ahead? Or is the impact on defense disproportionate to the literal run totals because the pitchers are affected?
I don’t know the answer to these questions, and I suspect that individual psychology may play into the results. The real point here is that normally when we talk about a club being able to afford to carry a bad bat because of some other perceived contribution, be it on defense or baserunning or clubhouse chemistry (he brings donuts before every day game), it’s just not true.
You can look at many a close race and find a team that lost by a game or two because they were willing to be complacent and accept a non-contribution from a regular based on a perception of value that was mostly illusory. All defense, no hitting = bad. All hitting, no defense = bad, but less bad than you would think because of the limited ability of a player to hurt a team at any one position. A combination = ideal.