It is, I suppose, consensus that Eli Whiteside is not merely not a good hitter, but is in fact a bad hitter. His major-league career numbers, sparse as they are, are such as rarely--very rarely--ever allow a man to continue at the major-league level; nor do his minor-league stats suggest that this is a SSS phenomenon. So is it folly to even carry Whiteside on the roster, much less play him frequently?
As the topic title suggests, defense is a consideration. Over 20 years ago, the redoubtable Craig Wright, in The Diamond Appraised, discussed at length, and made a strong case for, the importance of "CERA", Catcher's ERA (which, as he noted, had long been used in Japan, where managers often change the catcher instead of the pitcher when there's a problem). Since then, some have agreed and some (notably Keith Woolner) have disagreed. The reason analysts can differ so much on a numerical metric is that it is very hard to make decent measures of it--the problem being, of course, the ever-bothersome SSS issue. On almost every team that's ever been, there is one catcher who gets the great majority of the playing time, so the data for whoever is #2 is awfully weak.
Another of the problems with CERA is that it is discussed by a lot of people who don't understand what it is, or at least what it should be. It is not simply the ERA compiled while that man is catching. It has to be the effective ERA when normalized for all the different pitchers caught. That is, if Catcher X catches 200 innings of pitcher A and 100 innings of pitcher B, we need to halve Pitcher A's numbers with him (or double Pitcher B's), else we are measuring how good the pitchers were, not how good the catcher was. Moreover, CERA is meaningless except if we are comparing two catchers who have caught mostly or wholly the same pitchers for long enough to have meaningful numbers all round. A lot of people calculate what they call CERAs without normalizing for innings caught. (The ESPN stat listing, for example, doesn't, nor, I am told, does The Bill James Handbook.)
There's a decent article on the subject here. That article is miles and miles away from anything definitive, but it at least suggests that CERA differences for above-average catchers can range from as litle as .05 to as much as .50 of a run on the ERA. That at least gives us a broad working framework of plausibility in which to examine the extent to which defense might make up for a lack of offense. To proceed, we need, besides some estimate of the CERA difference, some estimate of offensive contributions. There are numerous runs-created-type formulae; not surprisingly, my favorite is my own, the "TOP" (Total Offensive Productivity"), which is handy because, among other things, it is presented as a number of seasonal runs: it is, in effect, what would be scored in one season by a team whose offense was nine exact clones of the man in question.
Regrettably, one cannot simply average TOPs for individual players (even weighted for playing time) to get a team TOP, because the TOP is a multiplicative product of two elements, which are (as is the case with all such formulae save linear-weights types) essentially an on-base factor and a runner-advance factor, and the average of products is not in general equal to the product of averages.
Sidebar example: in the first two lines below, the average of the C factors is 8; but line 3, which uses the average A value and the average B value, gives 9.
A x B = C
2 x 4 = 8
4 x 2 = 8
3 x 3 = 9
Nonetheless, we can get a broad-brush idea of differences in team results from changing those for one slot in the lineup. In the real world, the worst batters with an everyday job will have TOPs in the 600 range, or very, very occasionally the upper 500s (these are typically shortstops and catchers); the best, in the Pujols range, will have perhaps 1500 or so, though that is only a tiny number of outliers--1200s and 1100s are pretty good numbers. Eli Whiteside's career-to-date number is 553, awful; BM's is 669, pretty punk. By comparison, Joe Mauer's is 1122. (Utterly meaningless but amusing sidebar: right now, as I type, Mauer's 2010 TOP is 1172 and Whiteside's is 1207.)
Let's take, then, not the difference between Whiteside and BM, but between Whiteside and a rather good offensive-value catcher, to whom we will assign a TOP of 953, exactly 400 higher than Whiteside's career number (Brian McCann's career TOP is 930, so that's a sort of mental bookmark). A given man will, in the best of cases, get maybe 10% of his team's plate appearances. So, in very broad-brush terms, playing an Eli Whiteside every day as opposed to a Brian McCann-type catcher would cost about 10% of the 400-run difference, or 40 runs. Now 40 runs a season is a really big differential: at the usual 10-runs-a-game value, it means 4 more wins or losses, just from changing one man.
But now let's look at CERA. The plausible range of differentials, we saw, seems to be maybe .05 to .50. Let's hypothesize that Whiteside would have a CERA differential of 0.25 of a run, not minor but by no means stretching, or even approaching, the bounds of plausible (we will assume this differential to be over an "average" catcher). If one lowers a staff ERA by 0.25 of a run, that's roughly 40 runs over a season.
My, how interesting: a reasonable, perhaps even modest favorable CERA differential is worth the offensive difference between Eli Whitside and Brian McCann or another like him. I would call that big news. If we compare Whiteside to BM himself, the TOP difference is only 116, or about 12 seasonal runs; to make up 12 offensive runs lost by a better CERA, Whiteside's differential only needs to be about 0.08 of a run over Molina's.
Granted the hard data is fragmentary and SSS, but let's see what there is. I can't testify to the accuracy, but in a post to the Mercury-News board dated 22 April of this year, one person gave the following numbers (attributed to Baseball Reference):
Zito........... 4.79...........3.18............. -1.61
Is that proof? Of course not: nothing like it. Is that suggestive? You bet yer bippie. (An unadjusted CERA comparison, up to date for 2010, shows Molina at 3.16 and Whiteside at 2.76, a differential of -0.40; also not remotely probative but also assuredly suggestive.)
So the bottom line is that there is a credible--nay, strong--case to be made that despite Whiteside's miserable bat, he would actually a strong net gain for the team as the everyday catcher (especially over BM). If that sounds bizarre, go hunt up a copy of The Diamond Appraised and read Craig Wright's love song to Doug ("Eyechart") Gwosdz--whose name, I am pleased to say, I spelt aright on the first try.