Alex Avila can't hit right now. He could not produce a hit if he had the fanbase, voice and looks of Justin Bieber. He truly and honestly is hitting like a pitcher.
Player A: .130/.259/.130, 50% K rate
Player B: .222/.300/.278, 25.0% K rate
Obviously player one is Avila. You will be surprised to learn that player 2 is actually all of Detroit's pitchers in 2013. Both are extremely small samples, but they emphasize the point that needs to be made- Avila is not hitting the ball.
Does this mean that Alex is a liability to the team? Offensively, heck yeah. A wRC+ lower than the drinking age is going to cause some winces when he step up with two on and two out. This doesn't mean that Avila should be sitting, however,
A rough statistic I'm going to use in this is catcher ERA. This is a very imperfect statistic, given that certain catchers catch certain pitchers. Unfortunately, not all of us can be GWilson. For what it's worth, I believe Avila caught Verlander and Porcello most often last year, while Pena tended to get reps with Sanchez.
Avila caught 837 innings last year over 96 starts. Pena, on the other hand, started 55 games and caught 520 innings. Avila sported a sparkling catcher ERA of 3.40, while Pena's was a still very good 3.77. A lot of this can be attributed to pitch-framing and calling good games. Verlander reportedly has chemistry with Alex in terms of calling a game, something that can not be taken lightly after watching Verlander repeatedly fail to put away hitters against the Orioles with Holaday behind the dish (3 Ks in 8 IP).
Let's take this a little further and see how many runs over a season those statistics indicate him saving. Avila's ERA when extrapolated to 900 innings ( a little over 100 starts, which seems reasonable given his averages) produces 340 runs for the opposition. Pena's ( as a pretty bad game-caller he's probably not the best option, but unfortunately the only data size significant enough to matter from last year) produces 377 runs. Avila saved 37 runs per 100 games over his compadre, or almost four wins for the team.
I went ahead and did this excercise once more, this time using Avila and Laird in 2012. Avila came in at 3.61 (looking at you on that one, Drew Smyly), while Laird's catcher ERA was 4.09. Again, both samples are over 50 games, so there's probably some correlation here. Prorating these statistics to 100 games gives Avila 48 runs saved over an established, veteran signal caller. That probably won the division.
Is it possible that Dombrowski has found a market inefficiency with Avila and is exploiting his arb years for all of the surplus value he can? In a word, yes. However, it is important to take this analysis with a grain of salt, since it is quite possible that the backups have just caught worse pitchers over the past few years.
However, 85 runs in 2 years? That's something worth keeping around. It just might make that next leadoff strikeout a bit easier to bear.