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So how can we quantify a catcher's throwing arm using this data?  I've always quantified stolen base contributions by using Stolen Base Runs, which turn a player's stolen bases and stolen base percentage into a counting stat using what Pete Palmer calculated as the all-time necessary break even point for a stolen base success rate to translate into positive runs: 63.5%.  The formula is:

SBR = .3 * SB - .52 * CS

So it's real easy to translate this into Caught Stealing Runs for a catcher:

CSR = .52 * CS - .3 * SB

Basically then, if a catcher has a caught stealing rate of over 36.5%, he will have prevented runs for his team, whereas below 36.5% will give him a negative value.  Using this all-time mark of 36.5% is imperfect; the mark during Piazza's era as catcher was more like 33.3%, a significant difference.  For the moment, let's use the universal formula, and hope that it balances out with Bench being shafted from many caught stealings because base runners refused to run on his famous cannon.

CSR for selected catchers:

*Lavender denotes incomplete data 

Wow.  Here's a scary way to look at it: Piazza allowed only six fewer stolen bases than Rickey Henderson had in his career, and Rickey is the only player known to have more positive Stolen Base Runs than Mike Piazza has negative Caught Stealing Runs.  Head-and-shoulders above other catchers as Piazza is offensively, he is also feet-and-legs below them in terms of gunning down base runners.  Most catchers with arms as weak as Piazza's are either backups with few at bats or are quickly moved to another position, like Mike Stanley and Mickey Tettleton were.  As an aside, why wasn't Joe Torre kept behind the dish?  And is Derek Jeter the only Yankee who needs to find a new position ASAP?

So let's add up batting runs, stolen base runs, and caught stealing runs for some of our top catchers and observe how they line up:

* 64.3% of Yogi's games at catcher were played prior to SB/CS data availability.  Extrapolating his 27.8 CSR across his career, we arrive at 77.9 estimated CSR.  However, it's also worth noting that Yogi's defense early in his career was considered sub par.  His actual total is probably noticeably shy of 77.9. 

**Double play percentage is estimated assuming that every one in five plate appearances presents a hitter with a double play opportunity.  Since none of these catchers were leadoff hitters, that estimate is probably very close to reality.

Where should Piazza rank relative to Johnny Bench?  Quite a bit lower, I'm afraid. Also, unless Mickey Cochrane had -34 CSR in his career, he would rank higher than Piazza.  Hartnett would need -25 and Dickey would need -27.  It is unlikely that any of these three catchers had negative CSR totals, as they each averaged way more assists per game than Bench, Berra, and I-Rod (though it's worth noting that those totals were inflated by the prevalence of the sac bunt).   

Now, if we use a modern formula for Rodriguez and Piazza (.6 * CS - .3 * SB for a break-even point of 33.3%), we get "only" a -166.2 CSR mark for Piazza (for a total of 250.5) but an even higher mark of 157.2 for Rodriguez (total: 270.1).  So although that would close the gap between Piazza and our quintet of older catchers, he would still trail I-Rod no matter where we et the modern break-even point at. 

Additionally, Piazza has a worse double play rate than all of these catchers (except Rodriguez, and possibly Cochrane, for whom we have no data).  He has fewer assists per game than all of these catchers except Posada.  His fielding percentage is one point below the league average, whereas all of these other catchers are above (as high as +5 for Cochrane and +6 for Dickey and Hartnett).  Piazza's passed ball rate, which you would expect to be better than those of catchers who played with inferior equipment, is still worse than what Cochrane, Bench, Campanella, Dickey, and Berra put up, among others.

Where does Piazza rank among the all-time great catchers?  Much lower than Scott and I have him, for sure, and probably even lower than Asher, Tony, and Richard do.  But kudos to Rich for his ranking of Ivan Rodriguez, recognizing that for a position like catcher, defense really can be nearly as important as offense.