On the Importance of Throwing Out Basestealers.

Big debate over in one of the Kendall threads regarding catcher defense metrics and whether they appropriately weight things or, indeed, are even worth a hoot.  It's primarily between WURoyal and NYRoyal, with some other contributions (most notably from AxDxMx).  WURoyal is concerned that we're just not paying enough attention to the importance of preventing runner advancement.

However, that thread has turned into the Narrow Column, and it's become unwieldy... and in the process of trying to respond to it, I realized that it was probably worth a post on its own, because it will either incite more debate, or will serve as a primer on the individual play impact of something a lot of people either seem to think can't be measured or don't measure correctly themselves.

(I should also note that I started working on this post a couple of days ago; since then, d_f has outlined his figurations, which take some of the following into account as well.  But I'm going with the post anyway.)

In short: there is a value to a catcher against whom baserunners are afraid to run, but it's not nearly as important as you might think.

WURoyal would be correct in saying that a catcher who allows 3 SB/0 CS in 100 games is "better" than one who allows 30 SB/20 CS in 100 games, if all one is interested in is discussing who's got a better arm or something.

However:

Catcher Two up there is responsible for erasing 20 baserunners.  That is not insignificant.  The value of inducing the baserunner into retiring himself exceeds the value of keeping him from advancing a base.

You can see this by comparing run expectancy.  (I'm using the old 2002 numbers, because I'm lazy, but the general point still remains.)

Runner thrown out at second reduces run expectancy by .656 if there's nobody out, and by .457 if there's one out, and by .251 (to zero, of course) if there are two out.

Meanwhile, runner stealing second increases run expectancy by .236 with nobody out, .152 with one out, and .093 with two out.  (Both sets of figures assume a lone baserunner, also.)

As you see, the retirement of the runner weighs more to the defense's benefit than the advancement of the runner benefits the offense.  This is another way of expressing an axiom which has been key to sabermetric discussion for almost three decades now: the stolen base is not as valuable as people think, and a basestealer needs to succeed over 70% of the time to be in the plus column.

As we go through this exercise, let's use the one-out numbers in lieu of an average, just for simplicity's sake.

Now, if we assume both catchers play the same number of defensive innings (so that comparing them is equal), and assume the normal 70% success rate for basestealers, the first catcher (1) increases his opponent's run expectancy of .456 due to the three allowed SB; (2) decreases his opponent's run expectancy not one bit due to the 0 CS; and (3) decreases his opponent's run expectancy by five runs as a result of the 33 bases they didn't steal on him because of the 47 times they were apparently too scared to run on the guy.  (47 * .7 = 33)  Net result, he's decreased the opponent's run expectancy by about 4.5 runs.  That's not bad; it's sorta worth half a win, and it takes into account the effect of runners fearing his arm.

Note that you have to do this last step for the catcher in question.  Otherwise, you're claiming that his actions or inaction regarding baserunners have cost his team half a run defensively, period.  He has not; he has only cost his team half a run by allowing three SB as part of the overall package.  The fact that nobody wants to run on him is, in fact, a relevant data point -- one which I think most people mistakenly view as "unmeasurable."  Of course it's measurable; it's measurable by "the number of times runners didn't try to steal," but I should note that it does need to be leavened with a league-wide rate of recalcitrance to have actual meaning.*

Catcher two (1) increases his opponent's run expectancy by 3.04 runs due to the 20 SB allowed; (2) decreases his opponent's run expectancy by 13.71 runs due to the 30 guys he caught; and (3) nothing, because for purposes of our example he didn't have anyone fail to run on him.*  Net result?  He's decreased the opponent's run expectancy by well over TEN runs.

If we turn this around and say the second catcher only threw out 40% of attempted basestealers, then he "only" saves his team about 4.7 runs.  Still a smidge better than the first guy.

There's a reason for this, which people who focus way too hard on the value of preventing the stolen base always, always, always forget.  I talked about it before getting into the statistics, and I worked it into the overall formula at one point (when crediting the first catcher for the guys who didn't run on him) because it was necessary to do so in order to be intellectually honest:

The league average overall SB success rate is relevant when comparing catchers. A catcher who throws out 40% of basestealers is better than average.  A guy who throws out 28% of runners is slightly worse than a guy who does so 35% of the time, but the difference is much smaller than "28-35" makes it look -- because it's actually the difference between "-2%" and "+5%".

In a nutshell, this is really the bottom line.  You can, in fact, measure a catcher's cost or benefit to his team due to his arm.  It's not rocket science.  (Similarly, you can measure the effect of his glove behind the plate, although there will be some noise due to the "distinction" between WP and PB, and perhaps some lack of data regarding "wild pitches prevented", which John Buck incidentally was very good at.)  In fact, the only thing we can't measure is "handling the pitching staff".

I have no idea whether some form of this exact calculation is part of current catcher defense metrics, although I'm certain that the end result works its way into the final analysis in a somewhat similar fashion.  But it's the best way I could think of to explain the importance of SB/CS from the defensive side of things to my own satisfaction, and thus perhaps get the point across to other folks.  There is probably a structural flaw on my part here, for which I won't begrudge anyone the need to correct -- but even at that, I'm sure everyone who works sabermetrically will acknowledge that the results are at least on the right track.

* - Naturally, for league purposes, one must figure out the league-wide attempted SB rate and factor it into this somehow to equalize the effect for all catchers.  (That is, our second catcher in the example may also be entitled to credit for additional runners who did not run against him, and some penalty for being run on "too often" may need to be applied for others.)  I was just comparing two guys here, so consider that a quick-and-dirty bypass.