Last week, St. Louis Cardinals catcher Yadier Molina completed the latest in a long line of preternaturally perceptive plays at the plate. As he’d done so often before, Molina evaluated his competition, drawing upon a deep familiarity with that player’s tendencies derived from hours of prior research. He ran through his options, searching for the choice that might make his opponent hungry enough to offer at something too low and too slow. And then, satisfied, he flashed a signal so subtle that no one at the ballpark knew he’d made a move. Obeying some synthesis of instincts and intellect known only to him and unfazed by the pressure of the pennant race, Molina made the call for … crackers.

[mlbvideo id=”34751609″ width=”500″ height=”280″ /]

In this instance, Molina wasn’t active: His magic right hand, responsible for flashing thousands of successful signs, was encased in a cast following an operation to repair a torn thumb ligament that could cost him the rest of the regular season — and St. Louis the NL Central crown. With the Cardinals relying on backup Tony Cruz and stopgap George Kottaras (who’s since lost his roster spot in favor of a more experienced stopgap, A.J. Pierzynski), Molina played a prank on his brother Jose, who was catching for the visiting Tampa Bay Rays.

Judging by Jose’s smile, Yadier’s instincts remain intact. And in this case, we can easily trace his thought process from idea to execution to see why crackers were the correct call. Usually, however, Molina’s motivations aren’t so transparent, which leaves us to wonder: What is his non-cracker game calling worth? And how much is not having it costing the Cardinals as they make do with Pierzynski and Cruz (who’s escaped from the list of the game’s least-played players) while Molina heals?

Before we can attempt to assess that, we first need to understand more about the defensive facets of catching. Thankfully, while the value of Molina’s game calling has heretofore remained mysterious, the value of the position he plays is becoming a lot less opaque. Aside from Bill James and Billy Beane, it’s catchers who have benefited the most from the sabermetric movement. Aided by advances in technology, analysts have uncovered catchers’ hidden contributions and, in the process, turned former backups into statistical rock stars. And it’s about time that backstops received a PR assist from the statheads, because they’ve long been the players most in need of rebranding.

Although leaguewide offense behind the plate has been unusually strong in recent seasons, catcher has historically been the home of baseball’s weakest bats. It’s a position where defense is prized, but individual plays rarely capture the attention of spectators or ESPN producers; catchers create the fewest Web Gems. Unlike shortstops, catchers lack both the opportunity and the physical ability to attempt the acrobatics that have made light-hitting Andrelton Simmons one of the majors’ most-watched players. Catchers aren’t kinetic. Catchers crouch.

Via the center-field feed, catchers are always on our screens, seeming to blend, along with the umpire, into the scenery surrounding the real drama of baseball’s central combat between batter and pitcher. Given their typically bad bats, their face-obscuring protective gear, and their ubiquity on broadcasts, catchers are easy to tune out unless you train yourself to observe them. That goes double for fans in the park: As Roger Angell wrote in his 1984 New Yorker essay on catchers, “In the Fire,” “Because he faces outward … and because all of our anticipation of the events to come (in this most anticipatory of sports) centers on the wide green-sward before us and on its swift, distant defenders, our awareness of the catcher is glancing and distracted; it is as if he were another spectator, bent low in order not to spoil our view.”

Angell, who called catchers “invisible,” also acknowledged that they do “more things and (except for the batter) more difficult things than anyone else on the field.” Many of those things, though, were impossible to quantify when Angell was writing this piece, and for decades after. At most of baseball’s defensive positions, the job boils down to snagging batted balls and converting them into outs. But that’s the least important part of the catcher’s qualifications, the item at the end of the job description that’s “preferred” but not required. The catcher makes most of his impact not with the occasional eye-catching, out-of-zone play, but by accumulating fractional runs on thousands of calls and catches. The batter-pitcher confrontation that holds TV viewers’ eyes isn’t really one-on-one, because the catcher is a combatant, too, eking out extra strikes and keeping batters off-balance.

Great catch-and-throw guy; works well with pitchers; quiet behind the plate: These are compliments that baseball men have paid to backstops (particularly the kind who can’t hit) since the dawn of the sport. Through repetition, they’ve become the kind of clichés that roll right off the ear. And in baseball’s big data era, it usually takes a statistic to cut through those clichés and attract our attention. Sure, he works well with pitchers … but what is that worth?

The position hasn’t surrendered its secrets easily. Early sabermetric efforts, such as Craig Wright’s Catcher ERA and Keith Woolner’s Run Prevention Rate, either failed to demonstrate convincingly that game calling (a blanket term for a catcher’s nebulous impact on pitcher performance) was a consistent skill or concluded that it wasn’t one. “Professionals within the game insist that catchers make a gigantic difference and that the question is simply beyond the capability of statistics to find,” Woolner, who’s now the director of baseball analytics for the Indians, wrote in the 2006 Baseball Prospectus book Baseball Between the Numbers. “However, the further we look into catcher performance, the fewer places the elusive realm of catcher influence has to hide.”

Even as Woolner was writing, Major League Baseball Advanced Media was preparing to install Sportvision’s PITCHf/x system in every big league ballpark. With the aid of that pitch-tracking technology, analysts soon annexed much of the remaining territory in which the catcher’s influence had lurked, eluding earlier researchers. Their most groundbreaking work concerned the impact of pitch framing (the ability to influence the umpire’s call by making pitches look more like strikes), but better data has also led to refinement in other areas. Leaderboards for framing and blocking, controlling the running game, and fielding batted balls are now only a few clicks away.

Defensive ratings for non-catchers still rely on human-recorded batted-ball trajectories, which aren’t nearly as precise as PITCHf/x. Worse, while we know approximately where fielders gloved batted balls, we don’t know how far they had to go to reach them, an important question made even more complicated by increasingly common defensive shifts. As a result, considerable uncertainty surrounds our evaluations of non-catcher defenders. Behind the plate, though, fewer dragons remain on the map. In just a few years, catcher defense has gone from largely impenetrable to arguably more transparent and more predictive over small samples than any other position. PITCHf/x has taught us an amazing amount about pitching, but it’s probably changed our minds more about catching.

Jose Molina has enjoyed the most dramatic makeover, morphing from career backup to starter on the strength of the discovery that his framing alone has been worth close to 40 runs per full season. Even so, at age 39, the light-hitting Jose is barely hanging on. Yadier, however, has attained superstardom by combining quality leather with elite offense, finishing fourth in 2012 and third in 2013 in NL MVP voting and collecting six consecutive Gold Gloves, two Platinum Gloves, and a Silver Slugger Award. He’s acquired a reputation as a defensive wizard during a time when our understanding of what catchers do on defense has grown by leaps and bounds.

And yet, much of Yadier’s defensive reputation stems from a secret sauce. Like Jose, he excels at controlling the running game, racking up 6.5 Stolen Base Runs Saved per 150 games, according to Baseball Info Solutions. He’s an above-average blocker, too, and a good framer, but he’s not the receiving savant that Jose has been. Yadier’s signature value behind the plate comes from game calling, the one major component of catcher defense that has remained largely unexplored.

This spring, the New York Times’s Tyler Kepner spoke to Yadier Molina and many Molina admirers for a profile of the Cardinals catcher that was as convincing in its vision as it was frustrating in its lack of specifics. Kepner passed on praise from other players for Molina’s “impeccable pitch selection” and quasi-psychic ability to anticipate the thoughts of teammates and opponents alike, but the article included only one in-game example of a time when Molina had put those powers into practice. “The factors behind Molina’s pitch selection usually, and understandably, remain a mystery,” Kepner wrote. “Molina … would gain nothing by explaining his hundreds of decisions each game.”

To evaluate those decisions without Molina’s help, we’d have to be similarly psychic. As Kepner explained, Molina is a “master at improvisation based on clues he reads from his pitchers and opposing hitters.” Most of those clues, of course, don’t show up in the proverbial box score, so we have no way of knowing what Molina was thinking when he flashed the sign for any particular pitch. In light of the obstacles, it seems reasonable to reach the same conclusion Kepner did: “Only [Molina] has the answer key.”

We’re not completely stymied, however. Even though our instruments can’t detect game-calling ability directly, we can calculate it the same way that astronomers assess the magnitude of dark matter: by measuring its effect on other things. If we know the overall impact a catcher has on his pitchers, and we’ve accounted for everything he does that we can calculate, the rest is merely arithmetic. Whatever isn’t explained by framing, blocking, throwing, and fielding must be the inscrutable skill we seek.

The initial, overall number we need comes from comparing each pitcher’s performance with a given catcher to his performance with every other catcher, using a method that Tom Tango, coauthor of The Book: Playing the Percentages in Baseball and current consultant to the Cubs, dubbed “With or Without You” (or “WOWY”). Over a sufficiently large sample, most pitchers will be caught by a league-average cross section of catchers, so if a given pitcher’s performance improves when he’s working with a certain catcher, it’s a clue about that catcher’s value on defense. If the catcher makes all (or most) of his batterymates better, then it’s safe to say he’s good with the glove. Subtract his framing, blocking, throwing, and fielding skills from his overall impact, and we’ve solved for the unknown component: game calling.

Mitchel Lichtman, another coauthor of The Book and a former professional sports bettor and consultant to the Cardinals, performed the WOWY analysis and sent me the following standard deviations, which represent the spread in skill in each component of catcher defense. The higher the number, the greater the variation in skill among major league catchers.

Framing: 8.2 runs saved per 150 games

Game calling: 5.2 runs

Blocking: 1.44 runs

Throwing: 1.4 runs

Fielding: .42 runs

The standard deviation of fielding skill is small, which makes sense: Because catchers receive so few opportunities to field batted balls relative to players at other positions, and because most catchers aren’t especially mobile — say someone has a “catcher’s body” and everyone will know what you mean — there isn’t much separation between the best- and worst-fielding catchers over the course of a season. Framing, however, has a large standard deviation, which is also intuitive: Catchers have thousands of opportunities to turn borderline balls into strikes, and we know that some are notably better at doing so than others.

Game calling slots in below framing but above everything else, which suggests there’s a fairly wide variation in catchers’ game-calling skill. It’s important to note that in this case, “game calling” encompasses everything we don’t know how to quantify about catchers: the ability to soothe a pitcher’s psyche, to know when to make a mound visit, to spot mechanical problems and recommend fixes, or even to position other defenders, another area in which Molina reportedly excels. That 5.2-run standard deviation is almost certainly baking in factors beyond the basic decisions about how many fingers to put down and where to set up relative to the strike zone.

Still, this framework allows us to answer the key question posed earlier in the piece: What does losing Molina’s game calling cost the Cardinals? Lichtman estimates Molina’s game-calling talent at 8.6 runs per 150 games, which tells us that Molina is 1.7 standard deviations from the mean. If game-calling skill is normally distributed (i.e., described by a bell curve), being 1.7 standard deviations above the mean would put Molina in the top 5 percent of catchers. The stats support the popular perception.

Lichtman, adhering to the sabermetrician’s credo, notes that “the certainty of that estimate could be quite low,” but it gives us some sense of what Molina’s defensive (game-)calling card is worth: close to a win, and several million dollars on the free-agent market. Unfortunately, it tells us nothing about how Molina arrives at those 8.6 runs. We don’t know what he’s doing to distinguish himself.

Despite how much information we’re missing, we shouldn’t discount what we do have: a complete record of the type, location, and result of every pitch Molina has called over the past six-plus seasons (2008-14, the PITCHf/x era). With that depth of knowledge about his results, we should be able to infer something about his process. We’re a long way from explaining Molina’s game-calling skill, but we should be able to take some small steps toward describing it, chipping away at the margins of the mystery.

In some ways, Molina’s is an especially difficult case to study: The Cardinals have produced an unusual number of homegrown pitchers over the past several seasons, and Molina, when healthy, rarely takes days off, which means some St. Louis arms have small “without Molina” samples. On the plus side, we know (courtesy of Kepner) that Molina “calls every pitch on his own” and is rarely refused by his pitchers, so we can assume that each pitch is an extension of his will. And despite the composition of St. Louis’s staff, a six-plus-season sample of complete PITCHf/x data gives us more than enough material to work with in our WOWY: more than 115,000 pitches with Molina, and more than 175,000 deliveries from the same 80 pitchers to different catchers over that span. Here’s what the surface stats say:

Sample ERA K% BB% HR% BABIP With Molina 3.55 18.4 7.3 2.1 .302 Without Molina 4.30 18.0 8.8 2.7 .306

That looks like a huge “with Molina” effect, but it’s somewhat overstated: These stats (unlike Litchman’s) aren’t corrected for park, league, or team defense, and both the National League and Busch Stadium tend to depress scoring. To account for that, from here on out we’ll restrict our study to pitch-level stats rather than at-bat results.

As a first pass at cracking the game-calling code, we’re going to ask and answer 10 questions about the way Molina works. No one answer will give us the complete picture, but each will help us place a small part of the puzzle, rule out an explanation, or prompt ideas for further research. Call it the Socratic approach to game calling. All data comes from Brooks Baseball and Baseball Prospectus, with PITCHf/x pitch-type classifications provided by Harry Pavlidis of Pitch Info and research assistance by BP’s Rob McQuown.

1. Do pitchers work more quickly when they’re throwing to Yadi?

Despite the popular broadcaster bit about keeping fielders on their toes, working quickly isn’t necessarily a recipe for better defense. However, it could be a sign of greater comfort or confidence in a catcher, and the data does show that pitchers take about 1.3 seconds less between pitches when working with Yadi, excluding pickoff attempts, gaps of longer than 60 seconds (which are often mound visits or other stoppages in play), and at-bat-ending pitches.

Sample Pace With Molina 19.4 seconds Without Molina 20.7 seconds

Pitchers tend to slow down with runners on base and in scoring position, so it’s possible that what we’re seeing here is really another factor at work: Fewer runners reach base with Molina in action, so his pitchers throw a higher percentage of their pitches with no one on. Even if we look only at situations with runners on and/or in scoring position, though, some of the difference persists:

Sample Pace w/Runners On Pace w/RISP With Molina 23.7 seconds 23.6 seconds Without Molina 24.2 seconds 24.4 seconds

The verdict: Molina makes games move slightly faster.

2. Do coaches and managers make fewer mound visits when Yadi is catching?

Among the many Molina qualities that Cardinals manager Mike Matheny has praised is “the ability to be an extra coach out there.” In 2012, Matheny told Derrick Goold that he “often relies on Molina’s read on the pitchers,” which would seem to suggest less need for in-game intervention. We don’t know how often Molina makes solo mound visits, but we do know how often coaches and managers make the journey to the mound, and we’d expect to see fewer visits with Molina than we do without him. Here are the respective rates per 100 pitches, excluding visits that led to a pitching change:

Sample Mound Visits Per 100 Pitches With Molina 1.0 Without Molina 2.0

We’re not controlling for each coaching staff’s overall visit rate, but it’s still suggestive that coaches and managers feel compelled to talk to their pitchers personally half as often with Molina in the game. Like the faster average pitcher pace, a lower official mound visit rate is an effect of Molina’s acumen, not a cause, but it helps us corroborate all the quotes about comfort.

3. What is Yadi’s impact on overall pitch-type distribution?

Let’s take a look at the overall percentages of pitch types thrown by our pitcher cohort when caught and not caught by Molina:

With Molina, pitchers throw significantly fewer four-seamers (FA%) and more sinkers (SI%). They also throw more curveballs and fewer sliders. But can we be confident the difference is entirely attributable to Molina? Because the With Molina/Without Molina samples largely break down along Cardinal/non-Cardinal lines, there are two confounding factors we have to consider: former St. Louis pitching coach Dave Duncan and current pitching coach Derek Lilliquist, both of whom have preached throwing sinkers and aiming low in the zone to get ground balls. So, what does the graph look like if we compare Molina only to other Cardinals catchers (a sample of just more than 35,000 pitches)?

We still see a slight preference for sinkers over four-seamers and curveballs over sliders, but it’s much less pronounced. Clearly, much of the difference is a Cardinals-specific philosophy, not a Molina-specific philosophy. On the other hand, Molina seems to be more consistent in implementing the team’s chosen approach than his backups have been (although Cruz has done his best to become a Yadi clone). The impact of the pitching coach further complicates our attempt to understand Molina’s skill; if Duncan and Lilliquist are the architects of the St. Louis pitching approach, how much game-calling credit should they receive? Regardless, Molina deserves accolades for following their blueprint to perfection, but a plan with clear parameters — Keep the ball down, try to get grounders — would have a better chance of working even in Molina’s absence. Instincts, on the other hand, are nontransferable.

4. What about by count?

The two graphs in this GIF show the percentage change from overall pitch usage rates, with and without Molina, in a number of key counts, as well as combined counts when the pitcher had two strikes or was ahead or behind. “Fastballs” are four-seamers, sinkers, and cutters grouped together; “breaking balls” are combined curveballs, sliders, slow curves, and knuckleballs.

The takeaway here is that Molina is slightly more willing than most catchers to deviate from the “average” pitch distribution depending on the count. Molina reduces his fastball rate by more than 20 percent on 0-2 counts, but the other catchers aren’t quite so willing to “waste” a pitch. Consequently, the bars on the “Without Molina” graph are a bit more compressed.

5. Is Yadi more or less likely to call for repeat pitches?

One of the keys to pitch sequencing is avoiding predictability. However, a reluctance to throw back-to-back pitches of the same type would be just as predictable as a fondness for going back to the well, so it might be useful for a hitter to know whether a catcher has any clear preference. If Molina calls for one breaking ball, how likely is it that the following pitch will also be a breaking ball? And how likely is he to double down on the heat?

Sample If BB, % That Next Pitch Is BB If FB, % That Next Pitch Is FB With Molina 26.8 52.9 Without Molina 28.2 51.8

No difference to see here; move along.

6. Does Molina call for inside pitches more often?

Or, for that matter, more pitches over the middle or over the outside corner/off the outside edge?

Sample Inside% Middle% Outside% With Molina 28.3 21.1 50.6 Without Molina 28.1 21.5 50.5

Pitchers have thrown slightly more pitches over the middle without Molina, which could just barely be significant. However, we’re not controlling for count, so it’s possible that pitchers throwing to Molina are more likely to be in counts that make pitches over the middle scarcer.

7. Does Yadi tailor his pitch selection to batters’ pitch-type preference?

Kepner noted that “Molina often arrives six hours before a game to prepare.” Presumably, he doesn’t use all of that time to listen to “Eye of the Tiger.” Some of it must be devoted to studying batter tendencies so he can tailor his game-calling approach accordingly. So, does Molina call for fewer breaking balls (sliders, curveballs, slow curves, and knuckleballs) against good breaking ball hitters (defined as hitters with better results against breaking balls than against fastballs, by pitch type linear weights)?

Sample BB% Overall BB% to Good BB Hitters Change With Molina 20.5 19.2 -6.3% Without Molina 23.5 21.7 -7.7%

He does, but non-Molina catchers do so more. What about fastballs (four-seamers, sinkers, and cutters) to good fastball hitters?

Sample FB% Overall FB% to Good FB Hitters Change With Molina 69.3 67.1 -3.2% Without Molina 67.0 62.5 -6.7%

Again, the non-Molina catchers adjust their approach based on batter pitch-type preference more than Molina. If anything, Molina might be more interested in making the most of his pitchers’ strengths than in attempting to exploit his opponents’ weakness.

8. Does Yadi tailor his pitch selection to batters’ pitch height preference?

Just as we saw in the previous question, Molina does adjust his calls to stay away from batter strengths, but only slightly.

Sample High Pitch % Overall High Pitch % to Good High-Pitch Hitters Change With Molina 23.2 22.7 -2.2% Without Molina 27.8 26.3 -5.4%

Sample Low Pitch % Overall Low Pitch % to Good Low-Pitch Hitters Change With Molina 52.8 51.1 -3.2% Without Molina 47.7 45.0 -5.7%

Molina calls for fewer high pitches and more low pitches overall than his catching counterparts (not a surprise, in light of those sinkers), but he’s less likely to alter his approach to avoid his opponents’ preferred pitch location.

9. What is Yadi’s impact on plate discipline stats?

This time we’ll compare the percentage of pitches in Brooks Baseball’s rulebook strike zone (which is smaller than the one that’s typically called), the percentage of pitches that resulted in swings (overall, inside the zone, and outside the zone), and the percentage of swings that resulted in contact (also overall, inside the zone, and outside the zone).

There’s next to no difference, aside from a slight uptick in contact rate with Molina catching, probably because of the extra sinkers.

10. Are pitchers more likely to throw low breaking balls with a runner on third when Yadi is catching?

Earlier this year, Jeff Sullivan discovered that pitchers tend to throw slightly more low breaking balls with a runner on third than they do in other situations, presumably because the desire for a strikeout outweighs the risk of a run-scoring wild pitch or passed ball. He did find some anecdotal evidence that good blockers are more likely to test themselves (or that pitchers are more likely to trust those catchers) by risking a ball to the backstop, but it was a weak connection. Does it hold true for Molina?

Sample Low BB% Overall Low BB% With Runner on Third Change With Molina 8.7 11.7 +34.4% Without Molina 8.9 10.8 +20.4%

In most situations, Molina’s presence has no effect on the percentage of low breaking balls seen, relative to other catchers. With a runner on third, though, pitchers up the percentage more with Molina behind the plate than they do without him, a possible endorsement of his blocking abilities (or, since Molina mostly calls the shots, a sign of self-confidence).

So, what have we learned? Molina’s presence behind the plate makes games move slightly faster and cuts down on mound visits. He’s a devoted follower of the Duncan-Lilliquist sinker-first philosophy, and although he doesn’t skimp on advance scouting, he doesn’t go out of his way to target the soft underbellies of batters who excel against certain pitch types and in particular locations. He’s also somewhat more malleable depending on the count. These are nuggets, not epiphanies. “It’s almost a sixth sense for [Molina], pitch to pitch, the feel of what this guy’s adjustments are, what he’s looking for, what to throw with runners on base,” Lilliquist told Jonah Keri in May. As Kepner covered, it’s difficult to decipher the way a sixth sense works, but we can still come close to quantifying its effect.

Angell described the catcher’s game-calling routine as “the most familiar and the least noticed gestures in the myriad patterns of baseball.” Those movements are about to be noticed more often. “Someday, we will probably be able to figure out what constitutes good game-calling, based on batter, score, inning, runners, etc. and more accurately quantify game-calling,” Lichtman wrote in an email. “Right now, we don’t have the requisite knowledge and models to do that.” However, we do know enough to say that missing Molina’s game-calling skill makes the Cardinals’ climb noticeably steeper.