PITTSBURGH — To begin this post, I would like to remind the audience of a series of fortunate events detailed back in February, a timeline of transactions that appears to be quite consequential as related to the surprise Diamondbacks and their resurgent ace Zack Greinke.

On Dec. 2, new Diamondbacks general manager Mike Hazen announced the hiring of Mike Fitzgerald to lead the club’s analytics department, which was to take more prominent and influential place in the organization. It was Fitzgerald who was a primary table-pounder for free-agent-to-be Russell Martin and his presentation skills in the summer of 2012, when Fitzgerald was the No. 2 analytics official in Pittsburgh.

On Dec. 2, the Diamondbacks non-tendered Welington Castillo, the starting catcher who was most responsible for the Diamondbacks’ placing 26th in majors by framing runs saved last season. Castillo ranked 95th in framing runs saved last season, according to Baseball Prospectus.

And on Dec. 2, the Diamondbacks signed Jeff Mathis, the top-rated receiver available on the open market, to a two-year deal. In a part-time role with Miami, Mathis ranked 13th in framing runs last season. To date this season, he ranks eighth.

Dec. 2 was a busy day for the Diamondbacks, and some suspected it might also be an important day for Greinke, from whom the Diamondbacks needed a better season in 2017 to contend in the NL West and to justify his record contract.

Seven months later, Greinke is in the midst of a significant bounce-back season and by some measures — including strikeout rate, K-BB%, and swinging-strike rate — he’s never been more dominant.

There’s something of a trend developing. Last year, when Greinke was paired with one of the game’s poorest framers (combined with a suspect defense behind him), he endured one of his worst seasons of his career. In 2015, when Geinke was most often paired with an elite framer — Yasmani Grandal, who caught 26 of Greinke’s starts — he nearly won the NL Cy Young. In 2014, Greinke was paired with lesser receivers in A.J. Ellis and Drew Butera. He was still excellent but not as good as his career-best 2015 level.

Paired again with a well above-average receiver in 2017, Greinke is Greinke again.

Consider a series of pitches from last year that all crossed the plate in the PITCHf/x strike zone but were called balls nonetheless…

Here’s a slider that Castillo couldn’t stick:

There was this elevated fastball that took Castillo’s glove further out of the zone, giving the pitch an appearance of being higher than it was:

Here’s another pitch in the strike zone that Castillo failed to present cleanly. It resulted in a walk. Greinke really wanted it, as one can tell from his demonstrative hop on the mound:

Then consider Greinke’s better fortune in 2017, when Mathis has received all 12 of his starts…

This is a ball called as a strike:

And here’s another ball called as a strike:

Greinke is getting out-of-zone pitches called as strikes at a rate that’s 3 percentage points higher than last season. Greinke is getting more borderline pitches and is more often ahead in counts. But to how much of Greinke’s turnaround can we credit simply being paired with an elite framer?

I was curious how much Greinke thought we should credit Mathis, and I was curious what — beyond framing — Mathis might be doing to help the Diamondbacks staff. So I approached one of the game’s most cerebral and talented pitchers in the PNC Park visiting clubhouse last week with my questions.

Greinke praised Mathis for framing well, but he had doubts on the overall effect of his performance.

“I read an article [in the offseason] about how much better I was going to be because of Mathis,” Greinke said. “’If he steals 5% [more] strikes, he’s going to get ahead 5% more often…’ But in reality, that’s not really true. I had first-pitch strikes at 70% last year.”

Close. It was actually 67.8%, but it was a career high. This season, his first-pitch strike rate rests at 64.2%. (Curiously, opponents slashed .349/.344/.556 last season against 0-1 pitches from Greinke. This season, the line is .379/.367/.517.)

But overall, Greinke is ahead in the count on 32.2% of his offerings, the highest of the four years considered here. His out-of-zone swing percentage leads baseball, and he’s already induced 246 swings on pitches out of the strike zone, compared to 485 last season.

Greinke also has a career-low zone percentage (39.0%). Is that tied to having a better framer behind the plate, allowing him more confidence to nibble on the edges of the strike zone, knowing he stands a greater chance of getting the call?

Does a Mathis, did a Grandal, give Greinke more confidence? Greinke is aware of catchers’ framing numbers.

“If I’m commanding really good and I have someone who can really stick the ball, if I get two strikes on a guy, or I am feeling really good and I can really locate a pitch, then I might try occasionally to hit the perfect spot,” Greinke said. “But it’s only when I’m feeling really good, and I probably have a couple pitches to work with. Like, say it’s 0-1 or 1-2 and I try to locate. Instead of saying ‘OK, I am going to try and locate a fastball away and try to freeze him,’ I might say ‘I want to locate this ball at the bottom of the knees and on the outside corner where it might be a ball, but he’s so good [at receiving], he might get that call for me…’ It might work only once every 10 tries, but when a guy is good I will try it sometimes. But it’s still very rare that you change the game plan based upon who is [catching].”

Greinke did theorize about another possible benefit of framing that he didn’t think was quantified, and that is the influence of a catcher’s receiving reputation to compel batters to more often expand their zones, particularly with two strikes.

“When Grandal catches, yes, he’s stealing strikes, but he is also getting people swinging at more pitches,” Greinke said. “It might be tough [to measure] because guys might be ahead in the count a little more often [with a quality framer]. But it’s almost like when I’m pitching and the umpire doesn’t call a strike a strike, ‘Crap. I have to throw it more on the plate.’ If a hitter took a pitch and thinks it’s a ball but it’s called a strike, ‘Crap, now I have to chase that even further.’ It almost gets into the hitter’s or pitcher’s mind.”

Greinke believes that this is a phenomenon of framing but adds, “I don’t know if you can technically prove it.”

I took a look at his idea and did not find any overwhelming evidence in a search of Savant data.

According to detailed strike-zone data at Baseball Savant, of the pitches in the 50-50 hinterland, that gray area on the edge of the strike zone, batters swung at 57.2% of Greinke pitchers there last year, compared to a 56.6% rate in 2015 and a 56.4% rate this season.

We expect batters to be most anxious about framing skills when hitting with two strikes.

Overall this season, 37,769 pitches have been thrown out of the strike zone with two strikes. Of those, 14,657 have been swung at with two strikes (38.8%).

When Mathis is catching, it’s a 39.2% rate (264 swings on 673 pitches). Castillo’s rate, in Baltimore, is 37.5% (255/679).

But last season, when Castillo was catching, batters swung at out-of-zone pitches 41.5% of the time (1,065 swings vs. 2,561 two-strike pitches). In 2015, when Grandal caught Greinke, they combined for a 42.6% rate (962 swings vs. 2,258 pitches).

Are batters generally more aggressive?

Overall, MLB batters have a 45.01% swing rate this season. When Grandal is catching, batters swing at a 47.78% rate. When Mathis is catching, batters swing at a 46.11% rate. Castillo? 44.99%.

This brief study does not include the quality of a collective staff’s stuff or pitch type, or control for umpire bias. But it appears the much more important influence is the ability to keep strikes called as strikes and have balls on the edge of the zone called as strikes. And Greinke is benefiting from that this season.

Unlike when the Pirates signed Russell Martin largely due to his framing in 2012, framing metrics now are more available publicly and more widely understood and accepted. Martin wasn’t sure why the Pirates were so interested him after he hit .220 in New York. Mathis knew why the Diamondbacks were so interested in him in despite being a .196 hitter.

“That’s something I’ve done my whole life, try to make pitches look good,” Mathis said of framing. “I think it gives all pitchers confidence. We’re trying to stick pitches on the corner and make them look the best they can.”

Greinke said he has more confidence to pitch, say, inside to a left-handed hitter when he knows he has Grandal or Mathis behind the plate.

And while many of a catcher’s skills from blocking to throwing to receiving have been quantified, it’s possible that some of their more important attributes, like game preparation, like pitch-calling, like confidence-building are not able to be measured. Mathis has played a role in Greinke’s career-high slider usage, which is another considerable factor. Diamondbacks pitching coach Mike Butcher raves about Mathis’ game-calling, ability to read swings and preparation.

“I try to get on the same wavelength, stuff wise, knowing what they like to do, what they don’t like to do,” Mathis said. “The preparation side is what helps you build trust and confidence.”

Mathis has caught all 12 of Greinke’s starts this season. It appears as though he has gained his trust and done nothing to hurt his confidence level. And there are the quantifiable facts that he’s getting Greinke more calls at the corners, more often getting him ahead in the count. Greinke’s ERA- was a league-average 100 last year. This year, it stands at 74. While there are a number of factors involved in the turnaround, Mathis is a significant one. With the Diamondbacks looking like a contender in a watered-down NL, Mathis appears to be one of the more important offseason signings in the game.