With Derek Jeter retired and Alex Rodriguez basically a non-factor, the Yankees had to rebuild the left side of their infield this offseason, and they did that by trading for shortstop Didi Gregorius and re-signing third baseman Chase Headley. The Yankees are hoping those two will hold things down on the more glamorous side of second base for at least the next four years, the term of Headley’s deal. (Gregorius has five years of team control remaining.)

Headley performed very well during his limited time in pinstripes this past season while Gregorius has a little more than a full year of MLB time under his belt, so he’s more of an unknown. Both guys have similar profiles though — they’re defense-first players who do their best work catching baseballs, not hitting them. Headley’s been an average or better hitter basically his entire career, though his glove is his calling card. Gregorius definitely fits the all-glove, no-bat profile.

At the very least, the Yankees will have a much better infield defense next season, especially on the left side. How much better defensively? Substantially, really. On the order of two or three wins, I think. Maybe more. To get a better idea of just how improved the defense at short and third will be next season, let’s look at some Inside Edge data and compare the 2014 Yankees to the incoming Gregorius and returning Headley.

Shortstop

There’s no way to sugarcoat it: Jeter was a disaster in the field this past season. I mean, he’s been below-average in the field pretty much his entire career, but the 2014 season was his worst defensively. The combination of age and his broken ankle late in 2012 sapped whatever mobility he had left, and his arm left something to be desired as well. The Cap’n put Mark Teixeira’s scoop tool to work at first base this summer.

The Inside Edge data shows just how terrible New York’s defense at shortstop was during the 2014 season:

1-10% (remote) 10-40% (unlikely) 40-60% (about even) 60-90% (likely) 90-100% (almost certain) 2014 Yankees 0.0% 11.1% 35.3% 64.3% 95.3% 2014 MLB AVG 3.7% 24.1% 49.2% 74.1% 97.2% 2012-14 Gregorius 14.3% 25.0% 52.6% 69.2% 98.2%

Inside Edge is fairly straight forward. Batted balls are recorded by human stringers (so there is some scorer bias) and are split into six groups — the five in the table above plus “impossible,” which register at 0% league-wide — depending how difficult the play will be for the defender. For example, batted balls considered “likely” to be turned into an out are plays that are made 60-90% of the time, with the league average at 74.1%. Got it? Sure you do.

The 2014 Yankees, who had Jeter at short for 78.3% of their defensive innings, made no very difficult plays (“remote”) at shortstop and were comfortably below the league average when it came to making “unlikely,” “about even,” and “likely” plays. Long story short, anything not hit right to the shortstop was converted into an out at a considerably below-average rate. Jeter was that bad in the field. Everything was an adventure.

Gregorius, on the other hand, has been above-average at making every type of play since breaking into the league with the exception of “likely” plays, where he’s been a tick below-average but not Jeterian. Other young middle infielders like Adeiny Hechavarria and Dee Gordon have a similar Inside Edge profile and the thought is they have occasional lapses in concentration and botch the routine play. Tougher plays like “remote” and “unlikely” are all instinct. There’s no thinking.

In theory, those lapses in concentration can be fixed. Then again, they might not even be the problem. It’s just a theory. Baseball America has consistently ranked Gregorius among his organization’s top prospects throughout his minor league career, and over the years their defensive scouting reports have said “his hands are still somewhat erratic” (2010), “his hands are his biggest drawback defensively” (2011), and “he showed improved consistency (with his hands)” (2012). Hands that are “somewhat erratic” but showed “improved consistency” seem like the kind of thing that could contribute to his below-average rate of making “likely” plays.

Either way, the Yankees are getting a substantial defensive upgrade at short by replacing Jeter with Gregorius. Even with those bad hands or lapses in concentration or whatever, Gregorius has made plays at a much higher rate than Jeter these last few years, and it’s expected he will continue to do that going forward. His youth and athleticism mean Didi is more likely to improve going forward than crater and became a below-average gloveman. It’s been a very long time since the Yankees had an everyday shortstop as good as Gregorius defensively.

Third Base

Between the hobbled A-Rod and Kevin Youkilis and the defensively blah Jayson Nix, Yangervis Solarte, and Kelly Johnson, the Yankees have dealt with some really shaky hot corner play the last few years. Headley was a breath of fresh air after coming over at the trade deadline. He made every play he was supposed to make — that was an accomplishment for the 2014 Yankees — plus more than few highlight reel plays.

The Inside Edge data for the team’s third basemen this past season is pretty interesting:

1-10% (remote) 10-40% (unlikely) 40-60% (about even) 60-90% (likely) 90-100% (almost certain) 2014 Yankees 0.0% 41.2% 76.9% 77.5% 95.8% 2014 MLB AVG 2.7% 25.9% 57.9% 76.5% 95.9% 2012-14 Headley 2.4% 22.0% 72.9% 85.6% 97.4%

According to Inside Edge, the Yankees were well-above-average at making “unlikely” and “about even” plays at third base in 2014 and basically average at “likely” and “almost certain” plays. When it came to making something more than the routine play, the 2014 Yankees were collectively better than the 2012-14 version of Headley.

Of course, the 2014 Yankees and 2012-14 Headley are not mutually exclusive since he did play a few hundred innings at third for New York this summer. Let’s compare Headley’s defense to the team’s other third baseman this past season:

1-10% (remote) 10-40% (unlikely) 40-60% (about even) 60-90% (likely) 90-100% (almost certain) 2014 Non-Headley NYY 3B 0.0% 30.0% 75.0% 77.4% 94.2% 2014 Headley with NYY 0.0% 57.1% 80.0% 77.8% 99.1%

The team’s non-Headley third baseman were actually above-average at making non-routine plays and about average making “likely” and “almost certain” plays, so the hot corner defense wasn’t a total disaster. Headley, however, managed to improve on all of that across the board. So yeah, the Yankees were getting pretty good glovework at third, but Headley took it to another level.

Now, defense is like anything else in baseball, players can have good defensive years and bad defensive years. It’s like batting average. Robinson Cano hit .306 in 2007, .270 in 2008, then .320 in 2009. Did his talent level change those three years? No, that’s just baseball. The same applies to defense. The various defensive stats (not just Inside Edge) say 2014 was either the best or second best (behind 2010) defensive season of Headley career. He was still above-average from 2011-13, but not as good as 2014.

Given his track record, there’s a chance Headley’s defense going forward won’t be as good as it was this past season, and again, that isn’t to say it will be bad. To go back to Cano for an example, he hit .342 in 2006 and then .308 from 2007-14. He was awesome in 2006 and slightly less awesome from 2007-14. Headley’s defense was outstanding in 2014. It’ll probably be slightly less outstanding going forward, and that’s okay. As long as he continues to be above-average, he’ll be an upgrade on what the team was running out there the last two years.

Going from Jeter to Gregorius will be a substantial improvement for the 2015 Yankees. In fact, it might be the single biggest defensive upgrade at any position in baseball. Maybe second biggest behind the Allen Craig to Jason Heyward move the Cardinals made, but, either way, New York will be considerably better at short next year. They’ll be better at third base as well, just less so. With a ground ball-centric pitching staff, the improved defense on the left side of the infield figures to be very noticeable. It was an upgrade that had to be made.