Joey Gallo and Anthony Rizzo have each been traded to the Yankees, and it is not at all hard to see why. Gallo, who isn’t a free agent until after 2022, is a 27-year-old two-time All-Star who is having a fantastic year, thanks to the .379 OBP and .490 slugging that work out to a 139 OPS+, making him one of the top 25 qualified hitters in baseball. Rizzo is a 31-year-old three-time All-Star who is somewhat post-peak but brings a 115 OPS+ to the Yankees’ first-base position that had been baseball’s second-weakest.

But more importantly than any of that is this: They each hit left-handed. The Yankees have the second-fewest lefty plate appearances in baseball (867), and those plate appearances have been the third-weakest. Rougned Odor has been OK; Brett Gardner and Tyler Wade have not. How can you have a roster at Yankee Stadium, of all places, without a decent lefty bat?

You can’t, or shouldn’t, even though it was quite clear last winter this was going to be an issue. Now they have a pair, accomplished bats with a combined 388 career home runs between them, and you’re putting them into a ballpark that is generally considered to have baseball’s most homer-friendly right field. What does that look like?

It should help, probably. But not equally for both -- and maybe not as much overall as you might think.

How Gallo fits

When the topic comes up of how Gallo’s high-strikeout, high-power style will fit into a Yankees lineup that has plenty of that, how it does not add any lineup diversity, realize that it actually does. The Yankees have no good lefty bats; he's 40% better than average this year. The Yankees outfield defense is quite poor; Gallo, surprisingly to many given his size, is among the best outfield defenders. The Yankees ground into the most double plays in baseball (97); Gallo has hit into only nine in parts of seven seasons.

Sure, he strikes out a lot, but so does Shohei Ohtani. What Gallo brings is something the Yankees didn't have: A quality lefty hitter with a good glove.

Here’s what we know to be true. Over the last three years, Yankee Stadium is the fifth-best home run hitting park for lefty batters, increasing lefty homers by 17%. That is both “very high” and “probably not as high as you thought it would be.” Somewhat frustratingly, we can’t do a similar three-year ranking for Globe Life Field in Texas, because it only opened in 2020 and hasn’t seen a full season of baseball yet. But in a partial 2020, it was 21st (11% below average), and in a partial 2021, it’s 16th (2% below average).

Given the relatively limited data in Texas, put enormous grains of salt around those numbers, but otherwise, it’s probably safe to say that Gallo is going from a somewhat-below-average hitter’s park for lefty homers to a very good one. He’ll likely benefit. He’ll be happier there.

… except …

… Gallo mostly mashes his baseballs anyway. Over the last two years, only three lefties (Ohtani, Juan Soto and Corey Seager) have hit the ball harder in the air. Only one (Ohtani) has done so with a longer average distance. While Gallo might have the most left-handed homers since 2017, he's got the 70th-most left-handed doubles and triples.

His batted balls tend to either go out, or not be in the neighborhood; it’s not like Gallo is hitting wall-scrapers, for the most part. If the difference is that a home run in Texas (326 feet down the line) is merely a home run that went a few rows deeper in New York (314 feet down the line), well, it’s still a home run.

Beyond that, there’s this little secret about the short porch in Yankee Stadium, which is that it really only applies right down the line. That 314 at the foul pole is indeed the third-shortest, ahead of only Boston and San Francisco. But the 385 in the power alley in right-center is the eighth-deepest, which is part of why that lefty hitter home run factor isn’t as high as you want it to be. There’s not that much extra space in right field in Texas as opposed to New York. (Not that the rest of the field doesn’t matter, but Gallo pulls his flies and liners more than almost any other lefty alive, which is why you see such extreme shifts against him.)

All told, Texas has an outfield area of 104,211 square feet (fourth in baseball), and Yankee Stadium's is 98,962 (21st). That's both a big ranking difference and also merely an extra 5% of area to cover. Since wall height is a consistent eight feet around at both parks, it's entirely about that little section of red in the overlay image above. It's not nothing. It's not a huge thing.

Plus, since Statcast tracking can look at the trajectory of each batted ball and compare it to the distance and wall height of each of the other parks to tell you where it would or would not have gone out, we can eyeball some specific not-homers this year that would have left the yard in New York -- like, for example, this flyout in Houston.

This ball caught by Tampa Bay’s Brett Phillips? Makes it out of Yankee Stadium.

This double against the Twins? Just squeaks over the fence.

So it should help a bit, and we can put some numbers to that.

Gallo has 25 homers so far in 2021. According to Statcast tracking, 17 of them would have been out of every single park in the Majors; that's how crushed they were, which is a good reminder that many of his blasts are just gone, without any help or hindrance. Among players with at least 15 homers, that 68% rate of homers that would have been out of every single park is ninth highest. He hits his hard.

But if he’d hit all of his batted balls at Yankee Stadium -- and remember, he also has to play road games, so this isn't really a thing -- he’d have 29. That's a nice boost in 2/3 of a season. Forget 2020, as we would all like to, and go back to the previous full season in 2019, when Gallo hit 22. That year, his homer number would have been 25 in New York.

So will it help him? Sure, a little, because how could it not? His new home is simply smaller than his old home. But these things never quite have the impact that people hope they will, and you need not look much further than Giancarlo Stanton hitting 59 in spacious Marlins Park in 2017, then hitting 38 the next year as a Yankee, when we had much the same conversation. What's most likely to happen is that when he blasts a ball down the right field line, the short porch won't have turned a non-homer into a homer so much as it will just make it look more majestic, since it will have landed further back into seats.

How Rizzo fits

It’s a lot different for Rizzo, though, because he A) puts a lot more balls into play than Gallo and B) isn’t nearly as powerful. Earlier, we said that Gallo has the second-longest average distance on his fly balls and liners over the last two years, behind only Ohtani. Rizzo is 46th, with his 288 feet average nearly 20 feet shorter than Gallo’s 309; like his new teammate, he’ll be going from a park that’s somewhat below-average for lefty home runs to one that is better.

Because of that more-contact/less-power combination, Rizzo simply has more chances to be affected by a ballpark. For example, let’s look at 2019-21, and just find the number of fly balls and line drives each batter hit between 300 and 400 feet, a relatively broad range meant to show nothing more than the fact that Gallo is either striking out or making much more impressive contact than his new teammate.

Gallo: 87 batted balls
Rizzo: 156 batted balls

So while Gallo would get maybe two or three more home runs in a full season at Yankee Stadium, Rizzo might find himself benefiting even more.

That’s what the Statcast numbers say, anyway; he has 14 home runs this year, and if he had hit all his batted balls in Yankee Stadium, he’d have 23 homers. Again: That’s not considering road games, and the final two months of the season are not a full season, and all the usual caveats here apply. But when you look at Wrigley Field’s dimensions laid over those of Yankee Stadium’s …

… the differences are clear. Although the overall outfield square footage of Wrigley Field and Yankee Stadium are almost identical to the foot, their shapes are very different. Yankee Stadium is much deeper to left center field than Wrigley is, but it’s much shallower to right field than Chicago is, and that’s where Rizzo could really benefit.

Because, unlike Gallo, Rizzo really does do things like this a lot, flying out to Bryce Harper.

Or a very similar looking play, flying out to Avasail Garcia.

The truth is, over two months of the season, half of which will be spent playing in parks that aren’t Yankee Stadium, there’s really not that much change you’ll be able to see from your two new Yankee sluggers. But it’s not consistently applied either, because you’ll likely see Rizzo benefit more than Gallo, and if, in a big spot in late September or October, one of them pushes out one big homer that wouldn’t have been gone in their old parks, that might be all that matters. The park will help, a little. The players will help more.