It’s not that there’s nothing left to be done. Eventually, someone’s going to sign Yoan Moncada. Eventually, someone’s going to sign Hector Olivera. There’s no telling when a team might make a strong enough offer to grab a pitcher like Jordan Zimmermann, Stephen Strasburg, or Cole Hamels. It’s still the offseason — it’s still the middle of January. But for the most part, people are looking ahead, with the start of spring training a month away. With the Max Scherzer contract complete, all the big fish are accounted for. All the big fish, that is, but James Shields, who very much remains a free agent, with a very much unclear future destination.

The free-agent market at this point is terrible. As you’d expect it to be. Just yesterday, I was reading a rumor connecting the Astros to Ryan Vogelsong, even though the two parties involved were the Astros and Ryan Vogelsong, and that tells you a little bit about who remains out there. Shields is the exception, since, no matter how worried you are about the mileage on his arm, he appears a good-enough bet to contribute next year. The guy just needs to find a home. How might we be able to help him find a home?

What follows is simply an exercise. I wanted to find out who might stand to gain the most by signing James Shields as a free agent. There’s no easy way to turn that into math, considering all the different details, but we do have projections for 2015. We do have projected starting-rotation depth charts. While teams interested in Shields will be thinking about more than just one year, you figure next year is the most important of the years, since it’s the year in which Shields has the highest odds of being good.

So which rotations would improve the most with Shields? That’s what you’ll find in the table below. Because it’s all just based on Steamer, it’s not perfect, and I had to make some judgment calls with making space for Shields on each staff. Basically, I took Shields’ projection, added it to each rotation, and then took away innings from the back-end arms until the frames evened out. For the record, because some guys are projected to get innings as both starters and relievers, I had to make a few little adjustments that I don’t think changed much significantly. Anyhow, it’s the table you want, right? This is a table of projected WAR gains, for 2015, with a brand-new (but actually heavily-used) James Shields:

Team WAR Gain Reds 3.6 Phillies 3.5 Tigers 3.3 Braves 3.2 White Sox 3.2 Orioles 3.2 Rays 3.1 Angels 3.1 Athletics 3.0 Blue Jays 3.0 Diamondbacks 2.9 Astros 2.9 Cubs 2.8 Giants 2.6 Brewers 2.6 Padres 2.5 Marlins 2.5 Rangers 2.5 Pirates 2.3 Mets 2.3 Cardinals 2.2 Twins 2.2 Dodgers 2.1 Royals 2.1 Yankees 2.0 Rockies 2.0 Mariners 1.8 Red Sox 1.6 Indians 1.6 Nationals 0.8

So the Nationals wouldn’t improve much at all. We knew that, or we at least could’ve guessed that, but it’s funny. James Shields is going to sign for something in the rough vicinity of $100 million. If the Nationals gave him that contract, they would project to get better by less than one win. Stupid crazy Nationals.

Anyhow, the real interesting teams are the teams toward the top. Let’s go through them individually, since this table considers one thing and one thing only. Which of those teams would actually make sense?

Based on this, no team would improve more than the Reds, albeit by a small margin. The problem: the Reds don’t have money. This offseason, they’ve had to balance money coming in with money going out, so they’re not going to be involved in the Shields market. Simply can’t afford it.

The Phillies would get a lot better. This is because the Phillies, as currently constructed, suck. That’s also the reason the Phillies won’t be involved in the Shields market.

The Tigers are an interesting candidate. They’re familiar with Shields, and they’ve got David Price a year away from free agency. The current starting rotation doesn’t have depth, and it does have Alfredo Simon, who isn’t particularly good. But the Tigers also paid a decent price to get Simon from the Reds, and that would be strange if they didn’t think Simon could give them 150 innings or so. You definitely can’t rule the Tigers out, but they’re also not my most likely destination.

The Braves are like the Phillies, in that they suck. Now, they did pay for Nick Markakis, oddly enough, and that move doesn’t fit with a team that’s trying to rebuild, but Shields is going to cost twice as much as Markakis did. The Braves aren’t a candidate.

The White Sox have little rotation depth at all, and bringing in Shields would allow them to have a downright terrifying front four. The move might also boost them into favorite position in the AL Central. That’s the argument for. The argument against: Rick Hahn’s already had an incredibly busy offseason, and the team might be just about out of wiggle room. The payroll projects to be much higher than it was last year. The White Sox, perhaps, are a dark horse.

The Orioles, in theory, would improve, but it’s hard to see how they’d make space. Already, they have one too many starters what with Ubaldo Jimenez’s presence, and there’s growing buzz regarding the return of Dylan Bundy to the bigs. So, to me, Baltimore would be a surprise.

The Rays don’t have the money. Moving on.

The Angels suggest they don’t have the money. There are a lot of expensive players already on the payroll. They’ve done pretty well to accumulate a group of low-cost starters who can help them for a while. But given the state of the rotation, and given the state of the division, I don’t think you can rule the Angels out until Shields has actually signed somewhere else.

The A’s can’t afford it. Which brings us to the Blue Jays.

I like Marcus Stroman. I like him a lot. Yet a starting rotation includes five pitchers, not one, and right now, at the back, the Jays are looking at Aaron Sanchez, Daniel Norris, and/or Liam Hendriks. Sanchez has an undeniably awesome fastball, but in his career as a starter, he’s never really thrown strikes, and he hasn’t missed enough bats against advanced competition. Sanchez profiles better as a reliever, which is incidentally something the Blue Jays say they’re interested in finding. Norris has a better record of strikes than Sanchez, but he has very little experience at Double-A or higher, so he functions better as depth. I don’t think I need to tell you anything about Hendriks.

And, wouldn’t you know it, but the Blue Jays are in position to go to the playoffs. At least, they’re in position to contend for the playoffs, and they could win the AL East. So they’re in that delicate win-curve position, and a year from now, Mark Buehrle’s gone. R.A. Dickey is maybe gone. Shields wouldn’t block anyone. It’s hard to imagine a better fit than this.

Right after the Blue Jays, we see the Diamondbacks, who we know to be interested, but they’re not good, and they’ve conveyed that they probably won’t make the high bid. The Astros might have the money, but they’re still not really a James Shields away from being strong. The Cubs could make sense, but already they have too many rotation candidates, and they might prefer to roll with what they’ve got instead of making another expensive free-agent-pitcher acquisition. The Giants have publicly all but ruled themselves out. The Brewers like Jimmy Nelson too much. The Padres are probably too cash-strapped. And on, and on.

Other teams do fit. Aside from the Nationals, there’s no team James Shields wouldn’t fit, on paper. He’s a good player, and it might well be Shields ends up with a team that isn’t his best match. Players don’t always go to where those same players are the best matches. But for whatever it’s worth, as I write this, it seems to me the best match is in Toronto. They have an interest, and they have a need, and they have a team good enough to conceivably win the next World Series. I suppose you could consider the Blue Jays my James Shields favorite. Now I need to quit this and look at Twitter to see if it might’ve already happened.

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(Note: realized, during the course of this, that Dan Szymborski just wrote a similar piece for ESPN Insider, based on ZiPS instead of Steamer. That was a coincidence, but you get to read them both! If you want to. I don’t know what you want.)