Here is the story of the 2015 Toronto Blue Jays, presented in two easy graphs.

The Blue Jays have bludgeoned their opponents on offense but given most of that back on defense, so naturally, everyone — myself included — had them stocking up on improved pitching at the deadline. It was the path of least resistance, as it just shouldn’t be that hard to find someone better than Felix Doubront to take the hill every fifth day.

Instead, however, the Blue Jays decided to upgrade what was already a strength, adding another right-handed slugger to a line-up already deep in good right-handed hitters, swapping shortstops with the Rockies in a deal that takes them from Jose Reyes to Troy Tulowitzki. In no uncertain terms, this is an upgrade, as a healthy Tulowitzki remains the best shortstop in baseball, even if he hasn’t played like it this year. But it’s not the kind of upgrade we were expecting Toronto to make, and it’s certainly a bit unusual to see a team with the best offense in baseball use their prospect currency to add another hitter.

But unusual doesn’t mean incorrect. While I’m sure there will be plenty of people arguing that the Blue Jays should have taken the path of least resistance and upgraded the pitching staff instead, the reality in baseball is that a run is a run is a run. You win games by outscoring your opponents, and you don’t get any less credit for winning 7-5 than you do 5-3. Troy Tulowitzki will help the Blue Jays score more runs, so while he’s not going to help the team’s run prevention improve that much, those runs he creates will still count in the final tally.

When people argue against upgrading strengths, they’re really arguing for the presence of diminishing returns, but in baseball, the evidence actually supports the idea that adding a good hitter to an already good line-up actually returns a higher level of value, not a lower one. I wrote about this concept earlier this year; while people tend to want to balance out a team’s strengths and weaknesses, historical data actually shows that stacking good hitters has non-linear impacts, and the Blue Jays may actually get more of a benefit by adding a good hitter to their line-up than they would by adding an equivalent upgrade in the rotation.

This is why you want to use something like BaseRuns or a Markov Chain when modeling team run scoring, rather than just taking individual player’s linear weights and adding them together; in a good line-up, the whole really is greater than the sum of the individual parts, because good hitters create more opportunities for other good hitters to turn their production into runs. And because players tend to hit better with men on base than the bases empty, a good hitter can have a positive impact on his teammates performances as well, further increasing the non-linear value of adding a good hitter to a team already strong in run scoring.

So when you see comments about the Blue Jays not needing Troy Tulowitzki because scoring runs wasn’t the team’s problem, ignore them. There are no diminishing returns to scoring more runs; there is no point on offense to where the marginal value of a run scored is worth less than preventing a run from being allowed on defense. All that matters is the differential between runs scored and allowed, and you don’t get any extra credit for being above average at both as opposed to dominating in one and surviving at the other.

Teams upgrade their weaknesses out of convenience, not necessity. It’s usually just easier to replace your worst player with a mediocre one than swap out your solid player for a great one. But the Blue Jays were in a bit of a unique position, with a window to win that extends through 2016 but maybe not beyond that — Jose Bautista and Edwin Encarnacion are both free agents after next year, and while Russell Martin was a good addition, he’s not going to be an elite catcher forever — so Alex Anthopolous was wary to use his farm system to make a move that only helped this year’s roster without also upgrading next year’s Blue Jays team as well.

And while there are a lot of pitchers available right now, most of them are headed for free agency this winter, with Cole Hamels and Aroldis Chapman being the notable excpetions; the Blue Jays are on Hamels no-trade list and the price for Chapman is reportedly quite high, especially for a guy who throws just 15-20 pitches per appearance. So if Anthoplous found every team he called asking about his best young prospects — and that was reportedly the case when they tried to engage on Johnny Cueto — then upgrading at shortstop with a player who won’t leave this winter might very well be preferable.

Especially because the Jays were able to offset a large part of Tulo’s cost by shipping out Jose Reyes in the process. While Tulo remains an elite player, the combination of his health and substantial contract made him a risky acquisition for any other franchise; it’s tough to give up a ton of talent and take on the $100-ish million he’s still due for his decline years, especially when you have to count on him missing a big chunk of the season every year. But because the Blue Jays are subtracting the the $48 million that Reyes was going to be paid in 2016-2017, assuming they’d have paid his 2018 buyout instead of exercising that option year, the marginal cost increase here for Toronto is much less than what other teams would have had to take on.

Year With Tulo With Reyes Difference 2016 $20,000,000 $22,000,000 $2,000,000 2017 $20,000,000 $22,000,000 $2,000,000 2018 $20,000,000 $4,000,000 $16,000,000 2019 $20,000,000 $20,000,000 2020 $14,000,000 $14,000,000 2021 $4,000,000 $4,000,000 Total $98,000,000 $48,000,000 $50,000,000

The Blue Jays are taking on an extra $50 million in future commitments, but that extra cost is deferred well into the future, making the difference even smaller than that total. Using a four percent discount rate, the NPV of the two remaining contracts comes out to roughly a $42 million difference, so along with the prospects, that’s what the Jays are giving up to go from Reyes to Tulowitzki.

How big is that upgrade? Over the remainder of this season, the gap between the two shortstops is estimated at roughly one win, or roughly the same upgrade the Astros got by adding Scott Kazmir to their rotation, and again, that’s without considering the non-linear nature of run scoring. So, while going from Reyes to Tulowitzki might not be quite as impactful in 2015 value as landing a guy like Johnny Cueto, the upgrade is along the same lines as adding any of the next tier of pitchers.

And, of course, the Jays will still have Tulowitzki next year, when he projects to be roughly three wins better than Reyes. Going from Reyes to Tulowitzki isn’t as impactful as signing a premier free agent pitcher, but you’re not getting that kind of player by adding $50 million to your payroll either.

Which is why the Jays also had to part with some of their young talent in order to get this deal done. Because the deal isn’t known in its entirety as I write this, I’m going to hold off on declaring whether the return justifies the price, but we do know that Miguel Castro and Jeff Hoffman are part of the return going back to Colorado, with one other additional piece apparently in the deal as well.

Kiley McDaniel rated Hoffman as a 55 FV, placing him #67 on his pre-season Top 200, and confirmed that he’d keep the same grade on him after seeing him a few weeks ago. As a guy working his way back from Tommy John surgery, he’s certainly a high-risk prospect, but one with significant value given his upside. Castro, rated a 45+ FV on the same list, is also a pretty high-risk gamble, given that he’s basically all arm strength at this point, showing no real ability to get either big leaguers or Triple-A hitters out this year. The Blue Jays rushed him up the ladder, and perhaps the Rockies can get him back on track with a more cautious development plan, but he’s going to need more than just a poorly commanded fastball to turn into a good pitcher.

In terms of prospect value, these two look fairly similar to the two primary pieces the Reds got in exchange for Cueto. If the third prospect in the deal is the least valuable of the trio, then it may very well be that the Blue Jays paid less to get Tulowitzki than the Royals paid to get their rent-an-ace. Perhaps we’ll find out that the third prospect is actually another valuable piece, but as it stands right now, it seems like this may very well have been a better use of the team’s prospect currency than swapping it for a few months of a starting pitcher.

There are some legitimate concerns about the Jays now being too right-handed, as any team with a bullpen of sinker/slider righties can match-up against Donaldson-Tulo-Bautista-Encarnacion-Martin and get the platoon advantage through the middle of their order, and we can’t ignore the fact that Tulowitzki regularly lands on the disabled list, making his expected upgrade less of a sure thing than with a guy who has fewer health problems. This isn’t a risk-free acquisition, and if Tulowitzki’s reduction in power this year is more of a sign of things to come than a first-half aberration, this could end up backfiring.

But given the alternatives, upgrading for both 2015 and 2016 looks like a better idea for Toronto than just going all-in on this year, and the Blue Jays may have found a way to upgrade their roster as much by acquiring a hitter as they would have by acquiring an arm. They should still find a pitcher to replace Felix Doubront, but with Tulo around, the need for an ace is diminished. Sure, they don’t have a classic #1 starter, but they just made the best offense in baseball even better, and a run scored is just as valuable as a run prevented.