If hope springs eternal in spring training, then the waves of reality crash down around baseball’s summer trade deadline. With about 110 games’ worth of evidence, MLB teams have to stop gazing at the horizon and instead assess the ground on which they’re standing.

The evaluation seems simple: Look at the standings, see how your team is doing, behave accordingly. However, it doesn’t work that way, not functionally, in the calculating sphere of 2020s MLB front offices. Dissonance between the emotional direction of a team and a front office’s plotted trajectories and probabilistic forecasts can create bewildered fan bases, confusing decisions and rifts between players and leadership.

Even with more advanced methods at work, there is plenty of room for questioning decision-makers who often display more cynicism and less urgency than we’d like in the entertainment industry that is professional sports. But you need to understand that the standings are just that: standstill snapshots that don’t necessarily capture trajectories or even the whole picture of what has already happened.

Teams need more dynamic understandings of the state of play. There’s a whole diverse world within these two realms, but largely, analysts rely on a blend of peripheral numbers from the games that have been played and projections that chart likely outcomes for the future. Peripherals include run differentials and the expected win-loss mark derived from them, called Pythagorean records.

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At this point, projections — the mathematical formulas derived from past performance and reams of data on player tendencies — are a bedrock feature of following baseball, even if your main use for them is to hate what they say about your team. Major public systems available at FanGraphs and Baseball Prospectus echo the ways that teams size up their own chances, and they regularly set the bar in a complicated sport with a lot of moving pieces.

As former FanGraphs writer Jeff Sullivan (now a front-office analyst with the Tampa Bay Rays) documented in the 2010s, preseason projections remain more telling than the actual standings far deeper into the season than you might think. And updated projections — grounded by a computer’s blindness to narrative thrust, recency bias or wishful thinking — are generally more accurate in predicting the rest of the season than the results that have come before.

“Humans always want to believe they're smarter than human-designed machines or systems, and they especially distrust projections when they show something different from what's already happened,” Sullivan wrote. “When projections are at odds with evidence, projections are given funny looks.”

Projections will always be both imperfect and worthwhile. That’s especially true in a season with so many teams in such a tightly bunched playoff race. Having passed MLB’s annual fork in the road, either 20 or 21 of the 30 teams (depending on what you think of the Seattle Mariners’ soft-sell strategy) have positioned themselves to chase one of the 12 available postseason berths.

To reset the races as we barrel into August, I thought it might be useful, both as a retrospective on trade-deadline decisions and as a look at the possibilities of the stretch run, to apply three different lenses to the rest of the season: preseason projections, Pythagorean records and post-deadline projections via FanGraphs. I took the simple winning percentage from each viewpoint and applied it to the remaining games for each team to assemble the final playoff field that each mode of thinking would envision.

For comparison’s sake, here’s how the playoff picture would look if everything remained the same after Wednesday’s games:

AL East: Orioles | AL Central: Twins | AL West: Rangers

AL wild cards: Rays, Astros, Blue Jays

NL East: Braves | NL Central: Reds | NL West: Dodgers

NL wild cards: Giants, Phillies, Brewers (winning a tiebreaker over the Marlins)

Those standings, as you’ll see, matter a great deal. Entering Thursday, every team had between 51 and 56 games remaining, meaning we're about two-thirds through the slate, and some teams — the Tampa Bay Rays, the San Francisco Giants — have banked enough wins to render any potential regression toward preseason expectations mostly moot. However, while most of this season's baseball has already happened, we shouldn’t let that part of the story take on outsized stature as we explore the possibilities of how it will end.

There is still wiggle room, with plenty of time for jockeying, shuffling and outright turnabouts to take place before October. Still, the numbers give us some idea of the shape those dramatic shifts might take.

Preseason projections

AL East: Rays | AL Central: Twins | AL West: Astros

AL wild cards: Orioles, Rangers, Blue Jays

NL East: Braves | NL Central: Brewers | NL West: Dodgers

NL wild cards: Giants, Phillies, Marlins

All projection systems are slow to buy in to newfound excellence — by design. Most spikes toward greatness flame out and flatten toward our expectations. Some sudden developments, though, are obviously different than others. The Baltimore Orioles and Cincinnati Reds, surprise division leaders, have been riding waves of terrific, young prospects, which is inherently different from other projection-confounding successes, such as the bullpen-driven Orioles or the speed-and-defense Kansas City Royals of the 2010s.

If preseason forecasts hold true, the Reds would drop all the way out of the picture, while the Orioles would slide off their pace and into second in the AL East. A more interesting way to consider these teams? How much they have changed the projections’ mind. The Orioles have bumped their FanGraphs projection from a 76-win pace in the preseason to an 81-win pace in updated forecasts, while the Reds have nudged theirs only from a 70-win pace to a 73-win pace.

Pythagorean records

AL East: Rays | AL Central: Twins | AL West: Rangers

AL wild cards: Orioles, Astros, Blue Jays

NL East: Braves | NL Central: Cubs | NL West: Dodgers

NL wild cards: Giants, Phillies, Padres

Laser-focused on the more granular matter of runs scored vs. runs allowed, Pythagorean records are intended to strip the shine or smudge of luck from a team’s overall record. Clubs squeaking out a lot of one-run wins can’t necessarily be expected to continue that magic, for instance, while teams that often score eight runs in a game but lose every time they score three might achieve better clustering in the future.

That’s the theory, at least. Within seasons, there are legitimate team qualities that might throw this method off the scent of reality. Some teams really do have great bullpens that enable them to thrive in one-run games, or vice versa.

This season, the two main teams hoping their run differentials prove predictive of future success are the San Diego Padres and Chicago Cubs, perhaps not coincidentally two teams that defied their place in the standings to act as buyers at the deadline. By run differential, the Padres (+75 run differential) and Cubs (+77) — teams that have failed to maintain contact with the playoff race to this point — are viewed as the third- and fourth-best teams in the NL, full-on good squads primed to roar past the others in their vicinity and claim postseason footholds.

Chicago, which leapt to acquire corner infielder Jeimer Candelario at the trade deadline in lieu of trading away Cody Bellinger and/or Marcus Stroman, has a particularly appealing argument for winning the NL Central. After two straight blowout wins over the Reds, the Cubs are the only team in their division with a positive run differential, and they sit only three games back of first place. (Of course, one blind spot of this method is a lack of understanding that seven of Chicago’s runs in those past two games came against Luke Maile, a backup catcher tasked with pitching.)

A team that might be looking at this a different way? The Texas Rangers. Their Pythagorean record (68-40) is the best in the American League, but it significantly outstrips their real record (62-46) for the second straight season. As the Houston Astros breathe down their necks with better projections, the Rangers undoubtedly recognized the need to pursue depth on the pitching side — they aggressively dealt for Max Scherzer, Jordan Montgomery and Aroldis Chapman at the deadline — to balance out their offense-first team.

Post-deadline projections

AL East: Rays | AL Central: Twins | AL West: Astros

AL wild cards: Orioles, Rangers, Blue Jays

NL East: Braves | NL Central: Brewers | NL West: Dodgers

NL wild cards: Giants, Phillies, Marlins

In the version of this exercise that historically hews closest to accuracy, there are some noteworthy changes from the current state of things. Specifically, in these projections, the Rays, Astros and Brewers overtake upstart rivals for division crowns, and the Miami Marlins do just enough to stay ahead of the surging Padres, Cubs and Reds.

Notably, none of the scenarios above foresees Shohei Ohtani and the Los Angeles Angels scraping together enough wins to break through and make the playoffs, despite the organization’s decision to hold on to the two-way MVP favorite and add pieces around him. Hobbled by injuries — which the projection systems take into account via human-entered playing time expectations — the Angels are viewed as likely to maintain a pace just a tick above .500 when they need to play like an 88-win team (at least) to claim a postseason spot.

That said, Padres, Cubs and maybe even Angels fans can take heart in one unspoken fact about projections: They are inherently conservative. They just don’t predict wild collapses a la the 2011 Red Sox or juggernauts such as last season’s Dodgers, who played at a 113-win pace after the trade deadline. Projections sketch the line of best fit.

For a great many teams, the past month has been about landing within the margin for perspective-changing error. The next two months will be about forgetting what the statistics say and believing in a destiny that they will later say was never in doubt.