SAN FRANCISCO — The story of everything that matters this side of Los Angeles in the National League for the next week, if not the rest of the season, might be on display Tuesday in San Francisco.

That’s when Cubs right-hander Yu Darvish, whose last two starts finally began to support his intent to lead a playoff push this season, faces Giants left-hander Madison Bumgarner, who might be making his final home start with the team.

The Giants might be the most intriguing team to watch as the trade deadline nears and buyers wait for the direction they plan to take, with perhaps nobody as intriguing as Bumgarner if the hottest team in the NL decides to sell.

From a Cubs perspective, however, all eyes should be on Darvish, regardless of whether they have Giant bones to pick for left-handed bullpen help by next week (Will Smith, Tony Watson).

The enigmatic, big-money right-hander is on a scoreless two-start roll and has a chance for a career first if he can make it three in a row Tuesday. It would be a feat that finally might build enough trust in the faithful (and team officials) to believe he can have an impact befitting his contract when the Cubs need him most the next two months.

‘‘Absolute swagger,’’ Cubs manager Joe Maddon said of what he sees in Darvish these days. ‘‘When he walked off the mound the other day [after the second scoreless start], I thought to myself, ‘That’s probably what he looked like in Japan several years ago, winning all those MVPs.’ Just different.’’

Cubs first baseman Anthony Rizzo said Darvish is ‘‘more of an animal on the mound.’’ Maddon said he’s more ‘‘calculating’’ between pitches, leading to more confidence and command. Darvish said he’s feeling ‘‘120 percent’’ physically and mentally.

‘‘It’s perfect,’’ he said. ‘‘Everything.’’

Never mind what that might mean for a team trying to pull away in the National League Central and put itself in position for a strong October run.

The biggest question might be: How the hell did that happen?

This was a guy who melted as soon as he got to Chicago last season, eventually felt a twinge in his surgically repaired right elbow and made only eight starts.

Even this season, he had a 5.01 ERA and an NL-leading 20 home runs allowed at the All-Star break, without so much as back-to-back quality starts — or a home victory — since signing with the Cubs.

If any semblance of this two-start ‘‘trend’’ holds, the mile markers on Darvish’s road to productivity started with deciding independently to fire his Japanese interpreter and speak English with Chicago media.

What quickly followed was a swagger in spring training and a sense of humor that was increasingly revealed.

And then:

1. Slow-hand Yu. After spending his first eight starts of the season leading the majors in walks and fighting to pick up his tempo and find a better rhythm between pitches, he gave up on the tempo thing.

‘‘A lot of guys tell me about tempo, but I’m a slow guy,’’ he said after pitching into the sixth inning with no walks May 15 in Cincinnati. ‘‘I told [pitching coach] Tommy [Hottovy] I want to go slower. That makes me more comfortable.’’

His 2.1 walk rate per nine innings since then would be a career best for a season.

2. No pain, no duh. Darvish admitted that into June this season, his elbow problems remained in the back of his mind whenever he threw his fastball. That is the pitch that caused him the most pain in 2018.

At some point last month, he finally trusted the pain was gone and started to unleash the upper-90s fastball when and where he wanted. That has made his cutter, slider, changeup, curveball and all their variations nearly unhittable.

He had command of seven pitches in the opener on the second half and looked similar five days later.

3. Embrace the target. It might seem counterintuitive, but the four-time All-Star best known for World Series meltdowns and underachievement has had his best outings this season in the games he has acknowledged as big ones: when he faced the man he replaced on the Cubs, Jake Arrieta; when he pitched at hostile Dodger Stadium for the first time since his Game 7 debacle in the 2017 World Series against the Astros; and the post-All-Star-break opener he requested.

He has a 1.89 ERA in those starts, with 25 strikeouts and only five walks in 19 innings.

Big games? Darvish never has faced Bumgarner, whose epic performance in October 2014 earned him a World Series MVP award. He has faced the Giants only once, beating them with seven scoreless innings as a member of the Dodgers in 2017 in San Francisco.

‘‘He’s really responded to big moments this year,’’ Cubs president Theo Epstein said. ‘‘He really has a strong desire to contribute and to pull his weight and make up for some things that haven’t gone well initially. He’s starting to back up good intentions with performance.’’