SAN FRANCISCO — The Giants can take a bit of solace in the fact that bullpen help is on the way.

Before Monday’s 6-4 loss, San Francisco’s injury report featured nothing but positive news. Right-hander Joel Peguero was to start a rehab assignment with Triple-A Sacramento, and left-hander Sam Hentges could be nearing the start of one, too. Right-hander Jason Foley is throwing bullpens; lefty Reiver Sanmartin has started a throwing program off flat ground.

That group, particularly Hentges and Foley, will be welcome additions when they arrive. For now, following back-to-back crushing losses, manager Tony Vitello remains in search of a bullpen formula that sticks.

“Right now, I do think we’re a little more jumbled up than maybe the Phillies,” Vitello said before Tuesday night’s game against Philadelphia. “I think all of us could probably script out what they’re going to do tonight and tomorrow if plan A goes down. We’re not quite to that point, so we’ll just have to work for it.

“In the long run, maybe it makes us better because guys have to push themselves to the top of that list if they want to be out there in the most important or best situations.”

San Francisco opened the week with consecutive losses that saw the bullpen unable to protect a late lead. Sunday, the Giants allowed four runs in the eighth to the Mets, spoiling Logan Webb’s first great start of the season. Monday, they were done in by another four-run frame, this one to the Phillies in the seventh.

The Giants’ brass didn’t invest much into this team’s bullpen in the offseason, even with numerous high-leverage options available on the free agent market. Through 11 games, San Francisco’s bullpen ranked 21st in ERA (4.93) and 18th in FIP (4.79) and looked the part of a legitimate weakness.

Vitello said often during spring training that the Giants’ bullpen would be “fluid,” and that’s been the caseso far. He hasn’t named a closer, and there is no clear late-game hierarchy.

Take Ryan Walker, for example. Last Monday, Walker entered for the ninth inning to protect a 3-0 lead against the Padres. He allowed a two-run homer to Jackson Merrill but still secured the win. Four days later, Walker entered in the sixth after Robbie Ray recorded the first out of the sixth inning. Walker recorded the final two outs, and his evening was done.

Contrast that with the Phillies, who deployed a set succession of relievers to secure a win on Monday. With Philadelphia leading by two runs, manager Rob Thompson went with an unsurprising script: José Alvarado for the seventh, Brad Keller for the eighth, Jhoan Duran for the ninth.

Less than a year ago, former Giants manager Bob Melvin had a similar structure at his disposal. Tyler Rogers owned the seventh, Randy Rodríguez pitched his way to an All-Star team by dominating the eighth, and Camilo Doval reclaimed his role in the ninth. With Doval and Rogers having been traded and Rodríguez recovering from Tommy John surgery, Vitello doesn’t have that luxury.

The lack of a definitive late-game formula doesn’t mean Vitello and his coaching staff aren’t slowly starting to form one with their current group.

Vitello said Tuesday that the primary trait that the coaching staff is looking for in their relievers is strike-throwing. Naturally, the relievers who throw better will climb the ladder, while those who don’t will fall. In addition to finding their best relievers, Vitello said matchups and the timing of the game must also be considered.

“Nowadays, we’ve got all this analytical data that you’re probably a little ignorant to not take it into account a little bit,” Vitello said.

The three relievers whose stocks have slowly risen appear to be right-handers Blade Tidwell and Caleb Kilian, and left-hander Matt Gage, none of whom have allowed a run this season.

Vitello referred to Kilian and Tidwell as “stuff guys,” and the metrics back up that claim. Among all of the Giants’ pitchers, Tidwell and Kilain rank first and third, respectively, in FanGraphs’ Stuff+ metric, which looks at a pitch’s physical characteristics.

“As long as they’re willing to ram it in the zone or cram it in the zone, however you want to phrase it, it’s going to go well for them,” Vitello said. “They can get us out of some jams.”

The Giants’ manager also acknowledged that Walker and left-hander Erik Miller have the best track record of being leverage relievers. Vitello added that the team will feel more comfortable with Miller once he’s thrown more innings following his abbreviated spring training.

San Francisco’s bullpen could very well be stronger in May and June as relievers return from the injured list. But with the offense ranking last in runs per game, Vitello and company are still searching for a sustainable late-game formula that will help in the present.

Several regulars get day off

Right fielder Jung Hoo Lee, catcher Patrick Bailey and center fielder Harrison Bader were all given off days for Tuesday evening’s game against the Phillies.

In their place, Jerar Encarnacion started in right (batting seventh), Daniel Susac started behind the plate (batting eighth) and Jared Oliva started in center (batting ninth).

Additionally, Rafael Devers dropped to fifth in the order, the first time he’s hit lower than cleanup since 2021.