SAN FRANCISCO — It’s been a thrilling stretch for the Giants, but they actually are not atop the leaderboard in terms of the greatest shift in playoff odds over the past week. That honor belongs to a franchise legend.

From last Thursday through this Thursday, Bruce Bochy’s Texas Rangers saw their postseason odds improve by about 12 percent, per Baseball-Reference’s formula. The Rangers won six straight before dropping a couple to the Arizona Diamondbacks on Tuesday and Wednesday, but they also got plenty of help. The Seattle Mariners currently hold the third and final Wild Card spot in the American League and they dropped two of three in Cleveland last weekend before getting swept by the Rays this week.

In the National League, the Giants are hoping for a similar collapse from the pack in front of them, and they have put themselves in a position to capitalize if it happens. 

Winners of 10 of 11, the Giants are suddenly very much alive in the NL postseason race. Baseball-Reference gives them an 11.1 percent chance and FanGraphs has them at 4.3 percent. 

While that latter number is still extremely low, it’s a heck of a lot better than it was a couple of weeks ago. When they left San Diego last month after dropping three of four, they sat at 0.7 percent. The next night, a blown lead in Milwaukee cost them another game and dropped their FanGraphs’ odds to 0.4 percent.

The season was effectively over — and then the lineup decided to simply flip a switch. 

The Giants have scored 7.8 runs per game over the past 11 games, batting a combined .311 with a .908 OPS and more than two homers per game. Led by Rafael Devers and Willy Adames, the Giants have homered in 17 consecutive games, a San Francisco-era franchise record. During their 2-13 stretch at home in late July and early August, they never homered in even three consecutive games, and did it back-to-back games just once. 

“Seventeen is a lot, especially when you play in our park,” manager Bob Melvin told reporters in Denver on Wednesday. “It’s been a huge part of the resurgence at this point and it’s been mostly those guys in the middle of the order that we signed here long-term to do exactly that: Drive in runs, hit homers and hit for power.”

Everything has changed overnight, allowing the Giants to actually pursue October baseball, but they still need plenty of help. 

Aside from the obvious point that they have to continue to take every series and possibly pile up sweeps, the Giants need a team ahead of them to fall apart. The positive after the series at Coors Field is that they at least have multiple options now. 

The New York Mets hold the third Wild Card spot and sit four games ahead of the Giants, but they have the tiebreaker thanks to a sweep at Oracle in late July that helped push Buster Posey to sell at the deadline. The San Diego Padres have lost eight of 10 and sit five games ahead of the Giants, but again, they hold the tiebreaker. 

The Giants are essentially five back of the Mets and six back of the Padres, while sitting a game up on the Cincinnati Reds and 1 1/2 ahead of the St. Louis Cardinals and Arizona Diamondbacks. The latter two teams in the race will play a huge part in the Giants’ hopes down the stretch.

They visit Busch Stadium this weekend and then host the Cardinals on the final homestand of the year. They’ll also visit the Diamondbacks and host them, and do the same with the first-place Los Angeles Dodgers, who have plenty of issues of their own but lead the Padres by two games in the NL West. The final three games of the year will be against a Colorado Rockies club that the Giants have gone 8-2 against this year. 

The schedule isn’t difficult, although with the exception of the Rockies, the Giants won’t face any team that has packed it in. In St. Louis and Phoenix, they’re also hoping for a miracle. Those four series figure to be hard-fought, and any series against the Dodgers is a difficult one. 

The math says the Giants are a long shot to play in October, but stranger things have happened, and it’s where we come back to the Rangers. Their manager, Bochy, was in San Francisco in 2010 when the Giants overcame a six-game deficit with 32 to play. 

Until playoff odds hit 0.0 percent, teams will always hope for the best, and the Giants have at least put themselves in position to make things interesting. They’ll aim to make up a bit more ground over the next week while the Mets face the Reds and Phillies. 

“Better late than never, I guess, right?” Chapman said Wednesday. “It’s been a lot of fun. We obviously hit a rough patch, but I feel like we’re really coming into our own right now and playing good baseball. We’re really just trying to keep it rolling.”

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