The Rays weren’t the only winners on Tuesday. Brian Cashman even said on Monday that he hoped to see Tampa Bay and Houston reach Game 5 in the American League Division Series.

“Why not?” the Yankees general manager said in Minnesota after the Yankees advanced to the AL Championship Series, where they will await the winner of Thursday’s Game 5 between the Rays and Astros.

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Beyond the obvious benefit of hoping the Rays or Astros get worn out by Saturday, when the ALCS begins, there are many reasons why the Yanks were likely satisfied with Tampa Bay defeating Houston, 4-1, in Game 4. Here are a few:

If Houston wins, New York likely will avoid Cole and Verlander in Game 1

If the Astros win on Thursday, they will likely do so on the shoulders of Gerrit Cole, who was historically dominant in Game 2 of the ALDS. And that was merely a continuation of what’s been an untouchable run -- Cole is 17-0 with a 1.69 ERA over his past 23 starts, striking out 41.6 percent of the batters he’s faced in that stretch.

Cole would be lined up to start ALCS Game 3 on Tuesday on regular rest, which would be played in the Bronx. The AL Cy Young Award favorite made just one start against the Yankees during the season, pitching seven innings of three-run ball in a 6-3 Astros win on April 9 in Houston. He surrendered a first-inning homer to Luke Voit and walked a season-high three while striking out just six (his fourth-lowest mark in his 34 starts).

Worth noting: Cole has never pitched in relief or on short rest.

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Justin Verlander almost certainly wouldn’t pitch on short rest for his second straight start after arguably his worst outing of the year on Tuesday. That would line him up to pitch on regular rest for ALCS Game 2 on Sunday, which would be in Houston.

Verlander made two starts against the Yanks during the season, both Astros wins, though his 4.15 ERA against them was the second-highest against any club he faced at least twice. That won’t necessarily matter to Yankees fans, who remember Verlander willing Houston to an series-swinging win in Game 6 of the ALCS in 2017, when the Astros overcame a 3-2 deficit to advance to the World Series.

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All that said, Houston’s likely Game 1 starter wouldn’t be a picnic, either. Zack Greinke made two starts against the Yankees this season -- both with the D-backs before he was traded in July -- compiling a 2.13 ERA in those outings. Greinke is 4-4 with a 5.05 ERA in 15 career outings against the Yankees.

If Tampa Bay wins, New York likely avoids Morton and Glasnow early

Tyler Glasnow will start opposite Cole on Thursday, meaning he too would be lined up for ALCS Game 3. And the Rays will likely have huge pause to test Glasnow on short rest after he missed four months with a right forearm strain during the season. Coincidentally, Glasnow suffered his injury in a May 10 start at Yankee Stadium -- his lone outing against the Yanks this season -- where he gave up a season-high three four runs.

When healthy, the blossoming righty showed he was as elite as any AL starter. Glasnow possesses 97 mph fastball velocity, elicits some of the Majors’ weakest exit velocity and ranks in the top two percent in most Statcast metrics. At the time of his injury, Glasnow was 6-1 with a 1.86 ERA and .518 OPS against, both tops in the AL. On an abbreviated workload after returning, Glasnow had a 1.46 ERA and .475 OPS in four September outings, and his lone blemish in ALDS Game 1 was a two-run homer by José Altuve.

Morton might not be available in Game 1 either, given that -- barring an unlikely Rays blowout -- there is a very good chance he will pitch in relief on Thursday with all hands on deck. Morton, a favorite to finish third behind Cole and Verlander in AL Cy Young Award voting, dazzled in ALDS Game 3 with a slew of seemingly unhittable pitches. Also worth noting: Morton -- while still with the Astros -- came on in relief in Game 7 of the 2017 World Series to close out the Dodgers with four scoreless innings. This, however, came on three days of rest after starting Game 4. If he pitches on Thursday it will be two-days rest.

Two of Morton’s worst starts during the season were against the Yanks, when he gave up five runs each in losses at Yankee Stadium on May 19 and July 18. But they were also the opponent for one of his best, when he limited the Bombers to just one hit and zero runs over six innings on Sept. 25.

Home-field advantage is still in play

The Astros had the best record in baseball this season, earning them home-field advantage through the World Series, but if the Rays complete their ALDS comeback, the Yanks would have home-field advantage in the ALCS. That would be monumentally important for two reasons:

1. They were 8-1 against the Rays at Yankee Stadium this season.
2. They had the Majors’ third-best home record (57-24), while the Astros (60-21) had the best.

No team had more wins against the Rays than the Yanks’ 12, though New York did having a losing record (4-6) at Tropicana Field. The Yanks were swept in a three-game series at Minute Maid Park in April.