The team has played through injuries to multiple key contributors this year — Judge, Sanchez, Giancarlo Stanton, CC Sabathia, Severino and Betances have all spent time on the injured list — and have come out looking extremely strong. It will make the playoffs. It will likely win the division. Major leaguers are always playing to win. No one is questioning the Yankees players’ desire.But if New York wants to be top of the list, king of the hill, A-No. 1, then the front office’s optimism about the current injured players and the depth of the roster better prove to be correct over the next two months.If that faith isn’t rewarded, then this town will be a losing town. NEW YORK — Here are some names: Trevor Bauer, Marcus Stroman, Tanner Roark, Mike Leake, Zack Greinke.All of them were on the move before Wednesday’s MLB trade deadline. None of them went to the Yankees. It might be a little unfair to put it that way. There are always extenuating circumstances surrounding trades: asking prices, no-trade clauses, money changing hands and more. But the Yankees have swung and missed on a lot of opportunities in the past few years, seemingly as often as their major league lineup has at pitches in games. This week’s deadline was no different.MORE: Here’s how to watch ‘ChangeUp,’ an MLB whiparound show, for free on DAZNGeneral manager Brian Cashman was open about his failure to add an arm this July 31. He was open about not being close in trade talks. He rehashed the lines, several times, that asking prices were too high or his offers were underwhelming, or some combination of the two. He mentioned how he spoke with every team in baseball — except the Red Sox — to find starting pitching help. Those talks ultimately proved fruitless. The thing is, Cashman’s lack of success extends well beyond the trade deadline.Patrick Corbin, reportedly a free-agent target in the offseason, signed with the Nationals. Dallas Keuchel, unsigned through the spring and into the season, inked a deal with the Braves. Gio Gonzalez was signed to a minor league contract in March but left to pitch with the Brewers when he wasn’t called up to the big league squad. Those guys cost money, maybe a draft pick, and nothing else. All of them could be helping in the Bronx in some way.Yankees pitching has been an issue more in-your-face than the W.B. Mason ad on the right-field wall in Yankee Stadium. New York is 14th in MLB in starter ERA, a number that is skewed by the team’s use of openers for nine games this season (12 2/3 innings).J.A. Happ hasn’t pitched to his $17 million-per-year contract. James Paxton, expected to be a great No. 2 or a supplemental ace to Luis Severino, is having a career-worst year. Masahiro Tanaka’s ERA is flirting with 5.00. Not great, Bob!It’s a tradition as old as Monument Park, wearing pinstripes and shaving one’s beard: the Yankees not getting impact starting pitching at the deadline. Just look at some of their deadline acquisitions since 2000, without context:Jeff WeaverShawn ChaconJ.A. HappJaime GarciaSonny GrayLance LynnEsteban LoaizaIn 2019, it’s irrational to expect the Yankees, who have operated under strict self-imposed financial limitations for some time, to overpay (in cash and/or prospects) for pitchers who may or may not make a difference in a run to the World Series. Sure, other teams have to operate and negotiate in good faith, too, and any proposals that included starting second baseman Gleyber Torres would rightfully have been non-starters. Here’s the thing, though: The A’s, Diamondbacks, Mets and Reds — teams with worse records than the Yankees — traded for the likes of Bauer, Leake, Roark, Stroman and Zac Gallen at the deadline and didn’t give up a lot. Of the prospects moved in those deals, only two of them were in MLB Pipeline’s top 100 (Taylor Trammell and Seth Beer). So either Cashman was being slammed with a hefty “Yankee tax” by other teams looking to deal starting pitching, or the organization wasn’t committed to getting a deal done, either for fear of emptying the farm and mortgaging the future or because it didn’t care whether it made a deal.Brian Cashman explains why the #Yankees didn’t make a big trade at the deadline.#YANKSonYES pic.twitter.com/tu3oLarm6v— YES Network (@YESNetwork) July 31, 2019The Astros traded for Aaron Sanchez and Joe Biagini just before the deadline, and then at the last minute brought in an ace for a third straight season — this time, it was Zack Greinke. Houston gave up three of its top five prospects to get Greinke, sensing the need to — get this — not be content with its current roster and rotation as the team tries to win it all. There’s a concept.Identifying a weakness and fixing it is part of what separates championship teams from just good teams.GREINKE TRADE GRADES: Houston wins big, againYankees executives saying that they want to make a run at a championship and that they believe in improving their team while also playing keepaway with prospects and feigning an empty wallet is a bad look. Cashman has always said his job is to find players who are better than the ones currently on the roster, and to his credit, he appears to have tried this summer, but to think no one would have been interested in what the Yankees were offering seems far-fetched.The Yankees can preach fiscal responsibility, which has worked for them, to a point. They can preach building through the farm system, which they have done. But they definitely aren’t broke, and their major league core — which includes Torres, Aaron Judge and Gary Sanchez — was going to remain intact. Fans are smarter than ever; they know what’s happening. Emptying the farm for starting pitching help, or bullpen help, at this point in the season is what winning teams do. (See Houston above.)Assuming that Luis Severino, Dellin Betances and Jonathan Loaisiga will all return this season — and be healthy and effective — is being irresponsibly shortsighted. The organization should not preach depth and potential while, in the same breath, deciding not to make key upgrades to improve the pitching staff.