How much have the Yankees’ recent struggles cost them?

After a devastating weekend in Boston, the Yankees have recovered nicely. They are working through a smooth slate of games against bad teams, and a sweep of the White Sox got the team back on its feet. The bad taste of last week, though, still lingers.

The four-game sweep at the hands of the Red Sox that wrapped up a five-game losing streak will be remembered as a turning point of sorts. It left the Yankees 9.5 games back in the AL East, and pushed them closer to the American League’s other wild-card contenders. Moreover, the Yankees just seemed rudderless, with a battered rotation, an injured lineup, and no positive forward thrust to speak of.

It’s easy to get swept up in the emotions of it all. Losing sucks in general, but watching your team lose in crushing fashion to an arch-rival is among the worst feelings in sports. Combine the defeats in Boston with Sonny Gray’s demotion and questionable Twitter activity and J.A. Happ’s odd illness, and it was just a bad week to root for the Yankees.

Life goes on, though, and the Yankees have kept moving too, as evidenced by their better play this week. Now that the bitter memories of a nightmare in New England have been put aside a bit, it’s fair to ask: just how much did the Yankees lose last week? They lost five games, that’s to be sure, but what was the actual, concrete damage done to their overall hopes for the season? We can turn to playoff odds to get a more definitive answer.

In terms of the Yankees’ chances of simply qualifying for postseason play, they haven’t lost much. On July 31st, prior to embarking on their unsightly five-game losing skid, the Yankees had a 100% chance of making the playoffs by FanGraphs’ estimation. Baseball Prospectus’ PECOTA projections mostly agreed, giving the Yankees a 99.8% chance.

Now, ten days later, FanGraphs and BP both give the Yankees a 99.9% of making the postseason. The Yankees’ losing streak was devastating, but it didn’t actually make them any less likely to make it to October.

No, where the Yankees cost themselves was in World Series odds. Going back to the last day of July again, FanGraphs gave the Yankees a 12.4% chance of winning it all, fourth-best in all of baseball. Today, they have a 9.5% shot. BP initially gave the Yankees a 10.2% of winning the World Series, but now gives them a 7.9% chance.

That drop in odds obviously comes from the fact that the Yankees are now highly likely to play in the do-or-die wild-card game. The Yankees should be favorites in any one-game playoff, but simply having to participate in such a game is a deterrent to the Yankees hopes of capturing a championship.

Still, the upshot is that what the Yankees lost last week, in cold, calculating terms, is a few percentage points of World Series odds. The process may have been miserable, and the stink surrounding the team may have been pungent. But the Yankees are professionals, and any malaise they were stuck in over the weekend isn’t likely to stick. They will push through. They’re not dead, as evidenced by the projections still giving them a fine shot to win it all.

In fact, there’s even a silver lining to gleam from the forecasts. I find this chart, courtesy of FanGraphs, to be both enlightening and encouraging:

These are the World Series odds for the Yankees and Red Sox juxtaposed. You'll notice that it wasn’t until the past week that the Red Sox definitively pulled away. Before the Yankees went on their losing streak, they actually had higher title odds than the Red Sox did, 12.4% to 12.0%, despite trailing Boston by five games.

This suggests that even with all the struggles of the past few weeks, and all the dominance on display by the Red Sox, the Yankees are probably still as good as anyone strictly in terms of true talent, at least according to the projections. FanGraphs liked the Yankees’ roster enough to give them better odds to win the World Series than the Red Sox in spite of a substantial division deficit.

So while the Yankees did cost themselves last week, they probably didn’t lose quite as much as it felt they did. The AL East is unlikely to come back to New York this year, which is the primary damage the Yankees did to themselves. Yet they are still talented and alive, in with better than a puncher’s chance. The Yankees lost a few battles, but the war still rages.