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Clearing up the AL postseason picture

Let's get this American League postseason situation settled, shall we?

Technically, we've still got the AL West on the line and four teams eligible for two Wild Card spots with four days to play.

That sounds, um, complicated. Thankfully, the extreme mathematical probabilities insist it's less complicated than that, but not by much, really. At least we know that, by the end of the weekend (weather permitting), we'll either have complete clarity or one of the many, brain-shaking tiebreaker scenarios (those are covered here).

Here's the situation for each club still in the hunt:

Rangers (86-72)
Position: +2.5 games in the AL West
Chance of reaching postseason: 97 percent
Remaining schedule: Thursday through Sunday vs. Angels

As long as Texas wins one game against the Angels this weekend, it'll eliminate the Angels from the West picture, and ensure the Rangers of at least a Wild Card berth. And any combination of Rangers wins and Astros losses that adds up to two would take care of Houston. It would take an epic collapse for Texas to lose the West.

Video: DET@TEX: Fielder pads the lead with an RBI single

Yankees (86-72)
Position: +2.5 games for top AL Wild Card spot
Chance of reaching postseason: 99.5 percent
Remaining schedule: Thursday vs. Red Sox, Friday through Sunday at Orioles

The Yanks could have clinched a spot in the AL Wild Card Game presented by Budweiser had they defeated Boston on Wednesday night. Alas, they lost in extras. But the chances of the Yankees not only playing in that game but hosting it are very strong.

One more win, and the Yankees are in. Any combination of Yankee wins and/or Astros losses that adds up to two will ensure the Astros can't host the Wild Card Game, and the same "elimination number" applies to the Angels.

Simply because the mathematical odds of the Yankees hosting the Wild Card Game are so strong, the rest of this piece will operate on the premise that the Yankees are the AL's fourth seed and that only the AL West title and the fifth and final seed are up for grabs.

Video: BOS@NYY: Girardi discusses bullpen, not clinching

Astros (84-75)
Position: Half-game ahead of Angels for second Wild Card, 2.5 games back of Rangers in AL West
Chance of reaching postseason: 68.9 percent
Remaining schedule: Off Thursday, Friday through Sunday at D-backs

Unfortunately, the Astros are in a position in which they're playing a monumental season-ending series without the designated-hitter slot. But taking Wednesday's series finale at Safeco Field was huge, as it put them back in a postseason position. If they sweep the D-backs this weekend, they assure themselves of a Wild Card spot, at the very least.

The craziest scenario involving this club would be a sweep of the D-backs combined with an Angels sweep of the Rangers, which would create an Astros-Angels tie atop the West and necessitate a Monday tiebreaker. The Astros would host it, by virtue of their 10-9 record head-to-head, and the loser of the game would go to the Wild Card Game. The only other possibility for a West tie would be an Astros sweep of the D-backs combined with the Rangers losing three of four vs. the Angels. The Rangers would host that tiebreaker, by virtue of their 13-6 record vs. Houston.

Now, let's say the Astros don't sweep. If they lose one of three, they need the Angels to lose at least one of four in Texas (creating a tiebreaker, which the Astros would host) and the Twins could do no better than a tie (the Twins and Astros split their season series, so home-field advantage should they meet in a tiebreaker would go to the team with the better intradivision record). If the Astros lose two of three, they need the Angels to do no better than a split and the Twins to lose at least one of their final four. If they get swept by Arizona, they need the Angels to lose three of four and the Twins to lose at least two of four.

Video: HOU@SEA: Carter ties it with three-run blast in 6th

Angels (83-75)
Position: Half-game behind Astros for Wild Card spot and three games back of the Rangers in AL West
Chance of reaching postseason: 30.9 percent
Remaining schedule: Thursday through Sunday at Rangers

Wednesday's late-inning loss to the last-place A's darn near killed the Angels' chances of running down the Rangers. Nothing short of a four-game sweep in Arlington this weekend will get it done (and even then, they'd need the Astros to lose one of their final three to avoid a tie atop the division). But hey, better to have that possibility on the table than otherwise.

Even if the Angels go 3-1 this weekend, they'll need the Astros to lose at least one of their final three in Arizona in order to avoid elimination. In that scenario, the Twins would have to win out just to force a tie.

Dropping two or more of the four would obviously put the Angels in a much more dicey spot, perhaps holding out hope for a tiebreaker. As far as home-field advantage in a tiebreaker is concerned, the Angels hold the head-to-head edge on the Twins but, as mentioned above, not the Astros.

The good news for the Angels is that they've won 10 of their last 13 games, and they've played the Rangers very well this season, winning 10 of 15.

Video: OAK@LAA: Trout's shot to center gets Angels on board

Twins (82-76)
Position: 1.5 games back of Astros for second Wild Card
Chance of reaching postseason: 3.7 percent
Remaining schedule: Thursday at Cleveland, Friday through Sunday vs. Royals

Minnesota is the club that can really cause chaos when it comes to tiebreakers. But that's the basic point: The Twins could win out and still not necessarily be assured a postseason spot.

To be totally assured of a spot in that 4-0 scenario, they'd need the Angels to lose at least three of four against the Rangers and the Astros to lose at least two of their final three.

If the Twins win three of their final four, to be assured of a spot they'd need the Angels and Astros to get swept. If they split their final four, the absolute best they can do is a tiebreaker. And if they lose three or four of these remaining games, well, it's been an unexpectedly fun ride, all the same.

Video: MIN@CLE: Buxton crushes solo homer to right center

Now, regarding those tiebreakers. If the Twins win out, there are multiple ways a tiebreaker could occur. We would have a two-way tie if the Angels went 3-1 AND the Astros lost two or more OR if the Astros go 2-1 AND the Angels lose two or more. We would have a three-way tie if the Twins go 4-0, the Astros go 2-1 and the Angels go 3-1.

There are other tiebreaker scenarios if the Twins win three of their final four, but you get the idea. And again, the tiebreaker procedures are covered here.

Anthony Castrovince is a reporter for MLB.com. Read his columns and follow him on Twitter at @Castrovince.