Chaos.

Here are the American League standings on the morning of August 25th, after the Royals had lost seven games in a row, including five games at home against the White Sox and Marlins:

TEAM          W   L    GB

DETROIT      76  53   ---

TAMPA BAY    74  53   ---

TEXAS        75  54   ---

BOSTON       76  55   ---

OAKLAND      72  56   ---

CLEVELAND    70  59   2.5

BALTIMORE    69  59   3.0

NEW YORK     68  61   4.5

KANSAS CITY  64  64   8.0

The Royals had the ninth-best record out of 15 AL teams. They were as close (eight games) to the 13th-place Toronto Blue Jays as they were to a playoff spot, as represented by the A’s, who at the time held onto the second wild card.

I don’t have the ability to search ESPN’s playoff odds day-by-day, but Baseball Prospectus’ playoff odds are now available at MLB.com, and you can see how each team’s odds have gone up or down all season. On the morning of August 25th, the Royals’ playoff odds dropped to 0%. I assume they’re just rounding down, which means their actual odds were less than 0.5%.

Here are the standings right now:

TEAM          W   L    GB

BOSTON       89  59   ---

OAKLAND      85  61   ---

DETROIT      84  62   ---

TEXAS        81  64   ---

TAMPA BAY    79  66   ---

NEW YORK     79  68   1.0

CLEVELAND    78  68   1.5

BALTIMORE    77  69   2.5

KANSAS CITY  77  69   2.5

Baseball Prospectus’ odds for the Royals are now at 4.2% – and they were at 5.6% before the Rays – thanks for nothing, Wil Myers – won last night.

ESPN has the Royals’ odds at 12.8% (now down to 11.8% after the Indians took advantage of their schedule with another win against the White Sox this afternoon). If memory serves, those odds were around 3% when the Royals bottomed out three weeks ago.

So while the precise probability that the Royals are playoff-bound may differ between different models, they all agree that their odds have soared – somewhere between four-fold and ten-fold – in three weeks. They’ve roughly tripled just in the last week, since James Shields became the first starter in recorded history to give up 14 hits and not get out of the fourth inning.

This sudden wave of playoff excitement has come on awfully fast, is what I’m saying. And as much credit as the Royals rightfully deserve for it, at least as much credit has to go to Tampa Bay, without whose collapse none of this is possible.

Prior to the Rays’ win yesterday, the Royals had made up 8.5 games on the Rays in 18 days. That is an extraordinary pace. Consider that two years ago, when the Rays were themselves the beneficiary of a historic collapse by the Red Sox in September, they made up 8 games in 21 days to tie the standings. Meanwhile, the Cardinals made up 8.5 games in 22 days to do the same on Atlanta. (Of course, both Tampa Bay and St. Louis tacked on another game in another day, when both teams won game 162 while the Sox and Braves lost.)

The problem, of course, was that the Royals were 10.5 games behind Tampa Bay when this comeback started. The other problem was that there were no less than six teams between the Royals and Rays at the time – and while the Rays have dropped behind Texas, Boston, and Oakland, that still leaves three teams between the Royals and Rays. The Royals finally caught the Orioles yesterday, which means that they’ve gone from the ninth-best record in the league to…tied for eighth.

The Royals have closed what was a dispiriting gap between them and the other contenders. But all they’ve done, to this point, is put themselves in the mix of a wild five-teams-for-one-spot finish.

It’s actually somewhat more exciting than that, because the Rangers’ recent swoon puts them 4.5 games ahead of the Royals, and unlike the Rays, Texas still has games against the Royals – three in Kansas City next weekend. Sweep those games and the Royals would be 1.5 games behind the Rangers. So it’s basically six teams for two spots.

At this point, the greatest obstacle for the Royals isn’t the distance, it’s the traffic. (Apologies to whoever I stole that line from.) Two-and-a-half games to make up is doable if you’re only chasing one team, because you have two paths to victory – play really well, or play just okay while they play terribly. In 2011, the Rays were 17-10 in September, and just 6-4 in their last 10 games. The Cardinals were a little better at 18-8 and 7-3, but they went just 4-3 in the season’s final week. But each team was only chasing one team, and when that team collapsed they were in.

The Rays may continue to play terribly, but if they do, they very quickly won’t be the team the Royals are chasing. SOME team, whether it’s the Indians, the Rays, or the Yankees, will play well over the last 16 games of the season – and the Royals need to be at least one game better than the best of them just to force a tie. Realistically, the Royals need to go at least 12-4 if they’re going to play any more games after September 30th.

But I think a lot of fans would have taken that scenario at the start of the year – that a 12-4 finishing kick would lead to extra baseball, even if it just meant a wild card game or even a tiebreaker game just to get into the wild card game. Hell, I probably would have taken that.

I didn’t think the Royals would be in this position with 16 games left, and it’s fair to ask myself if I missed something in my analysis. But here’s the thing – the Royals are exactly where I expected them to be. They’re doing it differently than I thought – less offense and more run prevention – but before the season I made the formal prediction that they’d win 86 games, and right now they’re on pace to win 85.4 games.

So I don’t think I’ve misjudged the Royals. I might have misjudged the wild card race, though. My assumption was that, based on the quality of the other teams in the AL, that it would take at least 90 wins to make the playoffs – and that was before you account for the fact that the Astros changed leagues. Adding the Astros ought to make the playoff standards even higher, for two reasons:

1) When you add more teams but keep the number of playoff spots the same, the standards to be a playoff team go up, in the same way that it’s a lot harder to finish in the top 10 of your graduating high school class when there are 306 kids in your class instead of 17.

2) The Astros are such a bad team that they single-handedly improve the winning percentage of the other 14 teams in the league. The Astros are on pace to finish 55-107; accounting for the 18 intraleague games, that means that the average AL team would pick up 1.62 additional wins from playing the Astros. (Obviously the exact number depends on how many times you played them – AL West teams would pick up more wins, AL Central and East teams less.)

So I figured it would take 92 wins to make the playoffs. If that’s the case, the Royals would need to go 15-1 to get there. I remember Rocktober 2007 well enough to say that’s not impossible, but it’s not something worth believing in either.

And here’s the thing: three weeks ago, it looked like it would take 92 wins. The last playoff spot at the time was held by the A’s, who were on pace for 91.1 wins. Factor in the chance that someone could have caught the A’s from behind, and 92 wins seemed like a fair bet.

Except now, the Rays are clinging to that final wild card spot, and they’re on pace for 88.3 wins. Given the sheer number of teams right behind them, chances are someone will get a little hot down the stretch – but there just aren’t enough games left for that number to go up much higher.

My former colleague Clay Davenport, who was there when we founded Baseball Prospectus back in 1996, and was (I believe) the first person to ever use Monte Carlo simulations to project postseason odds, continues to do so at his own website. Clay adds an interesting wrinkle, which is that he also posts the average number of wins by whatever team wins each division as well as both wild card spots. This gives you an idea of what number to shoot for.

According to Clay, whatever team wins the second AL wild card averages around 88.9 wins. The first AL wild card averages 90.8 wins. Round those up to 89 and 91. 12-4 gets the Royals to 89 wins. That’s a difficult road, but it’s not impassable, or impossible. Hell, 14-2 might get the Royals to host the wild card game.

Three wins doesn’t sound like much, but this time of year, it’s the difference between difficult and impossible. The Royals have caught a break in that the standards to make the playoffs in the AL have suddenly lowered. They’re going to need a few more breaks to take advantage of the first one. This journey is still probably coming to an end sooner rather than later. But let’s enjoy every moment of it as long as we can.