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Number Theory: A Probability Guide to the Texans' Playoff Seed

How many of you remember high school math classes? Do you remember that one guy who would always sit in the far back and act like he was really interested in that day's lesson...until the teacher turned his/her back on him? Remember the faint (or not so faint) rumble of snoring radiating from that guy's desk as you stared numbly at a blackboard that had formulas and equations so elaborate and confusing that they might as well have written them in Tlingit?

Yeah, sorry about that.

As nice as it was to get a nap in that day, I really wish I'd stayed awake for that lesson on probability and odds. One, because maybe I wouldn't lose so much money at the casino once every five years when I can actually afford it, and two, because if I had, maybe I would not have spent so long (and destroyed so many sheets of paper in the process) figuring out just what kind seed the Texans could expect to have in this year's playoffs.

After hours of working out the odds, I present to you, my fellow fans and "math aficionados" (seriously SBN, the sooner we can write in sarcasm font, the better), the general seeding odds for your 2011-12 Houston Texans.

But before we jump, I would first like a moment of silence for the forest that died so that this post may live.

//drunk guy yells, "Woo!"

Thank you. On to the guide!

First the parameters.

Since the Texans are division winners (it still feels good to type that), they cannot finish the season with anything lower than a fourth seed. This guide focused specifically on the games remaining for the Patriots, Ravens, Steelers, and Broncos, since those are the only teams who have a snowball's chance of clinching or have already clinched their division.

With two games left, there are four possible outcomes for the Texans:

Win both games.
Win vs. Indy/Lose vs. Southern Kentucky.
Lose vs. Indy/Win vs. Southern Kentucky.
Lose both games.

The remaining schedule looks like this for all the teams involved:

Texans - @Colts, v.BE-SFs
Ravens - v.Browns, @Bengals
Steelers - v.Rams, @Browns
Patriots - v.Dolphins, v.Bills
Broncos - @Bills, v.Chiefs

These, in turn, give us potentially 375 different playoff possibilities (more on that later).

Let's start with the first scenario, and the one that I think is most likely to happen.

Texans Win Out

If the Texans win out, there is zero chance of them getting a four seed; the worst they could finish is third. Of the 64 possible endings to the season in this scenario, 60 of them would result in the Texans having a bye in the first round, or a 93.75% chance. Of those 60 endings, 44 of them would have the AFC's road to the Super Bowl go through Reliant Stadium.

The 16 outcomes that have the Texans claiming the second seed have either the Patriots or the Ravens, but not both, winning the rest of their games.

The one downside is every one of those 44 outcomes would require the Patriots and/or the Ravens to lose at least one game. The four outcomes where the Texans would have the three seed have the Patriots and Ravens also winning both of their remaining games. We don't want that to happen.

If you want to bypass the pithy commentary and just percentages, then here, enjoy. I'll just sulk in the corner until you're done.

64 Outcomes Possible:

1 Seed 44/64 - 68.75%
2 Seed 16/64 - 25%
3 Seed 4/64 - 6.25%
4 Seed 0/64 - 0%

Win Some Lose Some

As you can tell from the clever title, this assumes the Texans win one of their two remaining games. Probability-wise, there is absolutely no difference between whether the Texans lose to the Colts (pause for riotous laughter) or the Traitors, so they will be lumped together into one scenario. In this scenario, the Texans' chances for getting a bye week, let alone the top spot overall, take a serious nosedive. Since this takes the outcomes of two games into consideration, there are a total of 128 possible outcomes.

Of those outcomes, a scant 18 of them end up with the Texans receiving the number 1 seed in the playoffs. All of these outcomes are contingent on the Patriots losing to both Miami and Buffalo. As bad as New England's defense may be, I just can't imagine them losing both of those games, especially with what's still at stake.

Interestingly enough, the Texans' odds of getting a two seed don't really change much. In fact, they get just a hair better if they do lose one game. 34 of the 128 outcomes would result in a Texans two seed.

The biggest change comes in the likelihood of the Texans getting the three seed. 78 out of 128 outcomes give the Texans their first home game against the sixth seed. But that's the worst the Texans can finish in this scenario. Again, there is no way they can get the fourth seed in this case.

128 Outcomes Possible

1 Seed: 18/128 - 12.5%
2 Seed: 34/128 - 26.5%
3 Seed: 78/128 - 61.0%
4 Seed: 0/128 - 0%

The Nightmare Scenario

To be honest, if the Texans lose their last two games, they're going to have a lot more to worry about than just what playoff seed they'll get. They would have no momentum going into the wild card round, losing to two teams with a combined record, at this moment, of 8-20.

In this situation, any hope of getting a first-round bye has completely gone out the window. Anything the Steelers, Ravens, and Patriots do in this scenario becomes irrelevant to the Texans' playoff seed. No matter what these teams do, it will have no impact on which seed the Texans pick up.

The Broncos, on the other hand, would make a difference in where the Texans end up, and not for the better. With the Broncos as a factor, this raises the number of potential outcomes to 183 possibilities.

Basically it comes down to this: If the Texans were to lose to the Colts and the professional football team from Nashville, and Denver won both of its remaining games, the Broncos would get the third seed and the Texans would have the last division winner's spot as a four seed.

The nauseating part of this scenario, aside from losing out, is that this outcome occurs 61 out of 183 times; or more simply, 1/3 of the time.

The one bit of solace is I think this is probably the least likely outcome of the bunch. Also, if we can't beat the Colts and Traitors, the latter at home, then I'd say we simply wouldn't have deserved one of those first-round byes. Anyway, more numbers!

183 Outcomes Possible

1 Seed: 0/183 - 0%
2 Seed: 0/183 - 0%
3 Seed: 122/183 - 67%
4 Seed: 61/183 - 33%

On Thursday night, we can safely eliminate half of these outcomes. But as of right now, here are the cumulative, and very unofficial, playoff seeding odds:

375 Outcomes Possible

1 Seed: 62/375 - 16.5%
2 Seed: 48/375 - 12.8%
3 Seed: 204/375 - 65%
4 Seed: 61/375 - 16.3%

Next week, we'll recalculate the odds and see if the Texans can land that first-round bye, or if they're running head-first toward the nightmare scenario.

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