Playoff Probability Leverage for Week 12

[Stryker44]

Yeah, this doesn't look like the year for a 10-win team not to make the playoffs. Through 10 games, only 3 NFC teams have 7 wins.

Except one team in the NFC East is going to get dicked over by having a better record than a division winner, and not make the playoffs.

 

[JD_KaPow]

Probability and certainty are defined differently. You may consider perusing magic numbers to clinch etc.

Uh, no they're not. Certainty is defined as 100% probability. From Wikipedia: "Probability is the measure of the likelihood that an event will occur.[1] Probability is quantified as a number between 0 and 1 (where 0 indicates impossibility[2] and 1 indicates certainty)."

If the Cowboys beat Washington tomorrow, there are still scenarios that exist in which Dallas fails to make the playoffs. Those scenarios are highly improbable, but not impossible.

 

[gmoney112]

Wow, that Vikings/Lions game is huge. Should be a good game.

The Vikings trading a #1 for Bradford was one of the dumber decisions this year, especially when they may not even make the playoffs. I get winning "now", but take the lumps this year, get healthy, and having top 5 picks in each round of the draft would have set the Vikes franchise up for years. Now they don't even have a first rounder. Pretty stupid.

 

[jobberone]

Uh, no they're not. Certainty is defined as 100% probability. From Wikipedia: "Probability is the measure of the likelihood that an event will occur.[1] Probability is quantified as a number between 0 and 1 (where 0 indicates impossibility[2] and 1 indicates certainty)."

If the Cowboys beat Washington tomorrow, there are still scenarios that exist in which Dallas fails to make the playoffs. Those scenarios are highly improbable, but not impossible.

You appear confused. The likelihood of an event occurring if not the same as certainty of it. The probability value is somewhere between 0 and 1 where 1 is certainty. A 100% probability is not the same as it being certain or if you must 100% certain.

For example, it appears probable the Cowboys will clinch a playoff spot in the near future (2016); that is a probability. There's a 100% chance of rain today.....looks outside and the sun is shining with no rain. Later it rains.

The Cowboys clinched a playoff spot today....as an example. That is a certainty or a fact; when it happens.

 

[JD_KaPow]

You appear confused. The likelihood of an event occurring if not the same as certainty of it. The probability value is somewhere between 0 and 1 where 1 is certainty. A 100% probability is not the same as it being certain or if you must 100% certain.

One of us is confused, I'll grant you that. Stating that there is a 100% probability that something will occur is in fact the same as being certain that it will occur. By definition. If the thing does not in fact occur, then the original statement was erroneous.

For example, it appears probable the Cowboys will clinch a playoff spot in the near future (2016); that is a probability.

Correct.

There's a 100% chance of rain today.....looks outside and the sun is shining with no rain. Later it rains.

Okay...so?

The Cowboys clinched a playoff spot today....as an example. That is a certainty or a fact; when it happens.

Okay...so? The moment at which the Cowboys clinch a playoff spot is the moment at which the probability of them clinching a playoff spot reaches 100%. Before that moment, there are scenarios that exist in which they fail to make the playoffs, meaning that the probability of them reaching the playoffs is less than 100% until that moment. "Clinching" is, by definition, the point at which every possible path that remains leads to the playoffs.

 

[Prossman]

This team will probably drop a game or two but not much more than that. much to the medias distain. They a for real and very good just keep taking care of business ad no one can stop it.

 

[Proximo]

All numbers aside, bottom line is tomorrow's game is huge in terms of us pulling away from the pack vs getting pulled back in.

I really really think a win tomorrow will put us in great position to end up with the 1st seed. I know that may sound premature but it's going to be very hard for any team to catch us if we have 10 wins with 5 games left to play considering the lead we have on everyone else in the conference.

 

[jobberone]

One of us is confused, I'll grant you that. Stating that there is a 100% probability that something will occur is in fact the same as being certain that it will occur. By definition. If the thing does not in fact occur, then the original statement was erroneous.Correct.
Okay...so?
Okay...so? The moment at which the Cowboys clinch a playoff spot is the moment at which the probability of them clinching a playoff spot reaches 100%. Before that moment, there are scenarios that exist in which they fail to make the playoffs, meaning that the probability of them reaching the playoffs is less than 100% until that moment. "Clinching" is, by definition, the point at which every possible path that remains leads to the playoffs.

We'll just have to agree to disagree.

 

[Eric_Boyer]

One of us is confused, I'll grant you that. Stating that there is a 100% probability that something will occur is in fact the same as being certain that it will occur.

"Almost Surely" is the concept being discussed. A probability of 1 is not the same as something always happening.

So no, 100% probability is not the same as being certain.

 

[JD_KaPow]

"Almost Surely" is the concept being discussed. A probability of 1 is not the same as something always happening.

So no, 100% probability is not the same as being certain.

Wow.

When you calculate the odds of making the playoffs, 100% probability is absolutely the same as being certain. If there is a single path (set of game outcomes) that leads to a team not making the playoffs, the odds of them making the playoffs are necessarily less than 100%. That path may be incredibly unlikely, but that doesn't matter: there is still some non-zero probability of it happening.

If we're talking about the existential sense, in that they may not make the playoffs because global thermonuclear war causes the playoffs not to be played, then sure, whatever, but that just means that the probability is less than 100%. And I assume that's not what we're talking about here anyway. We're talking about the conditional probability that, given that the playoffs are played, the Cowboys will be in them. And that probability is less than 100% right now, and it will be less than 100% after tomorrow's game.

"Almost surely" is not a probability of 1. It's a probability of less than 1. That's what the "almost" part means.

These calculations are not difficult. And I can assure you that the number Burke has calculated is less than 100%. Not much less, but less. Because he knows how to do math.

 

[pancakeman]

Wow, that Vikings/Lions game is huge. Should be a good game.

The Vikings trading a #1 for Bradford was one of the dumber decisions this year, especially when they may not even make the playoffs. I get winning "now", but take the lumps this year, get healthy, and having top 5 picks in each round of the draft would have set the Vikes franchise up for years. Now they don't even have a first rounder. Pretty stupid.

I initially thought it was stupid, then later thought I was stupid for thinking it was stupid. But now I realize I was stupid for thinking I was stupid for thinking it was stupid.

 

[gmoney112]

I initially thought it was stupid, then later thought I was stupid for thinking it was stupid. But now I realize I was stupid for thinking I was stupid for thinking it was stupid.

 

[SlammedZero]

Obviously we want HFA-- but tbh, going on the road doesn't mean we're screwed. Even if Seattle were to win the #1 seed, I wouldn't count this Dallas team out. This team rises to the challenge, and a good ground game always travels well.

This is what I have been saying and people look at me like I'm crazy. Yes, of course you want to be home, but this team on the road just doesn't make me nervous. So, if push comes to shove, I believe this Cowboys team can still steal one on the road in the playoffs.

 

[Toruk_Makto]

If that's true, then 10 wins shouldn't be 100% playoff berth as the original post states.

Sure. But it also depends on how you look at things. What the OP's model is doing is not just looking at 10 wins and saying is that enough to make the playoffs. It's saying what is the projected number of wins for a team that has 10 of them in their 1st 11 games. Then when they find that projected number of wins they then look at what is the likelihood that...those number of wins makes the playoffs. For the Cowboys they are saying that it would be "certain."

Also if you're still a skeptic and want to use history as a guide...we clinched when we went 8-1. And based on history we win an about 13 games this season.

The takeaway should be that we're in great shape regardless of Thanksgiving's outcome.

http://fivethirtyeight.com/features/crunch-time-of-the-nfl-season-is-right-now/

 

[Sarge]

Some people cannot differentiate between possibility and probability.

Thank you! I was thinking the exact same thing.

 

[Broges74]

Wow, that Vikings/Lions game is huge. Should be a good game.

The Vikings trading a #1 for Bradford was one of the dumber decisions this year, especially when they may not even make the playoffs. I get winning "now", but take the lumps this year, get healthy, and having top 5 picks in each round of the draft would have set the Vikes franchise up for years. Now they don't even have a first rounder. Pretty stupid.

We got zeke and crew by taking the stand pat route besides the Butler and Cassell trades which weren't high picks .

 

[Eric_Boyer]

Wow.

When you calculate the odds of making the playoffs, 100% probability is absolutely the same as being certain. If there is a single path (set of game outcomes) that leads to a team not making the playoffs, the odds of them making the playoffs are necessarily less than 100%. That path may be incredibly unlikely, but that doesn't matter: there is still some non-zero probability of it happening.

If we're talking about the existential sense, in that they may not make the playoffs because global thermonuclear war causes the playoffs not to be played, then sure, whatever, but that just means that the probability is less than 100%. And I assume that's not what we're talking about here anyway. We're talking about the conditional probability that, given that the playoffs are played, the Cowboys will be in them. And that probability is less than 100% right now, and it will be less than 100% after tomorrow's game.

"Almost surely" is not a probability of 1. It's a probability of less than 1. That's what the "almost" part means.

These calculations are not difficult. And I can assure you that the number Burke has calculated is less than 100%. Not much less, but less. Because he knows how to do math.

https://en.wikipedia.org/wiki/Almost_surely

In probability theory, one says that an event happens almost surely (sometimes abbreviated as a.s.) if it happens with probability one.

The difference between an event's being almost sure and sure is the same as the subtle difference between something that happens with probability 1 and that happens always.

 

[JD_KaPow]

https://en.wikipedia.org/wiki/Almost_surely

In probability theory, one says that an event happens almost surely (sometimes abbreviated as a.s.) if it happens with probability one.

The difference between an event's being almost sure and sure is the same as the subtle difference between something that happens with probability 1 and that happens always.

Well, learn something new every day. You are correct about that (and thanks for the link). However, from the same article:

"In probability experiments on a finite sample space there is no difference between almost surely and surely, but the distinction becomes important when the sample space is an infinite set (because an infinite set can have non-empty subsets of probability zero)."

Determining whether teams make the playoffs depends on the outcomes of a finite (and quite small) number of games, so the distinction does not apply here. The Cowboys will not have a 100% chance of making the playoffs until they actually clinch a playoff spot.

 

[Kevinicus]

Interesting, though I would think Min and Detroit would be flipped considering if Detroit wins they would have the lead and the head to head tie breaker over Minnesota. That woulf hurt Min's chances immensely. On the other hand if Detroit loses, Min eoulf have the lead, but not the tie breaker. Much easier for Detroit to overcome.

Then you add in the fact that Min lost to Washington and Detroit beat them and the odds for Detroit on a wild card should be better as well. I am curious of what these probabilities are based on.

 

[NextGenBoys]

It's not really 100% (we won't have clinched anything). Even with a win tomorrow, it's still possible for the Cowboys to finish last in the NFCE.

Its possible, but incredibly improbable. Not really realistic.