how impossible is this? for math majors

[Hardboiled]

... if a team is expected to go 16-0, then their odds to go 16-0 are 1.000. In other words, this extreme example with its obvious results shows the meaningless of such reasoning.

Not the odds - the probability. Odds and probability are different representations. Under this example you are Certain is win every game. The odds are 1/0, which in math is undefined.

Odds gets thrown around a lot when the person means probability.

The probabilty of me pulling an ace out of a deck is 4/52.

Desired outcome/total outcomes

The odds are 4/48.

Desired outcomes/undesired outcomes.


As posters have noted, to attempt to be more acccurate, one would have to assign probilibities to every game. That would include team personnel, records, home field, strengths, weaknesses, more intangibles like pressure of being 13-0 or an opposing team being fired up. You can assign values to such things, but your values may be different some someone elses.

When someone says, I think Team A will catch Team B off guard, they are putting a value on something, over other things like record or personnel.

 

[PatsFaninAZ]

unless im mistaken, arent the 85 bears the only team to go 18-1 ever?

49ers, I think. The year before.

 

[psychoPat]

And if it came to that (which it won't),
the 49ers' and Bears' 18-1 seasons

would be a lot better than
a Patriots' 18-1.

 

[PatsFaninAZ]

I think the math is causing more confusion not less here.

What question exactly is being asked here? Is it "what is the probability that a team will go 19-0"? Let's say the methodology is correct -- that the way to figure that out is to figure out the probability of each of the 19 outcomes and then multiply.

Many people seem to think this can estimated -- for example, one can estimate that we had a .85 probability of beating the Browns.

But when? The probability changes minute to minute. Second to second.

For example, the probability that we would go 19-0 was extremely low when it was 4th down on the last drive in the Baltimore game. Similarly, it was extremely low when we were down to the Giants by 11 points. Whether it was lower than at the beginning of the season is tough to say. Similarly, whatever win percentage you might have had for week 7 during week 1 might change dramatically if our opponent's QB sustained an injury in week 3.

The probability of going 19-0 is, I would think, at the highest it's been all season right now. It should be exactly what you think the probabitliy of winning the super bowl is. But it could (and hopefully will) get higher, and certainly could go lower. Indeed, it will move after every instant of the game.

So, at the end of the day, I'm not sure the numbers help us come up with anything meaningful other than to vividly demonstrate that even for a dominant football team which is heavily favored to win each of its games, the likelihood that it will win them all is very low.

 

[jbb9s]

What are the chances that 3 teams in the same conference go undefeated and the 3rd team who doesn't get a bye wins 4 playoff games and goes 20-0?

 

[eom]

it's just idle speculation by the op to try and figure out what kind of odds the pats beat, if they end up beating them......
although, it really just ends up being a lot of undefined values and poor methodology -- not to knock the op.

it's fun to think about, I guess, and it's a long 2 weeks between games, but in the end you won't be coming up w/an accurate answer.
I'd be willing to bet on this much, however, if this same team could play together indefinitely, I don't think it would take them 454,000 more years, or whatever the original figure was, to come up w/an undefeated season.

 

[PatsWorldChamps]

49ers, I think. The year before.

really? seriously, what was the reg season record and playoff?

 

[PatsWorldChamps]

And if it came to that (which it won't),
the 49ers' and Bears' 18-1 seasons

would be a lot better than
a Patriots' 18-1.

why do you say that?

 

[PatsWorldChamps]

I think the math is causing more confusion not less here.

What question exactly is being asked here? Is it "what is the probability that a team will go 19-0"? Let's say the methodology is correct -- that the way to figure that out is to figure out the probability of each of the 19 outcomes and then multiply.

Many people seem to think this can estimated -- for example, one can estimate that we had a .85 probability of beating the Browns.

But when? The probability changes minute to minute. Second to second.

For example, the probability that we would go 19-0 was extremely low when it was 4th down on the last drive in the Baltimore game. Similarly, it was extremely low when we were down to the Giants by 11 points. Whether it was lower than at the beginning of the season is tough to say. Similarly, whatever win percentage you might have had for week 7 during week 1 might change dramatically if our opponent's QB sustained an injury in week 3.

The probability of going 19-0 is, I would think, at the highest it's been all season right now. It should be exactly what you think the probabitliy of winning the super bowl is. But it could (and hopefully will) get higher, and certainly could go lower. Indeed, it will move after every instant of the game.

So, at the end of the day, I'm not sure the numbers help us come up with anything meaningful other than to vividly demonstrate that even for a dominant football team which is heavily favored to win each of its games, the likelihood that it will win them all is very low.

when i started this thread, it was based on every team being 0-0. of course the probability changes, yeah, a 18-0 team has a good chance of going 19-0... but you will never see another 18-0 team in your life... if you wanted to compare this year to the likeliness of another team ever doing it, you have to use 0-0 teams. no one on this board will ever see 19-0 again, period... in fact, i bet the nfl will no longer exist before another 19-0 happens.

 

[Hardboiled]

the odds of you pulling an ace out of a deck are 4/52, not 4/48.

Nope. That's probability. As I wrote in the post, odds are a different calculation.

The probabilty of me pulling an ace out of a deck is 4/52. Desired outcome (4) /total outcomes (52)

The odds are 4/48. Desired outcomes (4) /undesired outcomes (48)

Odds is a comparsion (ratio) of the ways something can happen to the ways something can't happen (not the total).

People say "odds" but they are thinking probabilty (comparison using the total number of possible outcomes)

 

[Hardboiled]

i disagree. the odds of you pulling an ace are 1 in 13, or 4 in 52. odds implies payout, which would always include your original bet returned. probability does not include your wager returned.

PWC, I edited my post to explain further. If you look up probability and odds, I think you'll find odds actually means something other than what you think.

 

[PatsWorldChamps]

in an even money game (no house edge)... and you pick 1 card out of 13 (your ace)...in a break even game. so yeah, that should be called 12:1, since i am giving you your 1, plus 12 more.

 

[neuronet]

Odds and probability are different. This is explained at this math site for kids:
http://mathforum.org/library/drmath/view/56706.html

 

[PatsWorldChamps]

Odds and probability are different. This is explained at this math site for kids:
http://mathforum.org/library/drmath/view/56706.html

i agree.....

 

[makewayhomer]

really? seriously, what was the reg season record and playoff?

take a guess

15-1 Reg season, 3-0 playoffs

other teams made a run at undefeated, lost a game, then started resting guys when they clinched hfa. example is 91 Redskins, who were 14-2 but lost only 1 game with starters. Colts in 2005, 98 Broncos similar.

so, winning "all but one" has been done a couple times, and winning "all but one when you're trying" has been done a couple more.

what separates these teams from 19-0 is often a lot of luck. if you remember the 85 Bears loss to the Dolphins was a fluke-fest of tipped passes and weird plays that went the Dolphins way. the 91 Redskins 1 loss (with starters) was by 3 points to the Cowboys in a game where all kinds of little things could have changed for a Redskins win. and like I said above, if Ryan doesn't call that TO, then the Pats place in history would probably be alongside these teams

 

[crafty35a]

Why are the teams with the best records "lucky"? What about the team that finished 11-5 or 12-4 despite tons of bad luck? Wouldn't they balance off the 14-2 lucky one?

I fail to see where luck factors in at all. Even if you believe in it, it gets more than balanced off in a sample size this large.

This is just wrong. Imagine, for a moment, that each team has an equal chance of being lucky or unlucky in a given season, regardless of team quality. The lucky teams will tend to move towards the top of the standings. So MOST of the teams at the top will have been somewhat lucky, and most at the bottom will have been somewhat unlucky.

Of course it's possible to have outliers. Sure, it's possible to have a 12-4 team that was unlucky and in most seasons would have gone 14-2. It's just much less common than the reverse.

 

[Oswlek]

This is just wrong. Imagine, for a moment, that each team has an equal chance of being lucky or unlucky in a given season, regardless of team quality. The lucky teams will tend to move towards the top of the standings. So MOST of the teams at the top will have been somewhat lucky, and most at the bottom will have been somewhat unlucky.

Of course it's possible to have outliers. Sure, it's possible to have a 12-4 team that was unlucky and in most seasons would have gone 14-2. It's just much less common than the reverse.

So we should assume that all teams above 12-4 were only there because of luck? That is completely asinine. What about the 2003/2004 Patriots who were terribly unlucky with injuries yet won 14 games each season? A little luck and they might already have been 16-0.

What about the 11-5 Steelers of 2005 who lost their top 2 QBs for 2 or 3 games and Bettis for another 5 or so? Since they cruised to a title fairly easily, isn't it fair to assume that a little better luck and they were a 14-2 team?

There is absolutely no reason whatsoever to drop the probability due to some mystical "luck" factor. Hell, even if you believe it to be an important factor, that same "luck" manifests itself every single season! Will there be a season that every team has bad luck? Or GOOD luck for that matter? Of course not. So we know that a couple good teams will have good luck every year. Why should it be adjusted for again?

 

[crafty35a]

So we should assume that all teams above 12-4 were only there because of luck? That is completely asinine. What about the 2003/2004 Patriots who were terribly unlucky with injuries yet won 14 games each season? A little luck and they might already have been 16-0.

What about the 11-5 Steelers of 2005 who lost their top 2 QBs for 2 or 3 games and Bettis for another 5 or so? Since they cruised to a title fairly easily, isn't it fair to assume that a little better luck and they were a 14-2 team?

There is absolutely no reason whatsoever to drop the probability due to some mystical "luck" factor. Hell, even if you believe it to be an important factor, that same "luck" manifests itself every single season! Will there be a season that every team has bad luck? Or GOOD luck for that matter? Of course not. So we know that a couple good teams will have good luck every year. Why should it be adjusted for again?

Did you not read my post? I just said that there are obviously going to be exceptions, so this comment "So we should assume that all teams above 12-4 were only there because of luck?" is a strawman. I never said anything like that.

All I'm saying is that for the most part, true team quality is actually depressed towards the mean a bit more than you would expect if you just went by winning percentages.

YES, of course there are lucky teams every year. But statistically, what we really want is the team's true percentage chance of winning each game, which means we remove the small luck factor.

If you don't remove the luck factor, then you essentially have the possibility of a team that was already lucky getting even MORE lucky in the simulation. Which would falsely inflate the chances of a perfect season occuring.

 

[PatsFaninAZ]

really? seriously, what was the reg season record and playoff?

Are you serious? There are only two ways to go 18-1.

 

[Oswlek]

If you don't remove the luck factor, then you essentially have the possibility of a team that was already lucky getting even MORE lucky in the simulation. Which would falsely inflate the chances of a perfect season occuring.

This is patently false. If you admit that luck exists every single year, then there is no need to bother excluding it.

It does not matter whether the 4-5 12-4+ teams per year needed luck to be so. All that matters is that we consistently see 4-5 12-4+ teams per year. The only reason you would exclude luck is if you believe that the luck factor will diminish and we will see less 12-4+ teams in the future.