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Guarded optimism: historical look at 1st half vs 2nd half

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Old
12-05-2007, 08:47 AM
  #26
Hank
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Originally Posted by theShiba View Post
Whether or not we can agree that there is data to support this claim or not, you have to admit that is not equally likely to win or lose a given game. That would assume that training, coaching, motivation, etc. had no influence whatsoever on the outcome.
I should also add that you are assuming the other team isn't equally likely to do all of those things in order to beat the Ducks. Any given game the Ducks can and do lose to some really crappy teams that want it more and get better bounces (random luck) or better calls.

So yes, I do assume that its equally likely that *this* team will win or lose a game. I would not have said the same about last year's team.

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12-05-2007, 10:14 AM
  #27
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Originally Posted by Hank View Post
You are confusing two different things. The idea you keep coming back to is half of the results should be heads and half should be tails. That is true, if I flip the coin 1 million times I just know approximately half are heads without even looking. The more times I flip the closer to the truth that gets.

However that has nothing to do with the *next* flip. That next coin still can land heads or tails with a 50% chance.
OK I feel dumb. I think I just figured out where we're disagreeing. It took me long enough.

You're saying that I'm seeing the 2 halves of the season as 2 coin flips. And that I'm taking the results of the 1st half to try to make an argument on the results of the 2nd half. And I absolutely agree that that would be incorrect.

But I don't think that's what I did. I'm really only looking at 1 coin flip, the 2nd half of the season. The first half is something that happens no matter what, I don't care how many points they got in the first half. I'm not determining "heads" or "tails" on anything to do with the first half. I'm only looking at the 2nd half and seeing if it was *better* or *worse* than the 1st half.

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12-05-2007, 02:18 PM
  #28
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Originally Posted by obobo23 View Post
OK I feel dumb. I think I just figured out where we're disagreeing. It took me long enough.

You're saying that I'm seeing the 2 halves of the season as 2 coin flips. And that I'm taking the results of the 1st half to try to make an argument on the results of the 2nd half. And I absolutely agree that that would be incorrect.

But I don't think that's what I did. I'm really only looking at 1 coin flip, the 2nd half of the season. The first half is something that happens no matter what, I don't care how many points they got in the first half. I'm not determining "heads" or "tails" on anything to do with the first half. I'm only looking at the 2nd half and seeing if it was *better* or *worse* than the 1st half.
Close. I'm saying the point change (increase or decrease) of each prior season is a coin flip that has already happened. The point change this season is the next flip. You can't really predict the outcome of this next one based on the few we've already seen. Even if we had seen 1000's of seasons you still couldn't do it.

Just think about it logically. What possible bearing does it have now what a team did in 1997. Completely different players, coach, GM, styles of officiating, new parity in the league, etc, etc. This season is an event independent of what has happened in the past.

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12-05-2007, 07:35 PM
  #29
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Originally Posted by Hank View Post
Close. I'm saying the point change (increase or decrease) of each prior season is a coin flip that has already happened. The point change this season is the next flip. You can't really predict the outcome of this next one based on the few we've already seen. Even if we had seen 1000's of seasons you still couldn't do it.

Just think about it logically. What possible bearing does it have now what a team did in 1997. Completely different players, coach, GM, styles of officiating, new parity in the league, etc, etc. This season is an event independent of what has happened in the past.
Ah. Well that last part is something I conceded a couple posts ago:
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Originally Posted by obobo23 View Post
Now you're correct in that those 11 teams were actually different (different players, different coaches, growth/decline in skills etc). So in the end all this math may be useless. But it's better than nothing.

But going back to black boxes and your first paragraph, are you saying that it's not possible to guess the probability of the next button press/coin flip? Completely ignore the team, but think only about that "heads/tails" generating black box I presented earlier. Because it is possible to come to a close approximation after enough trials. Maybe not after only 11 button presses, but after a million tests you'd feel fairly confident that your guess is quite close the the actual probability (which would only be known by an all-knowing god).

Because that's where I'm most confused. It sounds like you're saying it's impossible to empirically determine (approximate at least) the probabilities of the different outcomes on the *next* independent trial. If that were true science wouldn't exist. Or the insurance industry for that matter.

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12-06-2007, 11:14 AM
  #30
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Originally Posted by obobo23 View Post
Because it is possible to come to a close approximation after enough trials. Maybe not after only 11 button presses, but after a million tests you'd feel fairly confident that your guess is quite close the the actual probability (which would only be known by an all-knowing god).
Well factor in that if probability is working correctly you'll never see a situation where 800k of 1 million coin flips are heads. 500k will be heads and 500k will be tails.

If you do see that highly unlikely scenario, exactly when will the trend change? On this next flip? The one after that? Maybe you'll see 100k more heads in a row... you just can't predict the future.

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Because that's where I'm most confused. It sounds like you're saying it's impossible to empirically determine (approximate at least) the probabilities of the different outcomes on the *next* independent trial. If that were true science wouldn't exist. Or the insurance industry for that matter.
Science doesn't try to predict anything. They formulate a theory of what they think will happen and then experiment to see if it actually does.

On the insurance industry, sure they know 10% (to pick a random number) of their 1 million customers will file a claim just like we know there should be 500k heads. They don't know which 10% and don't care.

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12-06-2007, 11:57 AM
  #31
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Originally Posted by Hank View Post
Well factor in that if probability is working correctly you'll never see a situation where 800k of 1 million coin flips are heads. 500k will be heads and 500k will be tails.
That's why I was talking about the "black box" and not the coin. Yes you'll never see 800k of a million coin flips be heads, because a coin should be 50%.

The black box is an unknown, we don't know what the ratio is. Not only don't we know, but the ratio could be anything. Like say 80% in my example. The black box could be a coin, and would thus be 50%. It could also be anything else though.

Think of it this way. There's the actual probability, P. This is based on what the black box is fundamentally. This number never changes, and is only known by an all-knowing god. It is the ideal probability, and what the results should be after any number of trials.

Then there's the guess G. I arrive at G by recording how many times the black box actually spits out heads. After only a few trials, chances are G is not that close to P. If I do a million trials, my calculated G will be different than your G after 1 million trials. But they probably be quite close to each other, and quite close to the true probability P.

In the original post, my guess G is 4/11. I don't have any idea what P is (and as said earlier this might not even apply because the 11 teams are different).

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Originally Posted by Hank View Post
Science doesn't try to predict anything. They formulate a theory of what they think will happen and then experiment to see if it actually does.

On the insurance industry, sure they know 10% (to pick a random number) of their 1 million customers will file a claim just like we know there should be 500k heads. They don't know which 10% and don't care.
But by formulating a theory and testing the theory, that's a prediction. So science is trying to predict something.

Same thing with insurance. In fact insurance is really a good analogy to what I was trying to do. After studying a lot of people, the insurance concludes that 10% will file a claim. Just like after studying a lot of button presses, hypothetical me would conclude that 80% of the time the black box will spit out "heads." And just like what I just did now (with far fewer cases and thus far fewer confidence that my results are right), in saying that 4/11 times the Ducks have performed quite a bit better in the 2nd half of the season.

Yes insurance doesn't know which 10%, but they know it should be 10%. And thus for any one person, there's a 10% chance he will file a claim. Or 90% chance of not filing a claim.


Maybe it's the word "predict" that's getting in the way? It's not quite predicting in the sense of saying "that person won't file a claim." It's "there's a 90% chance the person won't file a claim."

I get the feeling it's some kind of semantic/communication thing. It's obvious we're both intelligent people. I don't think any of the underlying arguments made by either are really wrong or even necessarily conflicting. But the end conclusion "you can make a prediction/you can't make a prediction" is different.

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12-06-2007, 12:49 PM
  #32
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Originally Posted by obobo23 View Post
The black box is an unknown, we don't know what the ratio is. Not only don't we know, but the ratio could be anything. Like say 80% in my example. The black box could be a coin, and would thus be 50%. It could also be anything else though.
And I'm saying the probability ratio doesn't matter for any one particular event. Should be and will be are two vastly different things.


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But by formulating a theory and testing the theory, that's a prediction. So science is trying to predict something.
Not so at all.

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Yes insurance doesn't know which 10%, but they know it should be 10%. And thus for any one person, there's a 10% chance he will file a claim. Or 90% chance of not filing a claim.
I almost touched on this. It does not mean each and every customer has a 10% risk. Some will have 30% risk and others 1% risk, etc, based on life style and random luck and a host of other factors. Who smokes, rides a motor cycle, sky dives vs vegetarians, don't drive at all, watch TV all day. That kind of thing.

You can't apply the overall probability to one single, independent event (one person's risk in this case).

Quote:
I get the feeling it's some kind of semantic/communication thing. It's obvious we're both intelligent people. I don't think any of the underlying arguments made by either are really wrong or even necessarily conflicting. But the end conclusion "you can make a prediction/you can't make a prediction" is different.
I agree that we continue to talk about two different things. You talk about what should happen overall, I about what will happen for one single event.

Think about a counter example of gambling... way back when I said Vegas would love you. You are the guy sitting in front of the slot machine for hours because it's "due" to pay out. The last 100 pulls lost so surely the next one will win. It won't, or at least its not any more likely to than any other pull.

But the casino knows it will pay out a set percentage of the time. Slanted in its favor of course.

You are talking about the casino's rate of payout. I'm talking about pull 101... does it win or lose.

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12-06-2007, 01:34 PM
  #33
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Originally Posted by Hank View Post
I agree that we continue to talk about two different things. You talk about what should happen overall, I about what will happen for one single event.

Think about a counter example of gambling... way back when I said Vegas would love you. You are the guy sitting in front of the slot machine for hours because it's "due" to pay out. The last 100 pulls lost so surely the next one will win. It won't, or at least its not any more likely to than any other pull.

But the casino knows it will pay out a set percentage of the time. Slanted in its favor of course.

You are talking about the casino's rate of payout. I'm talking about pull 101... does it win or lose.
I left out the rest of your post because I think this is the crux of the argument.

I am NOT the guy thinking the machine is due. You're absolutely right, that's the first thing they teach in statistics. Independent probability. Previous results have no affect on the next result.

I'm a guy who tested out the machine a lot. I'm just observing a bunch of people play the same machine over a few days. I'm trying to determine what the casino already knows, the set percentage the slot will pay out. Say 10% is the real number (of course it's nowhere near this, but it's a round number), and through my observations I see a 10.5% winning chance.

With that knowledge, when I do play the slots I'll go in with the expectation that the slot will win 10.5% of the time. I'm not assuming anything more. I don't care if I've played 100 times and lost all 100, I still expect there's a 10.5% chance of winning the next pull. This is all that I mean by "prediction." (Yes I'm slightly off from the 10% that the casino knows, but it's what I observed.)

Now if there were somebody out there stupid enough to bet with me, I could step back from the machine and just watch other people play it. Each time someone pulls the lever I bet with Dummy 1:1 that the person will lose. 90% of the time I'll be right (although I'm only expecting to be right 89.5% of the time). I clean up.

As an aside, in all honesty I hate gambling because I know it's slanted to the casino's favor. After realizing that the slot only wins 10% of the time and that the payout is less than 10:1 (casino's edge), I wouldn't bother.

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12-06-2007, 02:10 PM
  #34
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Originally Posted by obobo23 View Post
With that knowledge, when I do play the slots I'll go in with the expectation that the slot will win 10.5% of the time. I'm not assuming anything more. I don't care if I've played 100 times and lost all 100, I still expect there's a 10.5% chance of winning the next pull. This is all that I mean by "prediction." (Yes I'm slightly off from the 10% that the casino knows, but it's what I observed.)

Now if there were somebody out there stupid enough to bet with me, I could step back from the machine and just watch other people play it. Each time someone pulls the lever I bet with Dummy 1:1 that the person will lose. 90% of the time I'll be right (although I'm only expecting to be right 89.5% of the time). I clean up.
We're quite close. The problem you have applying the 10% probability is that you have to account for streaks of winners or losers by playing 1000's or even millions of times. The casino does. There is no end to the suckers coming though its doors.

You *should* clean up. But there is absolutely nothing preventing 100 winners in a row on that machine. It *could* happen.

To get back to the actual hockey debate (sort of), so you have two buckets: increased points and decreased points. You have 7/11 chance of going into bucket #1 and only a 4/11 chance into bucket #2. What happens to this season? Which bucket?

We have no idea and can't predict it. The past doesn't apply... "Independent probability. Previous results have no affect on the next result."

May be this season and next go into #2 and the next 5 into #1. May be some other combination. Who knows... its the future.

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