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

I'm pretty much as much a glass is half empty person as you'll ever meet. But I figured it'd be worth providing some perspective to our team, as miserable as it is right now.

Historically, the Ducks have been a very poor starting team, and tends to finish much stronger. I'm sure most of you already know this just from following the team, but let's actually put some numbers to this. Below I note how many points were earned in the 1st 41 games versus the last 41 games

07 half1

62

07 half2

48

06 half1

43

06 half2

55

04 half1

37

04 half2

39

03 half1

40

03 half2

55

02 half1

34

02 half2

35

Unfortunately, that's all the data I have, as the game-by-game results don't go back further.

So other than last year, the team has always been stronger in the 2nd half of the season than first half. I'm pretty sure it holds true for the other 2 playoff years, as well as 95-96 where Winnipeg beat us by a point.

Right now, we are on pace for 41 points at 41 games. And with there being so little separation in the West, that would keep us within striking distance of a playoff spot. The only problem is that to get ~95 points by the end would require 54 points in 41 games, which would be a rather difficult 27-14-0 (or so, depending on SOL).

Interestingly enough, in 03 and 06, when we made the playoffs, the jump was significant, whereas the years where we didn't make the playoffs the increase was trivial. Jan 2nd is the 42nd game. So if history holds true, the true test of whether they'll make the playoffs or not will be whether it turns it on after the new year or not.

The team has gotten hot like that before, so the playoffs are possible. But it'll be an uphill battle for sure.

Like the post but face it, WE SUCK right now and I do not see an upside to the season.

We'll be extremely lucky to make the playoffs let alone advance anywhere.

I may be totally wrong but what I have seen in these last couple of weeks is not promising to say the least.

Beginning of the season I was optimistic, I believed we would have a decent season, maybe finish 5-6 in the West, now I'm not so sure, we would have to catch fire and I do not see that happening without some serious changes.

And if serious changes do occur, I doubt the team will "gel" in time for a deep playoff run.

Historically, the Ducks have been a very poor starting team, and tends to finish much stronger.

07 half1

62

07 half2

48

06 half1

43

06 half2

55

04 half1

37

04 half2

39

03 half1

40

03 half2

55

02 half1

34

02 half2

35

Umm, your data doesn't support that claim. In one season the second half was worse, in two the second half was better and in the last two seasons the halves were equal.

A worse second half than what we are seeing now is just as likely based on this data.

Umm, your data doesn't support that claim. In one season the second half was worse, in two the second half was better and in the last two seasons the halves were equal.

A worse second half than what we are seeing now is just as likely based on this data.

Well that data was probably too little to support anything at all. A worse second half is not just as likely though. Because in 5 years analyzed the results would be 2 years better 2nd half, 2 years roughly the same (but still slightly better), and 1 year worse. So 4 out of 5 years they did better, just not a whole lot better.

And my conclusion in the end is different from what you quoted, which was the hypothesis that I started out with. My mistake for writing that poorly. The actual conclusion is not that we'd undeniably be better, but that there's a chance we get a lot better and a chance it stays roughly the same. Which I admit isn't much of a conclusion. It's like saying "if we get in the playoffs, it's because we did better."

Anyways I found some more records. So there's more numbers now. And I added a delta at the end to make the change easier to see.

07 half1

62

07 half2

48

Δ

-14

06 half1

43

06 half2

55

Δ

12

04 half1

37

04 half2

39

Δ

2

03 half1

40

03 half2

55

Δ

15

02 half1

34

02 half2

35

Δ

1

01 half1

35

01 half2

31

Δ

-4

00 half1

41

00 half2

42

Δ

1

99 half1

40

99 half2

43

Δ

3

98 half1

33

98 half2

32

Δ

-1

97 half1

35

97 half2

50

Δ

15

96 half1

34

96 half2

44

Δ

10

The sum total is 1 year worse, 2 years slightly worse (<= 4 points), 4 years slightly better, and 4 years quite a bit better.

So in the end, it seems like it's roughly 4/11 that we improve and make it into the playoffs. And 8/11 that we improve at least a little bit in the 2nd half of the season

Last edited by snarktacular: 12-04-2007 at 12:53 AM.

Like the post but face it, WE SUCK right now and I do not see an upside to the season.

We'll be extremely lucky to make the playoffs let alone advance anywhere.

I may be totally wrong but what I have seen in these last couple of weeks is not promising to say the least.

Beginning of the season I was optimistic, I believed we would have a decent season, maybe finish 5-6 in the West, now I'm not so sure, we would have to catch fire and I do not see that happening without some serious changes.

And if serious changes do occur, I doubt the team will "gel" in time for a deep playoff run.

Geez, calm your ****.

The team is going through a rough spell right now. They are without their leading goal scorer from last year, their captain, and have battled through injuries all year to this point. They are 12-12-4. Things could be MUCH worse. I refuse to think that this team will struggle to make the postseason.

So... for the statistics lovers out there, I did a quick work-up.

It all works out like this

(Over all 11 years)
1st Half Average = 39.45
2nd Half Average = 43.09

A quick T-test tells us that there is a significant difference between the two. (t=0.32 for anyone that cares)

Of course, the problem with averages, is that we could be in one of the years where the second half is WORSE than the first half, in which case, we're headed for a slide....

So... for the statistics lovers out there, I did a quick work-up.

It all works out like this

(Over all 11 years)
1st Half Average = 39.45
2nd Half Average = 43.09

A quick T-test tells us that there is a significant difference between the two. (t=0.32 for anyone that cares)

Of course, the problem with averages, is that we could be in one of the years where the second half is WORSE than the first half, in which case, we're headed for a slide....

After all, it's just data.

Thanks, I didn't feel like doing the statistics test. Partly because I'm not even sure what's the best way to do it. I almost think it should be a test of "better or worse in the 2nd half" with an expectation of 50% that it'll go one way or the other. But I've never taken a statistics class, what do I know.

yeah that's what I did.... average of 1st half and 2nd half... assuming that either half is equally likely to be greater or lesser....

The data works out to say that it is better in the 2nd half... your prediction is confirmed.

I didn't explain myself enough. You averaged all the seasons together and did a test that the sum total should be equal. I'm saying I think it should be 11 cases of "better or worse," with a 50% expectation. I think the statistical analysis should based off the fact that 8/11 (years where they improved) != 50%. Unfortunately there's probably not a lot of statistical power in only 11 cases.

I didn't explain myself enough. You averaged all the seasons together and did a test that the sum total should be equal. I'm saying I think it should be 11 cases of "better or worse," with a 50% expectation. I think the statistical analysis should based off the fact that 8/11 (years where they improved) != 50%. Unfortunately there's probably not a lot of statistical power in only 11 cases.

You're right that there isn't a lot to work with from 11 cases... that said, this is where I end my attempt at statistical analysis. You're talking about some complicated stuff, and I'm just not feeling like trying all that hard to figure out how to do calculations like that for the sake of saying.... it's going to be ok... maybe?

Anyway, I think the most important key is that can't say with much certainty that this isn't going to be "one of those years".

The team is going through a rough spell right now. They are without their leading goal scorer from last year, their captain, and have battled through injuries all year to this point. They are 12-12-4. Things could be MUCH worse. I refuse to think that this team will struggle to make the postseason.

Not upset at all, just calling it like I see it. I don't know how long we are going to "give them a chance" to come out of their slump, but the season is a 3rd of the way through already and like I said, it doesn't look promising.

Right now we are in 11th out of 15 teams in the West with 6 point separating these teams.

With Edmonton playing the way they are and the Yotes playing well also, we might finish above the Kings and Calgary but who knows, I did say I may be wrong and I hope so but we need something to happen soon.

Last edited by Twindad*: 12-04-2007 at 12:32 PM.
Reason: Spelling

yeah that's what I did.... average of 1st half and 2nd half... assuming that either half is equally likely to be greater or lesser....

The data works out to say that it is better in the 2nd half... your prediction is confirmed.

It doesn't work like that. One flip of the coin has absolutely nothing to do with any other so the chance of heads is 50% every time. The Ducks are just as likely to do worse this second half as they are to do better because this season has no connection to any other.

A worse second half is not just as likely though. Because in 5 years analyzed the results would be 2 years better 2nd half, 2 years roughly the same (but still slightly better), and 1 year worse. So 4 out of 5 years they did better, just not a whole lot better.

Ha, if you want to spin one and two point gains into "better" halves go ahead.

For all we know they are in the 6th year to make it 2-2-2... more likely to do worse to make it all work out nice and even like you want it to. I chose to spin the numbers that way :-)

It doesn't work like that. One flip of the coin has absolutely nothing to do with any other so the chance of heads is 50% every time. The Ducks are just as likely to do worse this second half as they are to do better because this season has no connection to any other.

Vegas would love you guys.

Yep... and if you read what we are actually saying through the entire post, you'd realize that we're agreeing that though it has happened more often than not, there is no reason to believe that it is any more or less likely.

Quote:

Originally Posted by theShiba

Of course, the problem with averages, is that we could be in one of the years where the second half is WORSE than the first half, in which case, we're headed for a slide....

Yep... and if you read what we are actually saying through the entire post, you'd realize that we're agreeing that though it has happened more often than not, there is no reason to believe that it is any more or less likely.

What you are actually saying is there is NO reason to read this thread. Coincidentally that's what I'm trying to say as well.

It doesn't work like that. One flip of the coin has absolutely nothing to do with any other so the chance of heads is 50% every time. The Ducks are just as likely to do worse this second half as they are to do better because this season has no connection to any other.

Vegas would love you guys.

I think your first statement of coins is wrong though. If you flip a coin over and over, and you're getting heads more often than tails, you can conclude that your chance to get heads on any given flip is greater. You are empirically determining that the coin is biased to land heads. Granted, with only 11 test cases you can't claim that with confidence. But as you flip more, and the trend continues, then your confidence increases.

Your second statement is correct though. In the end, the seasons don't really have a connection to each other. Just because it wasn't the same team each year. There's no definitive conclusion out of this small data. But let the fans have some optimism.

I think your first statement of coins is wrong though. If you flip a coin over and over, and you're getting heads more often than tails, you can conclude that your chance to get heads on any given flip is greater. You are empirically determining that the coin is biased to land heads. Granted, with only 11 test cases you can't claim that with confidence. But as you flip more, and the trend continues, then your confidence increases.

Flip a coin 1 million times. The next time it will either be a head or a tail. There is a 50% chance of each.

You're right that there isn't a lot to work with from 11 cases... that said, this is where I end my attempt at statistical analysis. You're talking about some complicated stuff, and I'm just not feeling like trying all that hard to figure out how to do calculations like that for the sake of saying.... it's going to be ok... maybe?

Anyway, I think the most important key is that can't say with much certainty that this isn't going to be "one of those years".

Oh and for the record, I don't think what I explained is any more complicated that what you did. I think you probably do the exact same thing you did, but use 8/11 instead of 39.5/(39+43). But then again I never took statistics so I'm probably just making stuff up.

Flip a coin 1 million times. The next time it will either be a head or a tail. There is a 50% chance of each.

Yes, if it's known ahead of time that the coin is unbiased. I'm saying if you don't know that and if you flip a coin 1 million times, you can use the results to determine what % it will be heads on any one flip. If you flip 1 million times and 800k times are heads, you can say, with a numerical amount of confidence based on how many times you flipped the coin, that the coin is actually 80% heads 20% tails.

Yes, if it's known ahead of time that the coin is unbiased. I'm saying if you don't know that and if you flip a coin 1 million times, you can use the results to determine what % it will be heads on any one flip. If you flip 1 million times and 800k times are heads, you can say, with a numerical amount of confidence based on how many times you flipped the coin, that the coin is actually 80% heads 20% tails.

You can't do that. It is very simple. The coin is ALWAYS unbiased to use your terminology.

What you know has nothing to do with how the coin lands.

You can't do that. It is very simple. The coin is ALWAYS unbiased to use your terminology.

What you know has nothing to do with how the coin lands.

Hmm. I think the problem is in the use of the word "coin." It has connotations of being an unbiased 50% object.

What I'm saying is you have a random-number-generating black box. You press a button, and the box spits out "heads" or "tails." So then what I was doing was to empirically determine what the odds of getting heads are. If you press the button 1 million times, and 800,000 times it spits out "heads," then you can say the box is 80% heads and 20% tails. It's also possible that the box was 50% heads. But with statistics you can determine what the chances of getting 800k heads if the box was 50% are. And they would probably be so low as to be essentially ruled out.

That's the essence of what tracking the past 11 seasons was. I went in looking for a trend. The numbers suggest a trend. I can't say "we WILL improve," but I can offer an informed guess that there's roughly a 4/11 chance we will. Of course with such small numbers, it's possible the real ratio is anything from 0 to 1. But it's just an approximation.

As another analogy, consider a baseball player. You have no idea how well he hits. But after some at bats, you can calculate his batting average. After awhile, you have a pretty decent estimate of the chances he'll get a hit in his next at bat.

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.

Last edited by snarktacular: 12-04-2007 at 10:20 PM.

What you are actually saying is there is NO reason to read this thread. Coincidentally that's what I'm trying to say as well.

And yet, facing extreme opposition from your own better judgment, you managed to persevere, and keep checking back to see what had been said.

Quote:

Originally Posted by Hank

You can't do that. It is very simple. The coin is ALWAYS unbiased to use your terminology.

What you know has nothing to do with how the coin lands.

If I wasn't clear about this before, then I am going to clarify now. THIS ISN'T A COIN. This is an athletic contest.

The coin does not try harder when it realizes it's not going to make the 50/50 mark. When it's halfway through the season, the coin doesn't care any more or less about the playoffs. Athletes do.

Coins cannot be influenced by coaches, and they certainly can't play smarter and learn to take advantages of what they have learned during the previous tests.

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.

Oh wait, I forgot... you're not reading this thread anymore.

Hmm. I think the problem is in the use of the word "coin." It has connotations of being an unbiased 50% object.

What I'm saying is you have a random-number-generating black box. You press a button, and the box spits out "heads" or "tails." So then what I was doing was to empirically determine what the odds of getting heads are. If you press the button 1 million times, and 800,000 times it spits out "heads," then you can say the box is 80% heads and 20% tails. It's also possible that the box was 50% heads. But with statistics you can determine what the chances of getting 800k heads if the box was 50% are. And they would probably be so low as to be essentially ruled out.

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.