Talk:Christmas tree hat

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So its limited edition, and tradeable... So basicaly its a new tradable rare... I thought this wasnt going to happen anymore... Swagniff^Talk 17:12, December 19, 2012 (UTC)

It's harder to get than fish mask, and stays here for much shorter, at least ^Talk Habblet 17:14, December 19, 2012 (UTC)

Only going to make it more valuable when they take it away.DiabolusMiles (talk) 03:40, December 20, 2012 (UTC)

Well, they did add the Fish mask and we all know how that ended up.Emoted Wolf (talk) 19:33, December 20, 2012 (UTC)

They only said they wouldn't drop free rares all over the place. This one can technically only be bouhgt with real-world money (ie SoF) or obtained through hours of playing (Took me 10 saved-up spins just to get the green present, still haven't gotten any others after 30 min of Runespan, so they're kind of rareish)

I hope to get one to save and at least one more to sell, although I have to decide...is it better for my OCD brain to get this and the mistletoe so I have everything, or save up for two of these...

N1ghtshade3 (talk) 00:44, December 21, 2012 (UTC)

Does any1 have enough gp in game to buy 2 and test this 50m hi alch, 100m low alch that it says on the wiki page, or is it known already some1 trolled the page?Good i snipr (talk) 03:35, December 21, 2012 (UTC)

Where/when did Jagex said they'd be completely removed on the 14th of January? 94.145.226.59 10:23, December 22, 2012 (UTC)

Its saying that the presents would be removed not the christmas tree hat. Bluest (talk) 21:35, December 22, 2012 (UTC)

Factual correction

"The Grand Exchange Price has risen exponentially [dramatically] every day it is updated since its release."

After fixing this, I noticed the change was reverted. Here is a little math lesson:

The price on March 26 was 23,296,136

The price on March 27 was 24,365,128

That is a rise in price of 1,068,992

If the price rose EXPONENTIALLY the next time it was updated, the market price of the Christmas Tree Hat on March 29th would be 1,142,768,261,192 (over 1 trillion gold), as exponentially would mean 1,068,992 x 1,068,992 = the new 1-day change.

Not only this, but immediately below this trivia entry is "The Christmas Tree Hat doubles in price every 15-16 days that it is updated." which is totally contradictory to the previous trivia entry. If the price rose exponentially, it would more than double (in fact, it would be millions of times higher than it was before) every single day it is updated.

Not once during any period of time since its release has the Christmas Tree Hat ever risen exponentially in price.  —The preceding unsigned comment was added by 98.28.71.125 (talk).

Exponential functions don't have to be squares. For example, 1,068,992^1.0001 is "only" 1070477.0294664 but it's still exponential. Also take note that the word wasn't used here literally; it's a common synonym for rapid growth. Your change is fine, but you shouldn't complain with a misguided understanding. MolMan 03:39, March 30, 2013 (UTC)

In that case, any increase or decrease can be considered "exponential". Regardless of whether its misuse has entered the common lexicon as meaning something entirely different, a less ambiguous term is more appropriate. In an encyclopedic entry, things should be described literally. I very seriously doubt the person was describing an increase using a rational exponent. You shouldn't stretch reasoning to preserve a flawed status quo. —The preceding unsigned comment was added by 98.28.71.125 (talk).

If you read the latter of my statement, you'd see I didn't care one way or the other about the change. MolMan 18:28, March 30, 2013 (UTC)

@unsigned user, if you knew anything about exponents, you'd realize that doubling every 15 days would mean it fits one of the most basic exponential graphs, 2^x (where x is the number of 15 day periods).  So in terms of months, that would be increasing at 4^x.  Nice try pretending to know math though.

If you just use Google you can see what some exponential graphs looks like Exponential curve

Now look at this curve. http://runescape.wikia.com/wiki/Exchange:Christmas_tree_hat   It's either exponential or geometric.  I guess you could just plug in the values and see which curve it fits better using a graphing calculator...

Also, time doesn't have to be in 1 day units man.  For something like this, you'd want to use some bigger chunks of time since this is basically like stocks and flucuates frequently for small intervals of time.98.237.74.88 20:00, April 6, 2013 (UTC)

In reply to "if you knew anything about exponents, you'd realize that doubling every 15 days would mean it fits one of the most basic exponential graphs" and "Also, time doesn't have to be in 1 day units man.":

Okay, did you not read the original entry that said "risen exponentially every day"? I'm not arguing that the price couldn't rise exponentially over (X units of time). The edit that I changed said the price has risen exponentially every day it is updated (we're not talking in terms of every 15 days, or in months, the original edit said every day) and that is what I was correcting. Your whole reply only proves my point. Nice job pretending to know what the hell you're talking about... man. —The preceding unsigned comment was added by 98.28.71.125 (talk).

It's over, can we just shut up. If you'd like to continue insulting each other about whose answer is right and whose is wrong (which you both are), please find another medium through which to do it. MolMan 22:36, April 17, 2013 (UTC)

You're both wrong, but you (most recent editor) more than most. The statement that the price has increased exponentially every day it's been updated, while misleading, is mostly accurate. It doesn't take a rock scientist to see this: plug in the values, and you'll see that the change in price from one day to the next has been fairly constant as a multiple of the previous price, 1.05. In recent days it's tailed off a bit, for some unknown reason, but nonetheless it can still be considered mostly exponential. What limited knowledge of exponential functions you appear to have seems to have given you the idea that exponential increases reflect a squaring of the previous value. Not only is this sometimes not the case, as Mol pointed out, it is never the case. Exponentially increasing functions simply rely on the previous value with a multiple greater than 1. That's what's happening here, and that's why the statement is correct.

Now, you might ask why it's exponential. The answer is that the true price has been above the median/guide price since the introduction of the item, and the median price has constantly been revised upwards. Due to limitations set by Jagex, this change can be no more than 5% of the previous value. There's some obfuscating factor where the change starts to be slightly less than 5% over time, but it's still basically accurate to say that the next price will be 5% more than the previous, up until the time that the median catches up with the true price. ʞooɔ 22:43, April 17, 2013 (UTC)

Multiple: A number that can be divided by another number without a remainder. 1.05 is not an integer and is not a multiple, and the fact that it is a decimal is indicative of a remainder. You are dubiously arguing that any increase at all is exponential, in which case my edit (the price has risen dramatically) stands as less ambiguous, less misleading, and therefore more accurate.  —The preceding unsigned comment was added by 98.28.71.125 (talk).

You're just laughably wrong. If a p_1 is 5% more than p_0, then the constant of increase, which I validly called a multiple, would be 1.05. What you are arguing is that for an increase to be exponential, the price must be squared every time (????). What I am saying, and what you haven't comprehended, is that if the price increases 5% every updated day, the increase is exponential. Since you managed to figure out what a multiple was through the book Times Tables Done Easy, maybe try looking at a slightly higher level book and figuring out what an exponential actually is. ʞooɔ 23:00, April 17, 2013 (UTC)

Read over my first post. Where did I say that the price must be squared every time? I used that as an example (i.e. including but not limited to). That said, your argument is based on a false premise.

"Exponential increases occur when the growth rate of a mathematical function is proportional to the function's current value."

The growth rate fluctuates each day it is updated and is therefore not proportional to the function's value at any given time an increase occurs. There goes you entire argument. In mathematics, "mostly exponential" is not exponential.  —The preceding unsigned comment was added by 98.28.71.125 (talk).

Your example would never be practical as the price would never be squared under any rational circumstance. Actually, scratch that, it's just completely wrong. And the growth rate is clearly proportional to the current price, with a slight bit of fuzziness due to unknown circumstances -- just as the dragon kiteshield only rose by about 4.7% per day on average, so does the tree hat. The rate of change has fluctuated between 4.5% and 5% every day. It's better to say it's an exponential increase, which for all intents and purposes it is, than to say it's drastically (weasel word) increasing. I think you just made a bad call and either misunderstood the point of the statement or misunderstood the meaning of exponential functions, because your original statement about the increase being 1,142,768,261,192 is so off-base that I can't fathom how you came to that conclusion. The rate of change is proportional to the item's current value. End of story. ʞooɔ 23:13, April 17, 2013 (UTC)

It is proportional "with a slight bit of fuzziness"? That is not proportional. Any fluctuation in the increase at all means it is not proportional and therefore not exponential. If the increase is proportional on any given day (i.e. it rose in price by 5% on one day) and only rose 4.5% the next, the rise in price is not proportional to the function. Hoever impractical it is, it is mathematics, and when it comes to fuzziness and unknown circumstances, you can say it resembles an exponential increase, you can say that on a graph it looks almost exactly like an exponential increase with an almost impercievable deviation, but it is not truly exponential. End of story, homie. —The preceding unsigned comment was added by 98.28.71.125 (talk).

"In recent days it's tailed off a bit, for some unknown reason, but nonetheless it can still be considered mostly exponential." Guess who said that 40 minutes ago? This dude! What I can't tell is whether you're suddenly latching on to my admission that the price increase lags slightly below 5% as a cheap way to win an argument, or if you actually meant that from the beginning but you were just singularly bad at articulating the point. In any case "Not once during any period of time since its release has the Christmas Tree Hat ever risen exponentially in price." is clearly incorrect and I hope you realize that. ʞooɔ 23:30, April 17, 2013 (UTC)

A cheap way to win an argument? Naw. I'd say I am "mostly right" for all intents and purposes, because practically speaking I can't always be right under any rational circumstance. I mean, you could say I was right with with a slight bit of fuzziness due to unknown circumstances. —The preceding unsigned comment was added by 98.28.71.125 (talk).

You claimed that the price had never experienced exponential growth, and that to do so the price would have to double. Not true. You claimed that the price could rise exponentially over a period of a month, instead of days. Nonsensical. For most of the item's existence, and to this day if not for Jagex's strange limitations, the price has experienced exponential growth. Nonetheless, a function of (1.04+rand()/100)^x would still be considered in the exponential function family even if it not directly proportional to the previous price. In any case, we cannot deal in pure mathematical truths -- it's anal to go after the difference between 4.7% and 5%, just as it's anal to go after rounding errors in the beginning causing the change to be 1.0500006046857966217068379597556 instead of 1.05. I don't really think you have any idea what you're talking about. Sorry. ʞooɔ 23:42, April 17, 2013 (UTC)

Quote where I said the price would have to double, and don't quote my example as that was just an example of an exponential increase, not the only circumstance.  "In any case we cannot deal in pure mathematical truths."... lol. Then don't use mathematical terms. It's not "anal", it's math, genius. I know you have no idea what you're talking about.  —The preceding unsigned comment was added by 98.28.71.125 (talk).

Well, exponential growth is also a financial term (no mathematical truths here, pal!) where the price closely resembles an exponential curve. So it's correct, just not in the field you seem to know so much about. I would argue that given that we're dealing with prices and not simply numbers (otherwise they'd be doubles, not integers), this is more accurate. And you said:

If the price rose EXPONENTIALLY the next time it was updated, the market price of the Christmas Tree Hat on March 29th would be 1,142,768,261,192 (over 1 trillion gold), as exponentially would mean 1,068,992 x 1,068,992 = the new 1-day change.

This implies that you thought exponential increase meant squaring the increase in value, which is not only generally wrong, but always wrong. That is never the case (note that you also said "would", not "could", but onward we go). ʞooɔ 23:49, April 17, 2013 (UTC)

Onward we go indeed. In my example, it "would", in general it "could". I implied nothing. Trust me, I wrote it. I would know. —The preceding unsigned comment was added by 98.28.71.125 (talk).

There is literally no exponential growth equation with integer values where f(x) = (f(x-1)-f(x-2))^2 for ANY value, let alone one relevant to this example. It doesn't work like that. ʞooɔ 00:02, April 18, 2013 (UTC)

Well, if you add enough fuzziness and unknown circumstances I'd say it resembles an exponential curve, even if it's not one, because after all, there's no point in being precise or anal about it, right?  —The preceding unsigned comment was added by 98.28.71.125 (talk).

I'm not going to take the ad hominem bait, but you said originally that the price of the hat on the 29th (call it t = 2) would be equal to the difference between the price on the 27th (t = 1) and the 26th (t = 0), squared. That makes absolutely zero sense, can you defend it? ʞooɔ 00:10, April 18, 2013 (UTC)

Since when is the amount of sense something makes proportionate to its factual accuracy? Do take the bait. I mean, math is subjective. If it resembles an exponential curve to me I can call it one, because there is no point in being anal about it since, you know, this whole article is just an opinion piece. Why get into the pure mathematical details?  —The preceding unsigned comment was added by 98.28.71.125 (talk).

See, now you're just being a dick. Can you answer the question or were you just horrendously wrong? ʞooɔ 00:21, April 18, 2013 (UTC)

Nah, I'm being practical. —The preceding unsigned comment was added by 98.28.71.125 (talk).

Still waiting for that mathematical defense instead of more snidery. ʞooɔ 00:32, April 18, 2013 (UTC)

Nah, I don't have to have a mathematical defense. We're discussing similarities and resemblances to mathematical functions, not math. —The preceding unsigned comment was added by 98.28.71.125 (talk).

It's funny because you already betrayed your ignorance with your first post, and yet you're trying to act like you know the game. ʞooɔ 00:37, April 18, 2013 (UTC)

Nah, you asked if I "can" give you an answer, not if I "would", which implies that you don't know the answer or what you're talking about, since implications are a matter of opinion and all. —The preceding unsigned comment was added by 98.28.71.125 (talk).

Are you actually getting anything out of this? Last five replies have been stalling and it's getting kind of tiring. ʞooɔ 00:45, April 18, 2013 (UTC)

Nah, for all intents and purposes they resemble informative pieces of information. —The preceding unsigned comment was added by 98.28.71.125 (talk).

Your mathematical skill is matched only by your rhetorical prowess. ʞooɔ 00:50, April 18, 2013 (UTC)

Except he's not borrowing anything mathematical from what you say. MolMan 00:54, April 18, 2013 (UTC)

Stahp plz Noobcaek ^ROBBEN_hulkOil4 I made this 00:51, April 18, 2013 (UTC)

Nah, I'd say my rhetorical prowess resembles that of an expert. Also, my original post was under the assumption that the exponent was an integer, not that the price would necessarily have to double or that the increase must be squared. To have anything other than an integer as the exponent is misleading at best, and although the price is increasing at an increasing rate, when the "fuzziness" is taken into consideration, it is not truly an exponential increase, it is simply an increase. —The preceding unsigned comment was added by 98.28.71.125 (talk).

Are you saying that because there are rounding and estimation errors, which there will be in any calculation, it's not a proper exponential? Noobcaek ^ROBBEN_hulkOil4 I made this 00:59, April 18, 2013 (UTC)

Yes, trolling with my previous statements. Almost Lincolnesque. You still haven't explained that situation though -- increasing an integer exponent by one would not square the value unless the base was 2 and it was the first day, as I said. And as I also said, neither of those circumstances at all fit the situation. So... ʞooɔ 01:03, April 18, 2013 (UTC)

No. I am saying that an increase one day of 5% and the next day 4.5% and the next day 6% and the next day 4% is not indicative of a true exponential function. It may resemble an exponential curve, but it isn't one. —The preceding unsigned comment was added by 98.28.71.125 (talk).

I don't believe I ever claimed in any part of this that it was a "pure" exponential function such that the increase would be constant (note that this would be impossible, regardless, for any integer prices, so it's a silly point to make a stand on). In my very first post here I noted that the rate was slowing down. You seem to think that exponential curves can only be of that simple, gradeschool form, and that's simply not true. And your original post actually makes less sense now that you've attempted to explain it. What are you even trying to make a point of? ʞooɔ 01:08, April 18, 2013 (UTC)

If you don't know what I'm trying to make a point of you have no business commenting. I'm trying to explain and you are throwing your preconceived point of view into what I am saying and not actually trying to understand my point. Pure exponential functions are the only exponential functions... otherwise any increase can be considered exponential. —The preceding unsigned comment was added by 98.28.71.125 (talk).

I would make a joke here about how useless pure mathematicians are, but you don't seem to have a grasp of the basics yet. ʞooɔ 01:14, April 18, 2013 (UTC)

I would make a joke about how you should have a firm grasp of pure mathematics before you go making generalizations and abstractions of it. —The preceding unsigned comment was added by 98.28.71.125 (talk).

I would make a joke about how none of responses are actually original... They're just reversals of what Cook is saying, slightly twisted to fit your lame argument.

http://i.imgur.com/ZC5JHSH.png

MolMan 01:22, April 18, 2013 (UTC)

I assure you that I do, I just don't think it's relevant when we're using adjectives to describe growth trends. On that note I must take my leave -- this stimulating discussion has left me drained. I do hope you think you've won this exchange. In the mean time I have added a note in the trivia section summing up the uniqueness of its price growth -- I hope it fits your high standards. ʞooɔ 01:27, April 18, 2013 (UTC)

It doesn't. —The preceding unsigned comment was added by 98.28.71.125 (talk).

Don't want to intervene into this conversation, but could the anon please remember to sign your posts with ~~~~ :). Thanks Haidro ^(talk) 01:25, April 18, 2013 (UTC)

Your reasoning for calling the increase exponential is about the same argument as saying 3 is not prime because its factors include 2 and 1.5. When people hear "exponential", they assume y in X^y is an integer, because if that isn't the case any increase at all can be considered exponential and the term is meaningless. —The preceding unsigned comment was added by 98.28.71.125 (talk).

"When people hear "exponential", they assume y in X^y is an integer"

So x^1.5 isn't exponential? Okay. ʞooɔ

Apologies, I meant a constant. I was still thinking about the 3 as a prime reference. I was about to edit that but I see you already commented. —The preceding unsigned comment was added by 98.28.71.125 (talk).

Delayed reply -- exponentials are of the form c^x, not x^c (where c is a constant). ʞooɔ 06:00, April 19, 2013 (UTC)

Blatantly false. That depends entirely on the intended application. A perfect example: You just used a variable (c) to describe a constant. You are clearly educated beyond your intelligence.

See: http://en.wikipedia.org/wiki/Exponential_function

"The exponential function is used to model a relationship in which a constant change in the independent variable gives the same proportional change (i.e. percentage increase or decrease) in the dependent variable."

e^x

In any given application (e.g. a Grand Exchange price graph), if the exponent (^x) varies it is not a constant change and therefore not an exponential function, however closely it may resemble one. A varying (^x) would result in a inconsistent (and therefore not proportional) change.

"In recent days it's tailed off a bit, for some unknown reason, but nonetheless it can still be considered mostly exponential."

That is not exponential growth, that is logistic growth. Exponential functions don't tail off. The fact that it constantly, consistently, and indefinitely increases is the very meaning of exponential. Once you plug in (^x) it cannot decrease or what you have is not an exponential function because the change is not constant.

See: http://en.wikipedia.org/wiki/Logistic_function

"The initial stage of growth is approximately exponential; then, as saturation begins, the growth slows, and at maturity, growth stops."

Approximately exponential is not exponential.

http://img585.imageshack.us/img585/1539/tumblrm7ubi46hiw1rvsnj6.gif —The preceding unsigned comment was added by 98.28.71.125 (talk).

Oh my god, you completely missed the point. You are so wrong that you have to know it at some level. x^c (say, x^2) is not an exponential expression. 2^x is. The whole point of an exponential equation is that the "x" value varies. Let's instead deal with bases and exponents. In polynomial equations, the base is what varies. In your e^x example, the multiplicative rate of change from one x value to the next is e. The fact that we can even take the change from one x value to the next guarantees that the x value varies! In exponential equations, the exponent varies! It's 7th grade stuff, man! And I clearly know what a logistic function is. Take a look at the Christmas tree hat's graph. Is the rate of change slowing down? No? Then it's not logistic! I claimed that the multiplicative rate of change (i.e. the 1.05, or the BASE) was going down slightly. The rate of change of the Christmas tree hat's price has always been increasing. God almighty, you make me laugh and cry at the same time. And try not to incorrectly use logistic functions when you still lack understanding of the difference between a polynomial and a exponential. Jesus. ʞooɔ 12:27, April 19, 2013 (UTC)

Oh, and you can probably tell I don't like arguing grade school math with imbeciles. ʞooɔ 12:30, April 19, 2013 (UTC)

http://img138.imageshack.us/img138/3329/calcy.png

The OP is right. The exponent or the base can be a variable depending on what you're doing. When you're making a price graph, if the exponent varies from day to day it's not an exponential curve. Any increase at all can be exponential the way you're wording it cook. —The preceding unsigned comment was added by 177.130.128.8 (talk).

Assuming you're not actually the same guy I've been arguing with for the past few days, x^2 and x^3 are not exponential functions. That's the difference between polynomials and exponentials. If the exponent is based on the number of days gone by, AND THE BASE IS NOT, then it's exponential. The way I'm wording it is that the base varies randomly between 1.04 and 1.05, and the exponent is the independent variable x. No matter how you slice it, that's exponential. ʞooɔ 18:11, April 20, 2013 (UTC)

In order to clear up some confusion, for a given function $f(x)$ to be exponential and not polynomial, there must exist a base (which is allowed to vary) $a$, an exponent $x$ such that $x$ is not constant, and an optional scalar $c\in\R$ (for our purposes, c is a real number): $f(x) = a^{cx}$. Functions in the form $f(x) = x^c$ where $c\in\R$, are called polynomial functions. Two of the buttons circled in the picture you linked are such functions. The other may be considered an exponential function with respect to $y$. Suppa chuppa ^Talk 18:15, April 20, 2013 (UTC)

A varying y in X^y will not produce and exponential curve. X^1.5 one day,  X^1.2 the next, and X^1.1 is not exponential growth, it is simply growth.

Exponential growth occurs when the growth rate of a mathematical function is PROPORTIONAL to the function's current value.

As the price changes, you will see that there is no direct correlation between the item's current price and the price it will be the next day. The growth is not proportional to the current value. You then go on to argue that there are limiting factors that prevent the price from rising truly exponentially, and eventually we all know the price is going to plateu (something exponential curves don't do). —The preceding unsigned comment was added by 177.130.128.8 (talk).

Exponential curves are of the form c^x where c is the base and x is the exponent. When I say "vary", I mean that it's the independent variable of the function. Not that it randomly varies in some weird way as you seem to think it does. So in y = c*x, x "varies" because it's the part that changes and creates the function. For that reason, y = x^2 is not exponential, nor is y = x^3, nor is anything of that form going to be exponential. You said "When people hear "exponential", they assume y in X^y is an integer". Any time that the exponent is fixed in an equation like that, it's not exponential! The very definition of an exponential equation is that the exponent varies. There ARE unknown limiting factors stopping the price from increasing at a truly exponential rate -- it's common knowledge that in most cases the price growth is capped at 5% of the previous price, but expensive items increase at a slightly lower maximal rate, between 4 and 5%. I said nothing of the price plateauing, because it's not going to. ʞooɔ 18:45, April 20, 2013 (UTC)

Oh, and evading your block is not cool. ʞooɔ

Multiple instances of name calling and profanity in a comment is cool though. Deleting it apparently isn't. The edit will remain as "approximately exponential". Anything else is misleading, as by your logic any increase over a period of time is "exponential". —The preceding unsigned comment was added by 177.130.128.8 (talk).

You're right, because it increased by 2 million yesterday, and if it was actually exponential then it would increase by 4 trillion today. Thank you for making this content decision for us. Also: you keep saying that by my logic any increase is exponential. This is false. When the exponent of the price function is the independent variable of said price function, then that increase is exponential. ʞooɔ 18:53, April 20, 2013 (UTC)

"For example, 1,068,992^1.0001 is "only" 1070477.0294664 but it's still exponential." - MolMan

The price today is 55,135,068.

55,135,068^1.0000000011 is 55,135,069

Of course that's an increase of only 1gp, but it's still exponential. If tomorrow we change the 1.0000000011 to increase the price by another 1gp, it's still exponential. A (y) in x^y that changes on a daily basis renders "exponential" meaningless. —The preceding unsigned comment was added by 177.130.128.8 (talk).

The whole point of an exponential equation is that the exponent changes based on the day! If something increases by 5% every day and the starting value, is, say, 1000, the equation would look like 1000*1.05^x. One day later, the price will be 1000*1.05^1. A day after that, 1000*1.05^2. A day after that, 1000*1.05^3. The exponent changes, and that's what creates exponential growth. Surely you realize that. ʞooɔ 19:42, April 20, 2013 (UTC) Having a (y) that changes in x^y is the exact definition of exponential. ʞooɔ 19:42, April 20, 2013 (UTC)

"I said nothing of the price plateauing, because it's not going to."

Oh? Because I'm pretty sure the price has consistently decreased every day this past week.

http://img59.imageshack.us/img59/1567/cthq.png

Even if you omit the past 6 days from the graph, you are an absolute idiot if you think that is exponential growth.

Exponential growth results in a curve that becomes continually closer to perfectly vertical, and at no point does it "tail off a bit" . In no way does the Christmas Tree Hat price even resemble exponential growth.

He's ba-ack! Clearly it's no longer exponential or anywhere close to that -- but that last time we talked, a week ago, it was still in approximately exponential form. Thanks for applying my words to the future. That being said, you posted a curve of the form 2^x, which of course will take off much more steeply than 1.05^x. Now, you should also realize that the exponent in here is not the number of days, but the number of price updates -- clearly if the price is constant from day 1 to day 2 (as happens with stepped graphs -- that's a different topic), then it generally won't be considered exponential to time. But it was (approximately) exponential to the number of price updates, which you can clearly see by looking at the data on Exchange:Christmas tree hat/Data and dividing each price by the previous price. It'll either be 1 (which is the case when the price doesn't change, again, stepped graphs), or 1.05, or between 1.045 and 1.05. That's why I said it's not perfectly exponential, as I said from the beginning -- but the change in price was, until the inevitable decline, based on the previous day's price. Not that hard to comprehend. ʞooɔ 01:38, April 27, 2013 (UTC)

Lol... just shut up and admit you were wrong.

"you posted a curve of the form 2^x, which of course will take off much more steeply than 1.05^x."

The Christmas Tree Hat was not 1.05^x or anything (^x) If it was, it would still be increasing, like all exponential functions do. It was an additional increase (or simply, an increase), not exponential. Players bought it under the assumption that the price would continue to rise (or because they liked the appearance), at no point in time was the increase proportional to the value (i.e. nobody bought it for 52 mil simply because it was worth ~50 mil). If it worked like that, players would buy bronze helms because they're worth 49 gp and the price would continually rise a given percent based solely on that fact. Again, at no point was the increase exponential. It was additional.

I knew the price would plateu very soon because that is nothing close to an exponential increase.

The price was simply (y) and experienced and increse. Any value given to (y) can be expressed as (a^b). that doesn't make it an "exponential" increase.

Calling the increase the Christmas Tree Hat expereinced "exponential" at any given time is like saying I was immortal a year ago because I didn't die. If you do die in the future, you were never immortal. If the price decreases in the future, the increase was never exponential.

We could keep changing the ^y in x^y and say that an item that was 10gp five days ago is 15gp now and experienced 5 days of "exponential growth". If you payed attention to the increases in the price (2 mil one day, 1.8 mil the next, 2.1 the next, etc.) you would see the increase was never proportional to the value. It was pretty fucking random.

Not that hard to comprehend.

Well...no. I acknowledged that it's no longer anywhere close to exponential. And you're under a common misconception about the difference between median price and true price -- the median price was clearly increasing roughly proportionally to the last price. That's due to the price changing limits that Jagex puts on almost all items, in that they cannot change by more than 5% a day in either direction. You are correct that "nobody bought for 52 mil simply because it was worth ~50 mil" -- the true price over the last four months has been all over the place. But until a week ago, the median price had been considerably below the true price, causing the median to rise by approximately 5% a day. Your claim "At no point was it exponential" is clearly false -- for the first 15 days of the item's existence, it increased by 5% of the previous price exactly, although with integer rounding errors as to be expected. For an example, the price 14 days after release was 1039472, which is extremely close to 525000*1.05^14 = 1039464. That's where the rounding error kicks in. For the first two months of its existence, the price increased by between 4.5% and 5% of the previous day's value. That's not perfectly exponential, but it's extremely close. After the 59th day there started to be "step" days in which not enough were traded for the price to change that day, but that's to be expected and I already acknowledged that.

The price was clearly approximately exponential until a week ago, which you can see by graphing the price data without the stepped days. It correlates 0.9994 with an exponential regression. For all intents and purposes it is exponential. And again, I want you to understand this -- that's the result of Jagex limiting median price changes to 5% of the previous price, so if something is continually above the median by more than that amount, its median price will continue to rise by 5% (or for some reason, 4.5% to 5% sometimes) of the previous price. That's what we saw here, and that's why I call it exponential.

As to your latest addition: That is not true. Nobody was claiming that the price would continue to be exponential forever -- that would clearly be impossible since the maximum price is about 2147 million and the equation 525000*1.05^x would run out of space at about x = 170. "If the price decreases in the future, the increase was never exponential" is incorrect -- the price increase over that period of time can clearly be considered exponential. The long-term price cannot, as obviously eventually the price will drop. Did you really think I meant that in a year the price would be 525000*1.05^365? Come on. ʞooɔ 03:04, April 27, 2013 (UTC)

I knew exactly what you meant... and you were wrong.

"the median price was clearly increasing roughly proportionally to the last price."

The definition of exponential does not include the word "roughly". At no point in time was the continued increase proportional to the value.

Roughly proportional makes no fucking sense. Either there is a direct correlation between the increase and the value or there isn't. If there are limiting factors, there are limiting factors, and the increase is not proportional because of them.

The argument broken down to suit your limited understanding:

You: 'Well if there weren't limiting factors...'

Me: 'Well, there are.'

"As to your latest addition: That is not true. Nobody was claiming that the price would continue to be exponential forever."

Again, you could call an increase of 1gp every day an exponential increase if you include external limiting factors. You are misusing a mathematical term, and you are a moron. For all intents and purposes (and hell, even for income taxes) 1.4 + 1.4 is  2... that doesn't make it mathematically correct. Don't be a fucking idiot by bending the rules of math to suit your arbitrary desire to call something exponential when it isn't.

"At no point in time was the continued increase proportional to the value." Look at the first 14 days. Also, continuing to insult me after your own mathematical failings will not end well. ʞooɔ 03:16, April 27, 2013 (UTC)

I should also add: you're again putting words in my mouth. At no point did I ever claim that the increase was perfectly exponential -- even such basic things as rounding prices would preclude that. Approximately exponential is mathematically acceptable term, so stop being so pedantic about something I never said. ʞooɔ 03:18, April 27, 2013 (UTC)

http://runescape.wikia.com/wiki/Christmas_tree_hat?diff=7909684&oldid=7863079

On April 18th, 2013 as an idiot with a rudimentary understanding of mathematics you said, and I quote, "The Christmas tree hat has seen one of the longest periods of exponential growth in its Grand Exchange price for any item.". You even reverted it multiple times when I took out the word exponential.

That is like me going onto a Wikipedia page and adding a trivia entry that says 2.4 + 2.4 is 4, and reverting it when someone corrects it by saying it is 4.8. 

I called you on your mistake (or at the very least, I gave a more accurate explanation), and now you are no longer arguing that the increase was exponential, but "approximately" exponential. That would be like me arguing that I never said 2.4 + 2.4 is "perfectly" 4 and that it should be assumed that I didn't intend it to mean "exactly". That's math. Math is exact. Again, don't be a fucking idiot.

In this case, "drastically" is no more a weasel word than "exponential" when the increase is NOT exponential. My watch is "for all intents and purposes" a Rolex and the ring I bought my wife is "approximately" a diamond. Get a fucking life.

I told you not to keep insulting me. See you in three days. ʞooɔ 03:39, April 27, 2013 (UTC)

April 19, 2013: "Oh, and you can probably tell I don't like arguing grade school math with imbeciles."

I had $4.00 yesterday. Today I have $5.00

Since $4.00 multiplied by 1.25 equals $5.00, I guess it's safe to say my money MULTIPLIED since yesterday. Just because I used multiplication that doesn't mean my money multiplied.

Any increase can be represented as an exponent (a $1.00 increase each day by the above definition is "exponential") that doesn't mean the increase was exponential. It's a useless buzz word and serves no purpose on this page other than hype.

Please express a dollar a day in the form of a^cx+b MolMan 00:19, August 21, 2014 (UTC)