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Growth of Geocaching: Linear or Exponential?


Guest travisl
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Guest travisl

him, I decided to look at the growth of the number of total caches over time.

 

pubimage.asp?id_=139103

 

It's showing pretty much linear growth since last summer, with the exception of the "summer bump" I noted in turquoise.

 

(To get the data, I just looked at the "date hidden" for every thousandth cache (1000, 2000, 3000, ...) and filled in with cache numbers 5, 125, 250, 500, and the most recent one, 15393.)

 

Since September, it's averaged just under 20 days to add 1000 caches (if we exclude the holiday slowdown). At its current rate, I expect to see cache number 20000 (GC4E20) placed on May 31.

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Guest Renegade Knight

That curve you have is an exponential curve. I've gotten 5 people interested since I started and I've only been interested in a month. I think you will find it pans out like a big S curve. We are going up fast right now. After a 'bit' (who knows how long that is) it will level out as people lose interest at about the rate as new ones are joining up.

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I would think that the growth in geocachers would certainly be increasing by an exponential function. If you take the known number of geocachers on a given date, and compare those values with the same criteria for a later date, we can apply this formula:

 

f(t)=ce^kt

 

By determining the constant value of "c", we can substitute that value in the formula and allow the function of time to equal any date in the future. (or past for that matter) In doing this, we can determine how many geocachers there will be on any given date, past or present.

 

To do a proof, simply calculate a value for a past date, and then compare that value to historical figures to see if the values correlate.

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Guest travisl

quote:
That curve you have is an exponential curve... I think you will find it pans out like a big S curve

 

It looks like it was exponential, up until the middle of August. Since then, it's been much more linear.

 

But yeah, it'd have to level out sometime. Even the growth of the internet has lost much of it's steepness in the last few years.

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Guest george71

quote:
Originally posted by mac:

To do a proof, simply calculate a value for a past date, and then compare that value to historical figures to see if the values correlate.


 

An alternate and easier proof would be to take plot the ln(# caches) over time and see if it came out to be a straight line.

 

Can someone do that really quick. I would but I don't have any way to post the resulting graph.

 

george

 

[This message has been edited by george71 (edited 26 February 2002).]

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if someone wants to send me values for number of geocachers on certain dates I will be happy to calculate the trend tonight when I get home. I didn't bring my calculator to work. If anyone has it, optimally I would use; The day geocaching began, and then any other two dates with the corresponding number of active geocachers on those dates. I can plot a graph of the answers and post that here in the next day or two after I receive the data to work with.

 

Cheers!

~macro~

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I would expect geocaching to grow with one of those epidemiological S-shaped curves, where the rate of increase is proportional to the product of the "infected" and "uninfected". You learn about geocaching the same way you pick up a disease -- you come into contact with someone who already knows.

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Wouldn't it be better to chart the number of geocachers rather than caches. If each new cacher keeps creating caches over a period of time, than the results you're tracking will increase faster since each person keeps adding to his cache count than a chart showing each person taking up the hobby distorting the trending.

Do we have the count of people that we can chart?

Do we have a count of the people actually loggin finds? Maybe looking and comparing all these variables would give a better understanding of the growth.

 

Alan

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quote:
Originally posted by blscearce:

I would expect geocaching to grow with one of those epidemiological S-shaped curves, where the rate of increase is proportional to the product of the "infected" and "uninfected". You learn about geocaching the same way you pick up a disease -- you come into contact with someone who already knows.


 

I think this is pretty accurate, however there will be error when you consider that some people learn about geocaching from news articles, or GPS related stories. I guess it comes down to how we define "contact"....but overall, I agree with your assessment...I hadn't thought about it that way.

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I would actually like to see a graph on geocaching "activity"

I arbitrarily define "activity" as a cache found, searched for but not found, or hidden. Other logs could be counted if an actual trip was made to the cache site- a maintenance run by the cache owner, for example.

 

This activity number will grow as a function of the number of active cachers instead of the number of hidden caches. The number of hidden caches will indirectly affect the activity as people exhaust the supply of easy to reach caches and their rate goes down.

 

Even average number of caches found per month per cacher might be an interesting number to track.

 

Even if the rate of caches planted has gone linear the activity could still be exponential at this point.

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quote:
Originally posted by Gliderguy:

I would actually like to see a graph on geocaching "activity"

I arbitrarily define "activity" as a cache found, searched for but not found, or hidden. Other logs could be counted if an actual trip was made to the cache site- a maintenance run by the cache owner, for example.

 

This activity number will grow as a function of the number of active cachers instead of the number of hidden caches. The number of hidden caches will indirectly affect the activity as people exhaust the supply of easy to reach caches and their rate goes down.

 

Even average number of caches found per month per cacher might be an interesting number to track.

 

Even if the rate of caches planted has gone linear the activity could still be exponential at this point.


 

A stat page would be cool and I'm sure its in the works.

 

- Lone Rangers

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An exponential correlation from cache 5000 has a correlation coefficient of 0.948. Taking it from cache 11000 (December 2, 2001) and you get a correlation coefficient of 0.997.

 

Using this second correlation, you get cache 20000 on April 20th, and cache 25000 on June 10.

 

(Note that cache 5000 has an out of sequence date.)

 

I graphed it too, but I'm not sure how to post that here.

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The growth never was exponential, so it's not fair to say it has flattened out. Here's a linear plot:

 

874448_200.gif

 

And here's the semi-log plot:

 

874448_300.gif

 

If the growth were exponential, the semi-log plot would make a straight line. Thus, it appears to have always been sub-exponential.

 

My estimate is that we'll hit 64K before June.

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quote:
Originally posted by fizzymagic:

My estimate is that we'll hit 64K before June.


 

Cache 65,000 was in fact posted in April. It appears that the rate of cache postings has been exponential for about a year.

 

This plot shows the caches posted by date (blue, a data point is at every thousand caches) and an exponential fit since cache 35,000 last September (pink):

 

55126_300.jpg

 

The r2 is 0.9993. Here it is with a semi-log scale:

 

55126_400.jpg

 

For interest, here is the number of caches posted per day, calculated over every 2,000 caches:

 

55126_200.jpg

 

My interpretation is that the rate of posting was hyperexponential, and it has since settled down to exponential. But, I only do this for a hobby (sad), so I may be wrong.

 

(Let me know if these images don't post; I'm reusing an unapproved cache to store them for a bit.)

 

There are three kinds of lies: lies, damned lies and statistics. - Attributed to Benjamin Disraeli

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