Centroid Data

Question

How is the centroid data calculated?

My centroid says its at N55 degrees. However, I've only found about 60 caches north of this point, the most northerly point being at N59.  I have found more than 150 caches in the southern hemisphere so this feels waaaaay off. Is N/S being ignored?

Cache centroid:

N 55° 11.597 E 004° 03.182 (Centroid is 493 km from home)

Answer 1

Why would that be a bug?

The problem is that you are thinking the earth looks like a flat map and not like a globe. I would guess almost all people makes the same mistake.

The centroid is the place where the sum of the distance to all caches is minimal
The shortest path on a sphere is the the great circle path and for long distances it is often in a surprising direction.
An easy way to find and understand it is using a rubber band and a globe.
If you stretch the rubber band between two point on the the globe it will follow the great circle path. And it is the shortest path on the surface.

The great circle path between London and Sidney is initial 60 degrees and the path is north of Moscow
https://dl.dropboxusercontent.com/u/27625662/Geocache/Great%20circle%20path%20London%20Sydney.jpg

All your finds in the far east has a great circle path starting north of due east. A line starting due east will go a bit north of Bombay and Perth
All of the USA and even Cuba is above a great circle due west.
The only finds you have with a initial south bearing is in souther Europe and in Israel
That is the reason the centroid is as fart north as it is.

An extrem example is if you had only two finds both 2 meters north of the Equator at
N00 00.001 E 00 0.000
And at a point 4 meters north of the opposite point of the earth at
N00 00.001 E 180 0.000
Your centroid would be on the north pole N90

Comments

Thanks for the good explanation. However, it does mean this isn't a very useful statistic for the layperson unless you live on the north or south poles :)

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Good explanation. When you look on the screenshot Target uploaded, you get it, how the centroid is calculated.

However, it "feels" not right, because one expects the path to go southeast through France, Switzerland, along the northern coast of the Mediterranean Sea and so forth to Australia, because one has the map of the world on his mind.

:-)

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Agreed. For me, a direct path would be more meaningful. For example, if I had two finds, N 51 30.483 W 000 07.731 and S 33 55.500 E 151 15.509 then having a centroid at N 8 47.491 E 075 33.889 would make more sense.

While undoubtedly the great circle path is technically correct, I can't see it be a useful/meaningful stat to geocachers.

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Well, for me it works quite well i think. But i don't have any "extreme" caches. Most of my 2600+ finds are in a 150km radius. When i cache more in the north east, then the centroid wanders in that direction. When i go to the west, then it wanders back west...

So, if you find more caches in your home region, the centroid will move closer. And the more finds you get, the more "correct" it will get.

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The metod of calculate a averages of the coord values like the example above (if am nog mistaken) makes no sense.


That would make sense if the coord was in a Cartesian coordinate system ie a flat earth. But not on a sphere and an average like that is in now way a direct path. The only way i can think of a direct path on the earth is a straight line trough the earth. And that would be the 3d centroid of the finds

A feeling from looking at maps expectationally from cylindrical projections give bad direction. And the classical Mercator projection that is useful for navigation at sea.
Zoom out max on the geocaching maps and look at the size of Greenland and South America and compare them. By looking would you guess that South America is 8 times the size of Greenland?
Or that Madagascar is 2.6 times the size of Great Britain
All map projection have it good and bad properties

Look instead at UN logo  or https://upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Azimuthal_equidistant_projection_SW.jpg/1024px-Azimuthal_equidistant_projection_SW.jpg

Or one centred at London  https://dl.dropboxusercontent.com/u/27625662/Geocache/AzimuthalMap%20london.pdf
That will give you a better ide how to look at direction on the earth


It is relay strange to average the longitude like that when a degree are different length depending on latitude. A degree latitude is between 111 km and 0 km between. A degree is only 70 km in London and down to 38 km in Northern Europé. It is strange when caches 111km and 38 km a part will have the same weight in average longitude

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Yes but my computer screen is flat and so this projection does make sense.

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No it still does not make any sense to just average the coord values The maps on the web uses Web Mercator https://en.wikipedia.org/wiki/Web_Mercator
The Mercator puts the poles at an infinity from the equator because the conversion from latitude to y pixel is not a linear equation.

The maps on gc.com only goes to approx 85 degree north and south.
To calculate the average position the cache icon are drawn on the map you have to convert pixel values and average the pixel values.

And that will still result is strange result because is assume a special importance of the prime meridian.
Ex a cacher from New Zeeland that have also finds in Hawaii might have their averages somewhere in Africa.


An the result will also be strange because there was a cache in the north pole and is two on the south pole. And others above/ below the 85 degree limit
http://project-gc.com/Tools/MapNESW?loop=10&submit=Filter
The caches on the south pole they are on the same place but have a longitudes of W 180° 00.000 and W 000° 00.000 and looks fare apart on the pgc maps. (they are not visible on the gc.com maps)

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It feels like you are over complicating it.

Regarding the New Zealand caches issue, you could just set each cacher's home location as their meridian. Solved.

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I don't think, that Target overcomplicates it. He just explains and gives examples, how the centroid is calculated.

The fact is, that you cannot compare flat maps with the given truth, that mother earth is an (almost) round ball. Point.

Maybe you should just work more often with Google Earth, rather than Google Maps. Just to get the right view.